Euclidean black hole vortices

NASA Technical Reports Server (NTRS)

Dowker, Fay; Gregory, Ruth; Traschen, Jennie

1991-01-01

We argue the existence of solutions of the Euclidean Einstein equations that correspond to a vortex sitting at the horizon of a black hole. We find the asymptotic behaviors, at the horizon and at infinity, of vortex solutions for the gauge and scalar fields in an abelian Higgs model on a Euclidean Schwarzschild background and interpolate between them by integrating the equations numerically. Calculating the backreaction shows that the effect of the vortex is to cut a slice out of the Schwarzschild geometry. Consequences of these solutions for black hole thermodynamics are discussed.

Martin Schwarzschild (1912-1997)

NASA Astrophysics Data System (ADS)

Trimble, V.

1997-12-01

Martin Schwarzschild, the ASP Bruce Medalist for 1965, died on 10 April 1997. A refugee from Hitler's Germany who firmly embraced his adopted country, Schwarzschild not only solved a number of fundamental problems in stellar structure and evolution but also taught the rest of the astronomical community how to do so with his 1958 text, Structure and Evolution of the Stars. At about the time of his 1979 retirement, he turned to a completely different question of how to model spheroidal galaxies self-consistently and sent another generation of students and collaborators forward toward the still somewhat distant solution. It is impossible for anyone who ever interacted with Schwarzschild to remain entirely solemn when remembering him. (SECTION: Obituary)

Surface tension and negative pressure interior of a non-singular ‘black hole’

NASA Astrophysics Data System (ADS)

Mazur, Pawel O.; Mottola, Emil

2015-11-01

The constant density interior Schwarzschild solution for a static, spherically symmetric collapsed star has a divergent pressure when its radius R≤slant \\frac{9}{8}{R}s=\\frac{9}{4}{GM}. We show that this divergence is integrable, and induces a non-isotropic transverse stress with a finite redshifted surface tension on a spherical surface of radius {R}0=3R\\sqrt{1-\\frac{8}{9}\\frac{R }{{R}s}}. For r\\lt {R}0 the interior Schwarzschild solution exhibits negative pressure. When R={R}s, the surface is localized at the Schwarzschild radius itself, {R}0={R}s, and the solution has constant negative pressure p=-\\bar{ρ } everywhere in the interior r\\lt {R}s, thereby describing a gravitational condensate star, a fully collapsed non-singular state already inherent in and predicted by classical general relativity. The redshifted surface tension of the condensate star surface is given by {τ }s={{Δ }}κ /8π G, where {{Δ }}κ ={κ }+-{κ }-=2{κ }+=1/{R}s is the difference of equal and opposite surface gravities between the exterior and interior Schwarzschild solutions. The First Law, {{d}}M={{d}}{E}V+{τ }s {{d}}A is recognized as a purely mechanical classical relation at zero temperature and zero entropy, describing the volume energy and surface energy change respectively. The Schwarzschild time t of such a non-singular gravitational condensate star is a global time, fully consistent with unitary time evolution in quantum theory. A clear observational test of gravitational condensate stars with a physical surface versus black holes is the discrete surface modes of oscillation which should be detectable by their gravitational wave signatures.

New Gauss-Bonnet Black Holes with Curvature-Induced Scalarization in Extended Scalar-Tensor Theories

NASA Astrophysics Data System (ADS)

Doneva, Daniela D.; Yazadjiev, Stoytcho S.

2018-03-01

In the present Letter, we consider a class of extended scalar-tensor-Gauss-Bonnet (ESTGB) theories for which the scalar degree of freedom is excited only in the extreme curvature regime. We show that in the mentioned class of ESTGB theories there exist new black-hole solutions that are formed by spontaneous scalarization of the Schwarzschild black holes in the extreme curvature regime. In this regime, below certain mass, the Schwarzschild solution becomes unstable and a new branch of solutions with a nontrivial scalar field bifurcates from the Schwarzschild one. As a matter of fact, more than one branch with a nontrivial scalar field can bifurcate at different masses, but only the first one is supposed to be stable. This effect is quite similar to the spontaneous scalarization of neutron stars. In contrast to the standard spontaneous scalarization of neutron stars, which is induced by the presence of matter, in our case, the scalarization is induced by the curvature of the spacetime.

New Gauss-Bonnet Black Holes with Curvature-Induced Scalarization in Extended Scalar-Tensor Theories.

PubMed

Doneva, Daniela D; Yazadjiev, Stoytcho S

2018-03-30

In the present Letter, we consider a class of extended scalar-tensor-Gauss-Bonnet (ESTGB) theories for which the scalar degree of freedom is excited only in the extreme curvature regime. We show that in the mentioned class of ESTGB theories there exist new black-hole solutions that are formed by spontaneous scalarization of the Schwarzschild black holes in the extreme curvature regime. In this regime, below certain mass, the Schwarzschild solution becomes unstable and a new branch of solutions with a nontrivial scalar field bifurcates from the Schwarzschild one. As a matter of fact, more than one branch with a nontrivial scalar field can bifurcate at different masses, but only the first one is supposed to be stable. This effect is quite similar to the spontaneous scalarization of neutron stars. In contrast to the standard spontaneous scalarization of neutron stars, which is induced by the presence of matter, in our case, the scalarization is induced by the curvature of the spacetime.

Interactive Visualization of a Thin Disc around a Schwarzschild Black Hole

ERIC Educational Resources Information Center

Muller, Thomas; Frauendiener, Jorg

2012-01-01

In a first course in general relativity, the Schwarzschild spacetime is the most discussed analytic solution to Einstein's field equations. Unfortunately, there is rarely enough time to study the optical consequences of the bending of light for some advanced examples. In this paper, we present how the visual appearance of a thin disc around a…

Exact Schwarzschild-like solution in a bumblebee gravity model

NASA Astrophysics Data System (ADS)

Casana, R.; Cavalcante, A.; Poulis, F. P.; Santos, E. B.

2018-05-01

We obtain an exact vacuum solution from the gravity sector contained in the minimal standard-model extension. The theoretical model assumes a Riemann spacetime coupled to the bumblebee field which is responsible for the spontaneous Lorentz symmetry breaking. The solution achieved in a static and spherically symmetric scenario establishes a Schwarzschild-like black hole. In order to study the effects of the spontaneous Lorentz symmetry breaking we investigate some classic tests, including the advance of perihelion, the bending of light, and Shapiro's time delay. Furthermore, we compute some upper bounds, among which the most stringent associated with existing experimental data provides a sensitivity at the 10-15 level and that for future missions at the 10-19 level.

The Dirac equation in Schwarzschild black hole coupled to a stationary electromagnetic field

NASA Astrophysics Data System (ADS)

Al-Badawi, A.; Owaidat, M. Q.

2017-08-01

We study the Dirac equation in a spacetime that represents the nonlinear superposition of the Schwarzschild solution to an external, stationary electromagnetic field. The set of equations representing the uncharged Dirac particle in the Newman-Penrose formalism is decoupled into a radial and an angular parts. We obtain exact analytical solutions of the angular equations. We manage to obtain the radial wave equations with effective potentials. Finally, we study the potentials by plotting them as a function of radial distance and examine the effect of the twisting parameter and the frequencies on the potentials.

Large Randall-Sundrum II black holes

NASA Astrophysics Data System (ADS)

Abdolrahimi, Shohreh; Cattoën, Céline; Page, Don N.; Yaghoobpour-Tari, Shima

2013-03-01

Using a novel numerical spectral method, we have constructed an AdS5-CFT4 solution to the Einstein equation with a negative cosmological constant Λ that is asymptotically conformal to the Schwarzschild metric. This method is independent of the Ricci-DeTurck-flow method used by Figueras, Lucietti, and Wiseman. We have perturbed the solution to get large static black hole solutions to the Randall-Sundrum II (RSII) braneworld model. Our solution agrees closely with that of Figueras et al. and also allows us to deduce the new results that to first order in 1 / (- ΛM2), the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7 / (- Λ).

Vacuum solutions around spherically symmetric and static objects in the Starobinsky model

NASA Astrophysics Data System (ADS)

ćıkıntoǧlu, Sercan

2018-02-01

The vacuum solutions around a spherically symmetric and static object in the Starobinsky model are studied with a perturbative approach. The differential equations for the components of the metric and the Ricci scalar are obtained and solved by using the method of matched asymptotic expansions. The presence of higher order terms in this gravity model leads to the formation of a boundary layer near the surface of the star allowing the accommodation of the extra boundary conditions on the Ricci scalar. Accordingly, the metric can be different from the Schwarzschild solution near the star depending on the value of the Ricci scalar at the surface of the star while matching the Schwarzschild metric far from the star.

Conformal Weyl Gravity and Perihelion Precession

NASA Technical Reports Server (NTRS)

Sultana, Joseph; Kazanas, Demosthenes; Said, Jakson, Levi

2012-01-01

We investigate the perihelion shift of planetary motion in conformal Weyl gravity using the metric of the static, spherically symmetric solution discovered by Mannheim and Kazanas. To this end we employ a procedure similar to that used by Weinberg for the Schwarzschild solution, which has also been used recently to study the solar system effects of the cosmological constant Lambda. We show that besides the general relativistic terms obtained earlier from the Schwarzschild-de Sitter solution, the expression for the perihelion shift includes a negative contribution which arises from the linear term gamma ray in the metric. Using data for perihelion shift observations, we obtain constraints on the value of the constant gammma similar to that obtained earlier using galactic rotational curves.

Schwarzschild and linear potentials in Mannheim's model of conformal gravity

NASA Astrophysics Data System (ADS)

Phillips, Peter R.

2018-05-01

We study the equations of conformal gravity, as given by Mannheim, in the weak field limit, so that a linear approximation is adequate. Specialising to static fields with spherical symmetry, we obtain a second-order equation for one of the metric functions. We obtain the Green function for this equation, and represent the metric function in the form of integrals over the source. Near a compact source such as the Sun the solution no longer has a form that is compatible with observations. We conclude that a solution of Mannheim type (a Schwarzschild term plus a linear potential of galactic scale) cannot exist for these field equations.

The two NUT-like solutions of Ernst equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu Yabo; Dong Peng; Deng Xuemei

By applying Ehlers transformation to Schwarzschild and Kerr solutions of Ernst equation and choosing the suitable coordinate transformations, the two NUT-like solutions, i.e., the so called NUT-Taub-like and the Kerr-NUT-like solutions are obtained which not only can, respectively, reduce to Schwarzschild and Kerr solutions when the parameter l{sup '}=0, but also can also reduce to the NUT-Taub metric and Kerr-NUT metric, respectively, when l{sup '} satisfies the some approximation. Meanwhile it is shown that in the NUT-Taub and Kerr-NUT solutions the range of value for the parameter l interpreted as the gravomagnetic monopole cannot be arbitrary and should be confinedmore » by mass of the source to vertical bar l vertical bar<

Course Lectures Abstracts of Participants Fellows Project Reports

DTIC Science & Technology

1990-10-01

Whitehead and Karl R. Helfrich 188 A Long Laboratory Salt Finger George Veronis 189 Applications of Compactly Supported Wavelets to the Numerical Solution...when it is negative, we have instability. This criterion for the onset of convection is called the Schwarzschild criterion, after one of the many who...and Astrophys. 85, 263-264 (1980) [14] Schwarzschild M., Harm R., Ap.J. 184, 5-8 (1973) [15) Shibahashi H., Osaki Y., Unno W., Publ. Astron. Soc

Analytical expression for a class of spherically symmetric solutions in Lorentz-breaking massive gravity

NASA Astrophysics Data System (ADS)

Li, Ping; Li, Xin-zhou; Xi, Ping

2016-06-01

We present a detailed study of the spherically symmetric solutions in Lorentz-breaking massive gravity. There is an undetermined function { F }(X,{w}1,{w}2,{w}3) in the action of Stückelberg fields {S}φ ={{{Λ }}}4\\int {{{d}}}4x\\sqrt{-g}{ F }, which should be resolved through physical means. In general relativity, the spherically symmetric solution to the Einstein equation is a benchmark and its massive deformation also plays a crucial role in Lorentz-breaking massive gravity. { F } will satisfy the constraint equation {T}01=0 from the spherically symmetric Einstein tensor {G}01=0, if we maintain that any reasonable physical theory should possess the spherically symmetric solutions. The Stückelberg field {φ }i is taken as a ‘hedgehog’ configuration {φ }i=φ (r){x}i/r, whose stability is guaranteed by the topological one. Under this ansätz, {T}01=0 is reduced to d{ F }=0. The functions { F } for d{ F }=0 form a commutative ring {R}{ F }. We obtain an expression of the solution to the functional differential equation with spherical symmetry if { F }\\in {R}{ F }. If { F }\\in {R}{ F } and \\partial { F }/\\partial X=0, the functions { F } form a subring {S}{ F }\\subset {R}{ F }. We show that the metric is Schwarzschild, Schwarzschild-AdS or Schwarzschild-dS if { F }\\in {S}{ F }. When { F }\\in {R}{ F } but { F }\

Static Solutions of Einstein's Equations with Cylindrical Symmetry

ERIC Educational Resources Information Center

Trendafilova, C. S.; Fulling, S. A.

2011-01-01

In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well-known cone solution, which is locally flat, but others in which the metric coefficients are powers of the radial coordinate and the spacetime is…

Linear perturbations of a Schwarzschild blackhole by thin disc - convergence

NASA Astrophysics Data System (ADS)

Čížek, P.; Semerák, O.

2012-07-01

In order to find the perturbation of a Schwarzschild space-time due to a rotating thin disc, we try to adjust the method used by [4] in the case of perturbation by a one-dimensional ring. This involves solution of stationary axisymmetric Einstein's equations in terms of spherical-harmonic expansions whose convergence however turned out questionable in numerical examples. Here we show, analytically, that the series are almost everywhere convergent, but in some regions the convergence is not absolute.

Quasinormal Frequencies of D-Dimensional Schwarzschild Black Holes: Evaluation via Continued Fraction Method

NASA Astrophysics Data System (ADS)

Rostworowski, A.

2007-01-01

We adopt Leaver's [E. Leaver, {ITALIC Proc. R. Soc. Lond.} {A402}, 285 (1985)] method to determine quasi normal frequencies of the Schwarzschild black hole in higher (D geq 10) dimensions. In D-dimensional Schwarzschild metric, when D increases, more and more singularities, spaced uniformly on the unit circle |r|=1, approach the horizon at r=rh=1. Thus, a solution satisfying the outgoing wave boundary condition at the horizon must be continued to some mid point and only then the continued fraction condition can be applied. This prescription is general and applies to all cases for which, due to regular singularities on the way from the point of interest to the irregular singularity, Leaver's method in its original setting breaks down. We illustrate the method calculating gravitational vector and tensor quasinormal frequencies of the Schwarzschild black hole in D=11 and D=10 dimensions. We also give the details for the D=9 case, considered in the work of P. Bizoz, T. Chmaj, A. Rostworowski, B.G. Schmidt and Z. Tabor {ITALIC Phys. Rev.}{D72}, 121502(R) (2005) .

Spectral methods in general relativity and large Randall-Sundrum II black holes

NASA Astrophysics Data System (ADS)

Abdolrahimi, Shohreh; Cattoën, Céline; Page, Don N.; \\\\; Yaghoobpour-Tari, Shima

2013-06-01

Using a novel numerical spectral method, we have found solutions for large static Randall-Sundrum II (RSII) black holes by perturbing a numerical AdS5-CFT4 solution to the Einstein equation with a negative cosmological constant Λ that is asymptotically conformal to the Schwarzschild metric. We used a numerical spectral method independent of the Ricci-DeTurck-flow method used by Figueras, Lucietti, and Wiseman for a similar numerical solution. We have compared our black-hole solution to the one Figueras and Wiseman have derived by perturbing their numerical AdS5-CFT4 solution, showing that our solution agrees closely with theirs. We have obtained a closed-form approximation to the metric of the black hole on the brane. We have also deduced the new results that to first order in 1/(-ΛM2), the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7/(-Λ).

Analysis of the Fisher solution

NASA Astrophysics Data System (ADS)

Abdolrahimi, Shohreh; Shoom, Andrey A.

2010-01-01

We study the d-dimensional Fisher solution which represents a static, spherically symmetric, asymptotically flat spacetime with a massless scalar field. The solution has two parameters, the mass M and the “scalar charge” Σ. The Fisher solution has a naked curvature singularity which divides the spacetime manifold into two disconnected parts. The part which is asymptotically flat we call the Fisher spacetime, and another part we call the Fisher universe. The d-dimensional Schwarzschild-Tangherlini solution and the Fisher solution belong to the same theory and are dual to each other. The duality transformation acting in the parameter space (M,Σ) maps the exterior region of the Schwarzschild-Tangherlini black hole into the Fisher spacetime which has a naked timelike singularity, and interior region of the black hole into the Fisher universe, which is an anisotropic expanding-contracting universe and which has two spacelike singularities representing its “big bang” and “big crunch.” The big bang singularity and the singularity of the Fisher spacetime are radially weak in the sense that a 1-dimensional object moving along a timelike radial geodesic can arrive to the singularities intact. At the vicinity of the singularity the Fisher spacetime of nonzero mass has a region where its Misner-Sharp energy is negative. The Fisher universe has a marginally trapped surface corresponding to the state of its maximal expansion in the angular directions. These results and derived relations between geometric quantities of the Fisher spacetime, the Fisher universe, and the Schwarzschild-Tangherlini black hole may suggest that the massless scalar field transforms the black hole event horizon into the naked radially weak disjoint singularities of the Fisher spacetime and the Fisher universe which are “dual to the horizon.”

Analysis of the Fisher solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abdolrahimi, Shohreh; Shoom, Andrey A.

2010-01-15

We study the d-dimensional Fisher solution which represents a static, spherically symmetric, asymptotically flat spacetime with a massless scalar field. The solution has two parameters, the mass M and the 'scalar charge' {Sigma}. The Fisher solution has a naked curvature singularity which divides the spacetime manifold into two disconnected parts. The part which is asymptotically flat we call the Fisher spacetime, and another part we call the Fisher universe. The d-dimensional Schwarzschild-Tangherlini solution and the Fisher solution belong to the same theory and are dual to each other. The duality transformation acting in the parameter space (M,{Sigma}) maps the exteriormore » region of the Schwarzschild-Tangherlini black hole into the Fisher spacetime which has a naked timelike singularity, and interior region of the black hole into the Fisher universe, which is an anisotropic expanding-contracting universe and which has two spacelike singularities representing its 'big bang' and 'big crunch'. The big bang singularity and the singularity of the Fisher spacetime are radially weak in the sense that a 1-dimensional object moving along a timelike radial geodesic can arrive to the singularities intact. At the vicinity of the singularity the Fisher spacetime of nonzero mass has a region where its Misner-Sharp energy is negative. The Fisher universe has a marginally trapped surface corresponding to the state of its maximal expansion in the angular directions. These results and derived relations between geometric quantities of the Fisher spacetime, the Fisher universe, and the Schwarzschild-Tangherlini black hole may suggest that the massless scalar field transforms the black hole event horizon into the naked radially weak disjoint singularities of the Fisher spacetime and the Fisher universe which are 'dual to the horizon'.« less

Static black hole and vacuum energy: thin shell and incompressible fluid

NASA Astrophysics Data System (ADS)

Ho, Pei-Ming; Matsuo, Yoshinori

2018-03-01

With the back reaction of the vacuum energy-momentum tensor consistently taken into account, we study static spherically symmetric black-hole-like solutions to the semi-classical Einstein equation. The vacuum energy is assumed to be given by that of 2-dimensional massless scalar fields, as a widely used model in the literature for black holes. The solutions have no horizon. Instead, there is a local minimum in the radius. We consider thin shells as well as incompressible fluid as the matter content of the black-hole-like geometry. The geometry has several interesting features due to the back reaction of vacuum energy. In particular, Buchdahl's inequality can be violated without divergence in pressure, even if the surface is below the Schwarzschild radius. At the same time, the surface of the star can not be far below the Schwarzschild radius for a density not much higher than the Planck scale, and the proper distance from its surface to the origin can be very short even for very large Schwarzschild radius. The results also imply that, contrary to the folklore, in principle the Boulware vacuum can be physical for black holes.

On the localisation of four-dimensional brane-world black holes: II. The general case

NASA Astrophysics Data System (ADS)

Kanti, P.; Pappas, N.; Pappas, T.

2016-01-01

We perform a comprehensive analysis of a number of scalar field theories in an attempt to find analytically five-dimensional, localised-on-the-brane, black-hole solutions. Extending a previous analysis, we assume a generalised Vaidya ansatz for the five-dimensional metric tensor that allows for a time-dependent, non-trivial profile of the mass function in terms of the bulk coordinate and a deviation from the over-restricting Schwarzschild-type solution on the brane. In order to support such a solution, we study a variety of theories including single or multiple scalar fields, with canonical or non-canonical kinetic terms, minimally or non-minimally coupled to gravity. We demonstrate that for such a metric ansatz and for a carefully chosen energy-momentum tensor which is non-isotropic in five dimensions, solutions that have the form of a Schwarzschild-(anti)de Sitter or Reissner-Nordstrom type of solution do emerge. However, the resulting profile of the mass function along the bulk coordinate, when allowed, is not the correct one for eliminating bulk singularities.

Four-dimensional black holes in Einsteinian cubic gravity

NASA Astrophysics Data System (ADS)

Bueno, Pablo; Cano, Pablo A.

2016-12-01

We construct static and spherically symmetric generalizations of the Schwarzschild- and Reissner-Nordström-(anti-)de Sitter [RN-(A)dS] black-hole solutions in four-dimensional Einsteinian cubic gravity (ECG). The solutions are characterized by a single function which satisfies a nonlinear second-order differential equation. Interestingly, we are able to compute independently the Hawking temperature T , the Wald entropy S and the Abbott-Deser mass M of the solutions analytically as functions of the horizon radius and the ECG coupling constant λ . Using these we show that the first law of black-hole mechanics is exactly satisfied. Some of the solutions have positive specific heat, which makes them thermodynamically stable, even in the uncharged and asymptotically flat case. Further, we claim that, up to cubic order in curvature, ECG is the most general four-dimensional theory of gravity which allows for nontrivial generalizations of Schwarzschild- and RN-(A)dS characterized by a single function which reduce to the usual Einstein gravity solutions when the corresponding higher-order couplings are set to zero.

Charged black holes in compactified spacetimes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Karlovini, Max; Unge, Rikard von

2005-11-15

We construct and investigate a compactified version of the four-dimensional Reissner-Nordstroem-Taub-NUT solution, generalizing the compactified Schwarzschild black hole that has been previously studied by several workers. Our approach to compactification is based on dimensional reduction with respect to the stationary Killing vector, resulting in three-dimensional gravity coupled to a nonlinear sigma model. Knowing that the original noncompactified solution corresponds to a target space geodesic, the problem can be linearized much in the same way as in the case of no electric or Taub-NUT charge. An interesting feature of the solution family is that, for nonzero electric charge but vanishing Taub-NUTmore » charge, the solution has a curvature singularity on a torus that surrounds the event horizon, but this singularity is removed when the Taub-NUT charge is switched on. We also treat the Schwarzschild case in a more complete way than has been done previously. In particular, the asymptotic solution (the Levi-Civita solution with the height coordinate made periodic) has to our knowledge only been calculated up to a determination of the mass parameter. The periodic Levi-Civita solution contains three essential parameters, however, and the remaining two are explicitly calculated here.« less

Exact vacuum solution to conformal Weyl gravity and galactic rotation curves

NASA Technical Reports Server (NTRS)

Mannheim, Philip D.; Kazanas, Demosthenes

1989-01-01

The complete, exact exterior solution for a static, spherically symmetric source in locally conformal invariant Weyl gravity is presented. The solution includes the familiar exterior Schwarzschild solution as a special case and contains an extra gravitational potential term which grows linearly with distance. The obtained solution provides a potential explanation for observed galactic rotation curves without the need for dark matter. The solution also has some interesting implications for cosmology.

Asymmetric Wormholes via Electrically Charged Lightlike Branes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guendelman, E.; Kaganovich, A.; Nissimov, E.

2010-06-17

We consider a self-consistent Einstein-Maxwell-Kalb-Ramond system in the bulk D = 4 space-time interacting with a variable-tension electrically charged lightlike brane. The latter serves both as a material and charge source for gravity and electromagnetism, as well as it dynamically generates a bulk space varying cosmological constant. We find an asymmetric wormhole solution describing two 'universes' with different spherically symmetric black-hole-type geometries connected through a 'throat' occupied by the lightlike brane. The electrically neutral 'left universe' comprises the exterior region of Schwarzschild-de-Sitter (or pure Schwarzschild) space-time above the inner(Schwarzschild-type) horizon, whereas the electrically charged 'right universe' consists of the exteriormore » Reissner-Nordstroem (or Reissner-Nordstroem-de-Sitter) black hole region beyond the outer Reissner-Nordstroem horizon. All physical parameters of the wormhole are uniquely determined by two free parameters - the electric charge and Kalb-Ramond coupling of the lightlike brane.« less

Lectures on gravitation

NASA Astrophysics Data System (ADS)

Das, Ashok

1. Basics of geometry and relativity. 1.1. Two dimensional geometry. 1.2. Inertial and gravitational masses. 1.3. Relativity -- 2. Relativistic dynamics. 2.1. Relativistic point particle. 2.2. Current and charge densities. 2.3. Maxwell's equations in the presence of sources. 2.4. Motion of a charged particle in EM field. 2.5. Energy-momentum tensor. 2.6. Angular momentum -- 3. Principle of general covariance. 3.1. Principle of equivalence. 3.2. Principle of general covariance. 3.3. Tensor densities -- 4. Affine connection and covariant derivative. 4.1. Parallel transport of a vector. 4.2. Christoffel symbol. 4.3. Covariant derivative of contravariant tensors. 4.4. Metric compatibility. 4.5. Covariant derivative of covariant and mixed tensors. 4.6. Electromagnetic analogy. 4.7. Gradient, divergence and curl -- 5. Geodesic equation. 5.1. Covariant differentiation along a curve. 5.2. Curvature from derivatives. 5.3. Parallel transport along a closed curve. 5.4. Geodesic equation. 5.5. Derivation of geodesic equation from a Lagrangian -- 6. Applications of the geodesic equation. 6.1. Geodesic as representing gravitational effect. 6.2. Rotating coordinate system and the Coriolis force. 6.3. Gravitational red shift. 6.4. Twin paradox and general covariance. 6.5. Other equations in the presence of gravitation -- 7. Curvature tensor and Einstein's equation. 7.1. Curvilinear coordinates versus gravitational field. 7.2. Definition of an inertial coordinate frame. 7.3. Geodesic deviation. 7.4. Properties of the curvature tensor. 7.5. Einstein's equation. 7.6. Cosmological constant. 7.7. Initial value problem. 7.8. Einstein's equation from an action -- 8. Schwarzschild solution. 8.1. Line element. 8.2. Connection. 8.3. Solution of the Einstein equation. 8.4. Properties of the Schwarzschild solution. 8.5. Isotropic coordinates -- 9. Tests of general relativity. 9.1. Radar echo experiment. 9.2. Motion of a particle in a Schwarzschild background. 9.3. Motion of light rays in a Schwarzschild background. 9.4. Perihelion advance of Mercury -- 10. Black holes. 10.1. Singularities of the metric. 10.2. Singularities of the Schwarzschild metric. 10.3. Black holes -- 11. Cosmological models and the big bang theory. 11.1. Homogeneity and isotropy. 11.2. Different models of the universe. 11.3. Hubble's law. 11.4. Evolution equation. 11.5. Big bang theory and blackbody radiation.

Deuterium Abundance in Consciousness and Current Cosmology

NASA Astrophysics Data System (ADS)

Rauscher, Elizabeth A.

We utilize the deuterium-hydrogen abundances and their role in setting limits on the mass and other conditions of cosmogenesis and cosmological evolution. We calculate the dependence of a set of physical variables such as density, temperature, energy mass, entropy and other physical variable parameters through the evolution of the universe under the Schwarzschild conditions as a function from early to present time. Reconciliation with the 3°K and missing mass is made. We first examine the Schwarzschild condition; second, the geometrical constraints of a multidimensional Cartesian space on closed cosmologies, and third we will consider the cosmogenesis and evolution of the universe in a multidimensional Cartesian space, obeying the Schwarzschild condition. Implications of this model for matter creation are made. We also examine experimental evidence for closed versus open cosmologies; x-ray detection of the "missing mass" density. Also the interstellar deuterium abundance, along with the value of the Hubble constant set a general criterion on the value of the curvature constant, k. Once the value of the Hubble constant, H is determined, the deuterium abundance sets stringent restrictions on the value of the curvature constant k by an detailed discussion is presented. The experimental evidences for the determination of H and the primary set of coupled equations to determine D abundance is given. 'The value of k for an open, closed, or flat universe will be discussed in terms of the D abundance which will affect the interpretation of the Schwarzschild, black hole universe. We determine cosmology solutions to Einstein's field obeying the Schwarzschild solutions condition. With this model, we can form a reconciliation of the black hole, from galactic to cosmological scale. Continuous creation occurs at the dynamic blackhole plasma field. We term this new model the multiple big bang or "little whimper model". We utilize the deuteriumhydrogen abundances and their role in setting limits on the mass and other conditions of cosmogenesis and cosmological evolution. We calculate the dependence of a set of physical variables such as density, temperature, energy mass, entropy and other physical variable parameters through the evolution of the universe under the Schwarzschild conditions as a function from early to present time. Reconciliation with the 3°K background and missing mass is made.

On some transonic aspects of general relativistic spherical accretion on to Schwarzschild black holes

NASA Astrophysics Data System (ADS)

Das, Tapas K.

2002-03-01

The equations governing general relativistic, spherically symmetric, hydrodynamic accretion of polytropic fluid on to black holes are solved in the Schwarzschild metric to investigate some of the transonic properties of the flow. Only stationary solutions are discussed. For such accretion, it has been shown that real physical sonic points may form even for flow with γ<4/3or γ>5/3. The behaviour of some flow variables in the close vicinity of the event horizon is studied as a function of specific energy and the polytropic index of the flow.

Non-Schwarzschild black-hole metric in four dimensional higher derivative gravity: Analytical approximation

NASA Astrophysics Data System (ADS)

Kokkotas, K. D.; Konoplya, R. A.; Zhidenko, A.

2017-09-01

Higher derivative extensions of Einstein gravity are important within the string theory approach to gravity and as alternative and effective theories of gravity. H. Lü, A. Perkins, C. Pope, and K. Stelle [Phys. Rev. Lett. 114, 171601 (2015), 10.1103/PhysRevLett.114.171601] found a numerical solution describing a spherically symmetric non-Schwarzschild asymptotically flat black hole in Einstein gravity with added higher derivative terms. Using the general and quickly convergent parametrization in terms of the continued fractions, we represent this numerical solution in the analytical form, which is accurate not only near the event horizon or far from the black hole, but in the whole space. Thereby, the obtained analytical form of the metric allows one to study easily all the further properties of the black hole, such as thermodynamics, Hawking radiation, particle motion, accretion, perturbations, stability, quasinormal spectrum, etc. Thus, the found analytical approximate representation can serve in the same way as an exact solution.

Large Black Holes in the Randall-Sundrum II Model

NASA Astrophysics Data System (ADS)

Yaghoobpour Tari, Shima

The Einstein equation with a negative cosmological constant ! in the five dimensions for the Randall-Sundrum II model, which includes a black hole, has been solved numerically. We have constructed an AdS5-CFT 4 solution numerically, using a spectral method to minimize the integral of the square of the error of the Einstein equation, with 210 parameters to be determined by optimization. This metric is conformal to the Schwarzschild metric at an AdS5 boundary with an infinite scale factor. So, we consider this solution as an infinite-mass black hole solution. We have rewritten the infinite-mass black hole in the Fefferman-Graham form and obtained the numerical components of the CFT energy-momentum tensor. Using them, we have perturbed the metric to relocate the brane from infinity and obtained a large static black hole solution for the Randall- Sundrum II model. The changes of mass, entropy, temperature and area of the large black hole from the Schwarzschild metric are studied up to the first order for the perturbation parameter 1/(-Λ5M 2). The Hawking temperature and entropy for our large black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7/(-Λ5). Figueras, Lucietti, and Wiseman found an AdS5-CFT4 solution using an independent and different method from us, called the Ricci-DeTurck-flow method. Then, Figueras and Wiseman perturbed this solution in a same way as we have done and obtained the solution for the large black hole in the Randall-Sundrum II model. These two numerical solutions are the first mathematical proofs for having a large black hole in the Randall-Sundrum II. We have compared their results with ours for the CFT energy-momentum tensor components and the perturbed metric. We have shown that the results are closely in agreement, which can be considered as evidence that the solution for the large black hole in the Randall-Sundrum II model exists.

Static solutions for fourth order gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nelson, William

2010-11-15

The Lichnerowicz and Israel theorems are extended to higher order theories of gravity. In particular it is shown that Schwarzschild is the unique spherically symmetric, static, asymptotically flat, black-hole solution, provided the spatial curvature is less than the quantum gravity scale outside the horizon. It is then shown that in the presence of matter (satisfying certain positivity requirements), the only static and asymptotically flat solutions of general relativity that are also solutions of higher order gravity are the vacuum solutions.

Relativistic Modelling of Stable Anisotropic Super-Dense Star

NASA Astrophysics Data System (ADS)

Maurya, S. K.; Gupta, Y. K.; Jasim, M. K.

2015-08-01

In the present article we have obtained new set of exact solutions of Einstein field equations for anisotropic fluid spheres by using the Herrera et al. [1] algorithm. The anisotropic fluid solutions so obtained join continuously to the Schwarzschild exterior solution across the pressure-free boundary. It is observed that most of the new anisotropic solutions are well-behaved and are used to construct the super-dense star models such as neutron stars and pulsars.

The Advanced Gamma-ray Imaging System (AGIS): Schwarzschild-Couder (SC) Telescope Mechanical and Optical System Design

NASA Astrophysics Data System (ADS)

Guarino, V.; Vassiliev, V.; Buckley, J.; Byrum, K.; Falcone, A.; Fegan, S.; Finley, J.; Hanna, D.; Kaaret, P.; Konopelko, A.; Krawczynski, H.; Krennrich, F.; Romani, R.; Wagner, R.; Woods, M.

2009-05-01

The concept of a future ground-based gamma-ray observatory, AGIS, in the energy range 20 GeV to 200 TeV is based on an array of 50-100 imaging atmospheric Cherenkov telescopes (IACTs). The anticipated improvement of AGIS sensitivity, angular resolution, and reliability of operation imposes demanding technological and cost requirements on the design of IACTs. In this submission, we focus on the optical and mechanical systems for a novel Schwarzschild-Couder two-mirror aplanatic optical system originally proposed by Schwarzschild. Emerging new mirror production technologies based on replication processes, such as cold and hot glass slumping, cured CFRP, and electroforming, provide new opportunities for cost effective solutions for the design of the optical system. We explore capabilities of these mirror fabrication methods for the AGIS project and alignment methods for optical systems. We also study a mechanical structure which will provide support points for mirrors and camera design driven by the requirement of minimizing the deflections of the mirror support structures.

Apparent violation of the principle of equivalence and killing horizons. [for relativity

NASA Technical Reports Server (NTRS)

Zimmerman, R. L.; Farhoosh, H.

1980-01-01

By means of the principle of equivalence the qualitative behavior of the Schwarzschild horizon about a uniformly accelerating particle was deduced. This result is confirmed for an exact solution of a uniformly accelerating object in the limit of small accelerations. For large accelerations the Schwarzschild horizon appears to violate the qualitative behavior established via the principle of equivalence. When similar arguments are extended to an observable such as the red shift between two observers, there is no departure from the results expected from the principle of equivalence. The resolution of the paradox is brought about by a compensating effect due to the Rindler horizon.

3rd Karl Schwarzschild Meeting - Gravity and the Gauge/Gravity Correspondence

NASA Astrophysics Data System (ADS)

Nicolini, Piero; Kaminski, Matthias; Mureika, Jonas; Bleicher, Marcus

2018-01-01

The Karl Schwarzschild Meeting 2017 (KSM2017) has been the third instalment of the conference dedicated to the great Frankfurter scientist, who derived the first black hole solution of Einstein's equations about 100 years ago. The event has been a 5 day meeting in the field of black holes, AdS/CFT correspondence and gravitational physics. Like the two previous instalments, the conference continued to attract a stellar ensemble of participants from the world's most renowned institutions. The core of the meeting has been a series of invited talks from eminent experts (keynote speakers) as well as the presence of plenary research talks by students and junior speakers.

Singularity-free anisotropic strange quintessence star

NASA Astrophysics Data System (ADS)

Bhar, Piyali

2015-04-01

Present paper provides a new model of anisotropic strange star corresponding to the exterior Schwarzschild metric. The Einstein field equations have been solved by utilizing the Krori-Barua (KB) ansatz (Krori and Barua in J. Phys. A, Math. Gen. 8:508, 1975) in presence of quintessence field characterized by a parameter ω q with . The obtained solutions are free from central singularity. Our model is potentially stable. The numerical values of mass of the different strange stars SAXJ1808.4-3658(SS1) (radius=7.07 km), 4U1820-30 (radius=10 km), Vela X-12 (radius=9.99 km), PSR J 1614-2230 (radius=10.3 km) obtained from our model is very close to the observational data that confirms the validity of our proposed model. The interior solution is also matched to the exterior Schwarzschild spacetime in presence of thin shell where negative surface pressure is required to hold the thin shell against collapsing.

Gravitational vacuum condensate stars.

PubMed

Mazur, Pawel O; Mottola, Emil

2004-06-29

A new final state of gravitational collapse is proposed. By extending the concept of Bose-Einstein condensation to gravitational systems, a cold, dark, compact object with an interior de Sitter condensate p(v) = -rho(v) and an exterior Schwarzschild geometry of arbitrary total mass M is constructed. These regions are separated by a shell with a small but finite proper thickness l of fluid with equation of state p = +rho, replacing both the Schwarzschild and de Sitter classical horizons. The new solution has no singularities, no event horizons, and a global time. Its entropy is maximized under small fluctuations and is given by the standard hydrodynamic entropy of the thin shell, which is of the order k(B)lMc/Planck's over 2 pi, instead of the Bekenstein-Hawking entropy formula, S(BH) = 4 pi k(B)GM(2)/Planck's over 2 pi c. Hence, unlike black holes, the new solution is thermodynamically stable and has no information paradox.

Gravitational field of a concentrated mass in Jordan—Brans—Dicke theory

NASA Astrophysics Data System (ADS)

Arutyunyan, G. G.; Papoyan, V. V.

1994-04-01

The problem of determining the gravitational field of a static, spherically symmetric, self-gravitating object is formulated. The small number of physically applicable exact solutions of the equations in Jordan—Brans—Dicke theory is augmented with new exact solutions describing the external gravitational field of the given body. Once a solution has been found, it can be rewritten in modified curvature, homogeneous, and other coordinates by appropriate gauging. In a special case the solution coincides with the well-known Schwarzschild solution.

Computerized series solution of relativistic equations of motion.

NASA Technical Reports Server (NTRS)

Broucke, R.

1971-01-01

A method of solution of the equations of planetary motion is described. It consists of the use of numerical general perturbations in orbital elements and in rectangular coordinates. The solution is expanded in Fourier series in the mean anomaly with the aid of harmonic analysis and computerized series manipulation techniques. A detailed application to the relativistic motion of the planet Mercury is described both for Schwarzschild and isotropic coordinates.

Global structure of static spherically symmetric solutions surrounded by quintessence

NASA Astrophysics Data System (ADS)

Cruz, Miguel; Ganguly, Apratim; Gannouji, Radouane; Leon, Genly; Saridakis, Emmanuel N.

2017-06-01

We investigate all static spherically symmetric solutions in the context of general relativity surrounded by a minimally-coupled quintessence field, using dynamical system analysis. Applying the 1  +  1  +  2 formalism and introducing suitable normalized variables involving the Gaussian curvature, we were able to reformulate the field equations as first order differential equations. In the case of a massless canonical scalar field we recovered all known black hole results, such as the Fisher solution, and we found that apart from the Schwarzschild solution all other solutions are naked singularities. Additionally, we identified the symmetric phase space which corresponds to the white hole part of the solution and in the case of a phantom field, we were able to extract the conditions for the existence of wormholes and define all possible classes of solutions such as cold black holes, singular spacetimes and wormholes such as the Ellis wormhole, for example. For an exponential potential, we found that the black hole solution which is asymptotically flat is unique and it is the Schwarzschild spacetime, while all other solutions are naked singularities. Furthermore, we found solutions connecting to a white hole through a maximum radius, and not a minimum radius (throat) such as wormhole solutions, therefore violating the flare-out condition. Finally, we have found a necessary and sufficient condition on the form of the potential to have an asymptotically AdS spacetime along with a necessary condition for the existence of asymptotically flat black holes.

Static black holes with back reaction from vacuum energy

NASA Astrophysics Data System (ADS)

Ho, Pei-Ming; Matsuo, Yoshinori

2018-03-01

We study spherically symmetric static solutions to the semi-classical Einstein equation sourced by the vacuum energy of quantum fields in the curved space-time of the same solution. We found solutions that are small deformations of the Schwarzschild metric for distant observers, but without horizon. Instead of being a robust feature of objects with high densities, the horizon is sensitive to the energy–momentum tensor in the near-horizon region.

Anisotropic solutions by gravitational decoupling

NASA Astrophysics Data System (ADS)

Ovalle, J.; Casadio, R.; da Rocha, R.; Sotomayor, A.

2018-02-01

We investigate the extension of isotropic interior solutions for static self-gravitating systems to include the effects of anisotropic spherically symmetric gravitational sources by means of the gravitational decoupling realised via the minimal geometric deformation approach. In particular, the matching conditions at the surface of the star with the outer Schwarzschild space-time are studied in great detail, and we describe how to generate, from a single physically acceptable isotropic solution, new families of anisotropic solutions whose physical acceptability is also inherited from their isotropic parent.

Exact solutions to force-free electrodynamics in black hole backgrounds

NASA Astrophysics Data System (ADS)

Brennan, T. Daniel; Gralla, Samuel E.; Jacobson, Ted

2013-10-01

A shared property of several of the known exact solutions to the equations of force-free electrodynamics is that their charge-current four-vector is null. We examine the general properties of null-current solutions and then focus on the principal congruences of the Kerr black hole spacetime. We obtain a large class of exact solutions, which are in general time-dependent and non-axisymmetric. These solutions include waves that, surprisingly, propagate without scattering on the curvature of the black hole’s background. They may be understood as generalizations to Robinson’s solutions to vacuum electrodynamics associated with a shear-free congruence of null geodesics. When stationary and axisymmetric, our solutions reduce to those of Menon and Dermer, the only previously known solutions in Kerr. In Kerr, all of our solutions have null electromagnetic fields (\\vec{E} \\cdot \\vec{B} = 0 and E2 = B2). However, in Schwarzschild or flat spacetime there is freedom to add a magnetic monopole field, making the solutions magnetically dominated (B2 > E2). This freedom may be used to reproduce the various flat-spacetime and Schwarzschild-spacetime (split) monopole solutions available in the literature (due to Michel and later authors), and to obtain a large class of time-dependent, non-axisymmetric generalizations. These generalizations may be used to model the magnetosphere of a conducting star that rotates with arbitrary prescribed time-dependent rotation axis and speed. We thus significantly enlarge the class of known exact solutions, while organizing and unifying previously discovered solutions in terms of their null structure.

Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity. III: nonspherical Schwarzschild waves and singularities at null infinity

NASA Astrophysics Data System (ADS)

Frauendiener, Jörg; Hennig, Jörg

2018-03-01

We extend earlier numerical and analytical considerations of the conformally invariant wave equation on a Schwarzschild background from the case of spherically symmetric solutions, discussed in Frauendiener and Hennig (2017 Class. Quantum Grav. 34 045005), to the case of general, nonsymmetric solutions. A key element of our approach is the modern standard representation of spacelike infinity as a cylinder. With a decomposition into spherical harmonics, we reduce the four-dimensional wave equation to a family of two-dimensional equations. These equations can be used to study the behaviour at the cylinder, where the solutions turn out to have, in general, logarithmic singularities at infinitely many orders. We derive regularity conditions that may be imposed on the initial data, in order to avoid the first singular terms. We then demonstrate that the fully pseudospectral time evolution scheme can be applied to this problem leading to a highly accurate numerical reconstruction of the nonsymmetric solutions. We are particularly interested in the behaviour of the solutions at future null infinity, and we numerically show that the singularities spread to null infinity from the critical set, where the cylinder approaches null infinity. The observed numerical behaviour is consistent with similar logarithmic singularities found analytically on the critical set. Finally, we demonstrate that even solutions with singularities at low orders can be obtained with high accuracy by virtue of a coordinate transformation that converts solutions with logarithmic singularities into smooth solutions.

Black Hole Information Problem and Wave Bursts

NASA Astrophysics Data System (ADS)

Gogberashvili, Merab; Pantskhava, Lasha

2018-06-01

By reexamination of the boundary conditions of wave equation on a black hole horizon it is found not harmonic, but real-valued exponentially time-dependent solutions. This means that quantum particles probably do not cross the Schwarzschild horizon, but are absorbed and some are reflected by it, what potentially can solve the famous black hole information paradox. To study this strong gravitational lensing we are introducing an effective negative cosmological constant between the Schwarzschild and photon spheres. It is shown that the reflected particles can obtain their additional energy in this effective AdS space and could explain properties of some unusually strong signals, like LIGO events, gamma ray and fast radio bursts.

Instability of enclosed horizons

NASA Astrophysics Data System (ADS)

Kay, Bernard S.

2015-03-01

We point out that there are solutions to the scalar wave equation on dimensional Minkowski space with finite energy tails which, if they reflect off a uniformly accelerated mirror due to (say) Dirichlet boundary conditions on it, develop an infinite stress-energy tensor on the mirror's Rindler horizon. We also show that, in the presence of an image mirror in the opposite Rindler wedge, suitable compactly supported arbitrarily small initial data on a suitable initial surface will develop an arbitrarily large stress-energy scalar near where the two horizons cross. Also, while there is a regular Hartle-Hawking-Israel-like state for the quantum theory between these two mirrors, there are coherent states built on it for which there are similar singularities in the expectation value of the renormalized stress-energy tensor. We conjecture that in other situations with analogous enclosed horizons such as a (maximally extended) Schwarzschild black hole in equilibrium in a (stationary spherical) box or the (maximally extended) Schwarzschild-AdS spacetime, there will be similar stress-energy singularities and almost-singularities—leading to instability of the horizons when gravity is switched on and matter and gravity perturbations are allowed for. All this suggests it is incorrect to picture a black hole in equilibrium in a box or a Schwarzschild-AdS black hole as extending beyond the past and future horizons of a single Schwarzschild (/Schwarzschild-AdS) wedge. It would thus provide new evidence for 't Hooft's brick wall model while seeming to invalidate the picture in Maldacena's ` Eternal black holes in AdS'. It would thereby also support the validity of the author's matter-gravity entanglement hypothesis and of the paper ` Brick walls and AdS/CFT' by the author and Ortíz.

On the stability of dyons and dyonic black holes in Einstein-Yang-Mills theory

NASA Astrophysics Data System (ADS)

Nolan, Brien C.; Winstanley, Elizabeth

2016-02-01

We investigate the stability of four-dimensional dyonic soliton and black hole solutions of {su}(2) Einstein-Yang-Mills theory in anti-de Sitter space. We prove that, in a neighbourhood of the embedded trivial (Schwarzschild-)anti-de Sitter solution, there exist non-trivial dyonic soliton and black hole solutions of the field equations which are stable under linear, spherically symmetric, perturbations of the metric and non-Abelian gauge field.

A Classical Based Derivation of Time Dilation Providing First Order Accuracy to Schwarzschild's Solution of Einstein's Field Equations

NASA Astrophysics Data System (ADS)

Austin, Rickey W.

In Einstein's theory of Special Relativity (SR), one method to derive relativistic kinetic energy is via applying the classical work-energy theorem to relativistic momentum. This approach starts with a classical based work-energy theorem and applies SR's momentum to the derivation. One outcome of this derivation is relativistic kinetic energy. From this derivation, it is rather straight forward to form a kinetic energy based time dilation function. In the derivation of General Relativity a common approach is to bypass classical laws as a starting point. Instead a rigorous development of differential geometry and Riemannian space is constructed, from which classical based laws are derived. This is in contrast to SR's approach of starting with classical laws and applying the consequences of the universal speed of light by all observers. A possible method to derive time dilation due to Newtonian gravitational potential energy (NGPE) is to apply SR's approach to deriving relativistic kinetic energy. It will be shown this method gives a first order accuracy compared to Schwarzschild's metric. The SR's kinetic energy and the newly derived NGPE derivation are combined to form a Riemannian metric based on these two energies. A geodesic is derived and calculations compared to Schwarzschild's geodesic for an orbiting test mass about a central, non-rotating, non-charged massive body. The new metric results in high accuracy calculations when compared to Einsteins General Relativity's prediction. The new method provides a candidate approach for starting with classical laws and deriving General Relativity effects. This approach mimics SR's method of starting with classical mechanics when deriving relativistic equations. As a compliment to introducing General Relativity, it provides a plausible scaffolding method from classical physics when teaching introductory General Relativity. A straight forward path from classical laws to General Relativity will be derived. This derivation provides a minimum first order accuracy to Schwarzschild's solution to Einstein's field equations.

Modified gravity in Arnowitt-Deser-Misner formalism

NASA Astrophysics Data System (ADS)

Gao, Changjun

2010-02-01

Motivated by Hořava-Lifshitz gravity theory, we propose and investigate two kinds of modified gravity theories, the f(R) kind and the K-essence kind, in the Arnowitt-Deser-Misner (ADM) formalism. The f(R) kind includes one ultraviolet (UV) term and one infrared (IR) term together with the Einstein-Hilbert action. We find that these two terms naturally present the ultraviolet and infrared modifications to the Friedmann equation. The UV and IR modifications can avoid the past Big-Bang singularity and the future Big-Rip singularity, respectively. Furthermore, the IR modification can naturally account for the current acceleration of the Universe. The Lagrangian of K-essence kind modified gravity is made up of the three-dimensional Ricci scalar and an arbitrary function of the extrinsic curvature term. We find the cosmic acceleration can also be naturally interpreted without invoking any kind of dark energy. The static, spherically symmetry and vacuum solutions of both theories are Schwarzschild or Schwarzschild-de Sitter solution. Thus these modified gravity theories are viable for solar system tests.

Tidal Forces in Dyonic Reissner-Nördstrom Black Hole

NASA Astrophysics Data System (ADS)

Sharif, M.; Kousar, Lubna

2018-03-01

This paper investigates the tidal as well as magnetic charge effects produced in dyonic Reissner-Nordström black hole. We evaluate Newtonian radial acceleration using radial geodesics for freely falling test particles. We establish system of equations governing radial and angular tidal forces using geodesic deviation equation and discuss their solutions for bodies falling freely towards this black hole. The radial tidal force turns out to be compressing outside the event horizon whereas the angular tidal force changes sign between event and Cauchy horizons unlike Schwarzschild black hole. The radial geodesic component starts decreasing in dyonic Reissner-Nordström black hole unlike Schwarzschild case. We conclude that magnetic charge strongly affects the radial as well as angular components of tidal force.

Comment on ;Acceleration of particles to high energy via gravitational repulsion in the Schwarzschild field; [Astropart. Phys. 86 (2017) 18-20

NASA Astrophysics Data System (ADS)

Spallicci, Alessandro D. A. M.

2017-09-01

Comments are due on a recent paper by McGruder III (2017) in which the author deals with the concept of gravitational repulsion in the context of the Schwarzschild-Droste solution. Repulsion (deceleration) for ingoing particles into a black hole is a concept proposed several times starting from Droste himself in 1916. It is a coordinate effect appearing to an observer at a remote distance from the black hole and when coordinate time is employed. Repulsion has no bearing and relation to the local physics of the black hole, and moreover it cannot be held responsible for accelerating outgoing particles. Thereby, the energy boost of cosmic rays cannot be produced by repulsion.

Characteristics of transonic spherical symmetric accretion flow in Schwarzschild-de Sitter and Schwarzschild anti-de Sitter backgrounds, in pseudo-general relativistic paradigm

NASA Astrophysics Data System (ADS)

Ghosh, Shubhrangshu; Banik, Prabir

2015-07-01

In this paper, we present a complete work on steady state spherically symmetric Bondi type accretion flow in the presence of cosmological constant (Λ) in both Schwarzschild-de Sitter (SDS) and Schwarzschild anti-de Sitter (SADS) backgrounds considering an isolated supermassive black hole (SMBH), with the inclusion of a simple radiative transfer scheme, in the pseudo-general relativistic paradigm. We do an extensive analysis on the transonic behavior of the Bondi type accretion flow onto the cosmological BHs including a complete analysis of the global parameter space and the stability of flow, and do a complete study of the global family of solutions for a generic polytropic flow. Bondi type accretion flow in SADS background renders multiplicity in its transonic behavior with inner "saddle" type and outer "center" type sonic points, with the transonic solutions forming closed loops or contours. There is always a limiting value for ∣Λ∣ up to which we obtain valid stationary transonic solutions, which correspond to both SDS and SADS geometries; this limiting value moderately increases with the increasing radiative efficiency of the flow, especially correspond to Bondi type accretion flow in SADS background. Repulsive Λ suppresses the Bondi accretion rate by an order of magnitude for relativistic Bondi type accretion flow for a certain range in temperature, and with a marginal increase in the Bondi accretion rate if the corresponding accretion flow occurs in SADS background. However, for a strongly radiative Bondi type accretion flow with high mass accretion rate, the presence of cosmological constant do not much influence the corresponding Bondi accretion rate of the flow. Our analysis show that the relic cosmological constant has a substantial effect on Bondi type accretion flow onto isolated SMBHs and their transonic solutions beyond length-scale of kiloparsecs, especially if the Bondi type accretion occurs onto the host supergiant ellipticals or central dominant (CD) galaxies directly from ambient intercluster medium (ICM). However, for high mass accretion rate, the influence of cosmological constant on Bondi accretion dynamics, generically, diminishes. As active galactic nuclei (AGN)/ICM feedback can be advertently linked to Bondi type spherical accretion, any proper modeling of AGN feedback or megaparsecs-scale jet dynamics or accretion flow from ICM onto the central regions of host galaxies should take into account the relevant information of repulsive Λ, especially in context to supergiant elliptical galaxies or CD galaxies present in rich galaxy clusters. This could also explore the feasibility to limit the value of Λ, from the kinematics in local galactic-scales.

Confluent Heun functions and the physics of black holes: Resonant frequencies, Hawking radiation and scattering of scalar waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vieira, H.S., E-mail: horacio.santana.vieira@hotmail.com; Centro de Ciências, Tecnologia e Saúde, Universidade Estadual da Paraíba, CEP 58233-000, Araruna, PB; Bezerra, V.B., E-mail: valdir@fisica.ufpb.br

We apply the confluent Heun functions to study the resonant frequencies (quasispectrum), the Hawking radiation and the scattering process of scalar waves, in a class of spacetimes, namely, the ones generated by a Kerr–Newman–Kasuya spacetime (dyon black hole) and a Reissner–Nordström black hole surrounded by a magnetic field (Ernst spacetime). In both spacetimes, the solutions for the angular and radial parts of the corresponding Klein–Gordon equations are obtained exactly, for massive and massless fields, respectively. The special cases of Kerr and Schwarzschild black holes are analyzed and the solutions obtained, as well as in the case of a Schwarzschild blackmore » hole surrounded by a magnetic field. In all these special situations, the resonant frequencies, Hawking radiation and scattering are studied. - Highlights: • Charged massive scalar field in the dyon black hole and massless scalar field in the Ernst spacetime are analyzed. • The confluent Heun functions are applied to obtain the solution of the Klein–Gordon equation. • The resonant frequencies are obtained. • The Hawking radiation and the scattering process of scalar waves are examined.« less

Antigravity: Spin-gravity coupling in action

NASA Astrophysics Data System (ADS)

Plyatsko, Roman; Fenyk, Mykola

2016-08-01

The typical motions of a spinning test particle in Schwarzschild's background which show the strong repulsive action of the highly relativistic spin-gravity coupling are considered using the exact Mathisson-Papapetrou equations. An approximated approach to choice solutions of these equations which describe motions of the particle's proper center of mass is developed.

Kerr-Newman black holes with string corrections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Charles, Anthony M.; Larsen, Finn

We study N = 2 supergravity with higher-derivative corrections that preserve the N = 2 supersymmetry and show that Kerr-Newman black holes are solutions to these theories. Modifications of the black hole entropy due to the higher derivatives are universal and apply even in the BPS and Schwarzschild limits. Our solutions and their entropy are greatly simplified by supersymmetry of the theory even though the black holes generally do not preserve any of the supersymmetry.

Kerr-Newman black holes with string corrections

DOE PAGES

Charles, Anthony M.; Larsen, Finn

2016-10-26

We study N = 2 supergravity with higher-derivative corrections that preserve the N = 2 supersymmetry and show that Kerr-Newman black holes are solutions to these theories. Modifications of the black hole entropy due to the higher derivatives are universal and apply even in the BPS and Schwarzschild limits. Our solutions and their entropy are greatly simplified by supersymmetry of the theory even though the black holes generally do not preserve any of the supersymmetry.

A new class of relativistic stellar models

NASA Astrophysics Data System (ADS)

Haggag, Salah

1995-03-01

Einstein field equations for a static and spherically symmetric perfect fluid are considered. A formulation given by Patino and Rago is used to obtain a class of nine solutions, two of them are Tolman solutions I, IV and the remaining seven are new. The solutions are the correct ones corresponding to expressions derived by Patino and Rago which have been shown by Knutsen to be incorrect. Similar to Tolan solution IV each of the new solutions satisfies energy conditions inside a sphere in some range of two independent parameters. Besides, each solution could be matched to the exterior Schwarzschild solution at a boundary where the pressure vanishes and thus the solutions constitute a class of new physically reasonable stellar models.

Accretion onto a noncommutative geometry inspired black hole

NASA Astrophysics Data System (ADS)

Kumar, Rahul; Ghosh, Sushant G.

2017-09-01

The spherically symmetric accretion onto a noncommutative (NC) inspired Schwarzschild black hole is treated for a polytropic fluid. The critical accretion rate \\dot{M}, sonic speed a_s and other flow parameters are generalized for the NC inspired static black hole and compared with the results obtained for the standard Schwarzschild black holes. Also explicit expressions for gas compression ratios and temperature profiles below the accretion radius and at the event horizon are derived. This analysis is a generalization of Michel's solution to the NC geometry. Owing to the NC corrected black hole, the accretion flow parameters also have been modified. It turns out that \\dot{M} ≈ {M^2} is still achievable but r_s seems to be substantially decreased due to the NC effects. They in turn do affect the accretion process.

Geometric scalar theory of gravity beyond spherical symmetry

NASA Astrophysics Data System (ADS)

Moschella, U.; Novello, M.

2017-04-01

We construct several exact solutions for a recently proposed geometric scalar theory of gravity. We focus on a class of axisymmetric geometries and a big-bang-like geometry and discuss their Lorentzian character. The axisymmetric solutions are parametrized by an integer angular momentum l . The l =0 (spherical) case gives rise to the Schwarzschild geometry. The other solutions have naked singular surfaces. While not a priori obvious, all the solutions that we present here are globally Lorentzian. The Lorentzian signature appears to be a robust property of the disformal geometries solving the vacuum geometric scalar theory of gravity equations.

Stability and instability of Ellis and phantom wormholes: Are there ghosts?

NASA Astrophysics Data System (ADS)

Nandi, K. K.; Potapov, A. A.; Izmailov, R. N.; Tamang, A.; Evans, J. C.

2016-05-01

It is concluded in the literature that the Ellis wormhole is unstable under small perturbations and would either decay to the Schwarzschild black hole or expand away to infinity. While this deterministic conclusion of instability is correct, we show that the Ellis wormhole reduces to the Schwarzschild black hole only when the Ellis solution parameter γ assumes a complex value -i . We shall then reexamine the stability of Ellis and phantom wormholes from the viewpoint of local and asymptotic observers by using a completely different approach, viz., we adapt Tangherlini's nondeterministic, prequantal statistical simulation about photon motion in the real optical medium to an effective medium reformulation of motions obtained via Hamilton's optical-mechanical analogy in a gravity field. A crucial component of Tangherlini's idea is the observed increase of momentum of the photons entering a real medium. We show that this fact has a heuristic parallel in the effective medium version of the Pound-Rebka experiment in gravity. Our conclusion is that there is a nonzero probability that Ellis and phantom wormholes could appear stable or unstable depending on the location of observers and on the values of γ , leading to the possibility of ghost wormholes (like ghost stars). The Schwarzschild horizon, however, would always certainly appear to be stable (R =1 , T =0 ) to observers regardless of their location. Phantom wormholes of bounded mass in the extreme limit a →-1 are also shown to be stable just as the Schwarzschild black hole is. We shall propose a thought experiment showing that our nondeterministic results could be numerically translated into observable deterministic signatures of ghost wormholes.

Resolving the Schwarzschild singularity in both classic and quantum gravity

NASA Astrophysics Data System (ADS)

Zeng, Ding-fang

2017-04-01

The Schwarzschild singularity's resolution has key values in cracking the key mysteries related with black holes, the origin of their horizon entropy and the information missing puzzle involved in their evaporations. We provide in this work the general dynamic inner metric of collapsing stars with horizons and with non-trivial radial mass distributions. We find that static central singularities are not the final state of the system. Instead, the final state of the system is a periodically zero-cross breathing ball. Through 3+1 decomposed general relativity and its quantum formulation, we establish a functional Schrödinger equation controlling the micro-state of this breathing ball and show that, the system configuration with all the matter concentrating on the central point is not the unique eigen-energy-density solution. Using a Bohr-Sommerfield like "orbital" quantisation assumption, we show that for each black hole of horizon radius rh, there are about e rh2 / ℓpl2 allowable eigen-energy-density profiles. This naturally leads to physic interpretations for the micro-origin of horizon entropy, as well as solutions to the information missing puzzle involved in Hawking radiations.

Black holes in loop quantum gravity: the complete space-time.

PubMed

Gambini, Rodolfo; Pullin, Jorge

2008-10-17

We consider the quantization of the complete extension of the Schwarzschild space-time using spherically symmetric loop quantum gravity. We find an exact solution corresponding to the semiclassical theory. The singularity is eliminated but the space-time still contains a horizon. Although the solution is known partially numerically and therefore a proper global analysis is not possible, a global structure akin to a singularity-free Reissner-Nordström space-time including a Cauchy horizon is suggested.

Mass quantization of the Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Vaz, Cenalo; Witten, Louis

1999-07-01

We examine the Wheeler-DeWitt equation for a static, eternal Schwarzschild black hole in Kuchař-Brown variables and obtain its energy eigenstates. Consistent solutions vanish in the exterior of the Kruskal manifold and are nonvanishing only in the interior. The system is reminiscent of a particle in a box. States of definite parity avoid the singular geometry by vanishing at the origin. These definite parity states admit a discrete energy spectrum, depending on one quantum number which determines the Arnowitt-Deser-Misner mass of the black hole according to a relation conjectured long ago by Bekenstein M~nMp. If attention is restricted only to these quantized energy states, a black hole is described not only by its mass but also by its parity. States of indefinite parity do not admit a quantized mass spectrum.

Naked shell singularities on the brane

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seahra, Sanjeev S.

By utilizing nonstandard slicings of 5-dimensional Schwarzschild and Schwarzschild-AdS manifolds based on isotropic coordinates, we generate static and spherically-symmetric braneworld spacetimes containing shell-like naked null singularities. For planar slicings, we find that the brane-matter sourcing the solution is a perfect fluid with an exotic equation of state and a pressure singularity where the brane crosses the bulk horizon. From a relativistic point of view, such a singularity is required to maintain matter infinitesimally above the surface of a black hole. From the point of view of the AdS/CFT conjecture, the singular horizon can be seen as one possible quantum correctionmore » to a classical black hole geometry. Various generalizations of planar slicings are also considered for a Ricci-flat bulk, and we find that singular horizons and exotic matter distributions are common features.« less

Maximally slicing a black hole.

NASA Technical Reports Server (NTRS)

Estabrook, F.; Wahlquist, H.; Christensen, S.; Dewitt, B.; Smarr, L.; Tsiang, E.

1973-01-01

Analytic and computer-derived solutions are presented of the problem of slicing the Schwarzschild geometry into asymptotically flat, asymptotically static, maximal spacelike hypersurfaces. The sequence of hypersurfaces advances forward in time in both halves (u greater than or equal to 0, u less than or equal to 0) of the Kruskal diagram, tending asymptotically to the hypersurface r = 3/2 M and avoiding the singularity at r = 0. Maximality is therefore a potentially useful condition to impose in obtaining computer solutions of Einstein's equations.

Revisiting the analogue of the Jebsen-Birkhoff theorem in Brans-Dicke gravity

NASA Astrophysics Data System (ADS)

Faraoni, Valerio; Hammad, Fayçal; Cardini, Adriana M.; Gobeil, Thomas

2018-04-01

We report the explicit form of the general static, spherically symmetric, and asymptotically flat solution of vacuum Brans-Dicke gravity in the Jordan frame, assuming that the Brans-Dicke scalar field has no singularities or zeros (except possibly for a central singularity). This general solution is conformal to the Fisher-Wyman geometry of Einstein theory and its nature depends on a scalar charge parameter. Apart from the Schwarzschild black hole, only wormhole throats and central naked singularities are possible.

Martin Schwarzschild (1912 - 1997)

NASA Astrophysics Data System (ADS)

Pfau, Werner

The Chairman of the Astronomische Gesellschaft honored Martin Schwarzschild, who was the first to be presented with the Karl Schwarzschild Medal of the Astronomische Gesellschaft in 1957. An account of his life and work is given.

Black holes in higher derivative gravity.

PubMed

Lü, H; Perkins, A; Pope, C N; Stelle, K S

2015-05-01

Extensions of Einstein gravity with higher-order derivative terms arise in string theory and other effective theories, as well as being of interest in their own right. In this Letter we study static black-hole solutions in the example of Einstein gravity with additional quadratic curvature terms. A Lichnerowicz-type theorem simplifies the analysis by establishing that they must have vanishing Ricci scalar curvature. By numerical methods we then demonstrate the existence of further black-hole solutions over and above the Schwarzschild solution. We discuss some of their thermodynamic properties, and show that they obey the first law of thermodynamics.

General Wahlquist metrics in all dimensions

NASA Astrophysics Data System (ADS)

Hinoue, Kazuki; Houri, Tsuyoshi; Rugina, Christina; Yasui, Yukinori

2014-07-01

It is shown that the Wahlquist metric, which is a stationary, axially symmetric perfect fluid solution with ρ +3p=const, admits a rank-2 generalized closed conformal Killing-Yano tensor with a skew-symmetric torsion. Taking advantage of the presence of such a tensor, we obtain a higher-dimensional generalization of the Wahlquist metric in arbitrary dimensions, including a family of vacuum black hole solutions with spherical horizon topology such as Schwarzschild-Tangherlini, Myers-Perry and higher-dimensional Kerr-NUT-(A)dS metrics and a family of static, spherically symmetric perfect fluid solutions in higher dimensions.

Exact solutions and phenomenological constraints from massive scalars in a gravity's rainbow spacetime

NASA Astrophysics Data System (ADS)

Bezerra, V. B.; Christiansen, H. R.; Cunha, M. S.; Muniz, C. R.

2017-07-01

We obtain the exact (confluent Heun) solutions to the massive scalar field in a gravity's rainbow Schwarzschild metric. With these solutions at hand, we study the Hawking radiation resulting from the tunneling rate through the event horizon. We show that the emission spectrum obeys nonextensive statistics and is halted when a certain mass remnant is reached. Next, we infer constraints on the rainbow parameters from recent LHC particle physics experiments and Hubble STIS astrophysics measurements. Finally, we study the low frequency limit in order to find the modified energy spectrum around the source.

Curved spaces before Einstein: Karl Schwarzschild's cosmological speculations and the beginnings of relativistic cosmology (German Title: Gekrümmte Universen vor Einstein: Karl Schwarzschilds kosmologische Spekulationen und die Anfänge der relativistischen Kosmologie)

NASA Astrophysics Data System (ADS)

Schemmel, Matthias

In contrast to most of his collegues in astronomy and physics, the German astronomer Karl Schwarzschild immediately recognized the significance of general relativity for physics and astronomy, and played a pioneering role in its early development. In this contribution, it is argued that the clue for understanding Schwarzschild's exceptional reaction to general relativity lies in the study of his prerelativistic work. Long before the rise of general relativity, Schwarzschild occupied himself with foundational problems on the borderline of physics, astronomy, and mathematics that, from today's perspective, belong to the field of problems of that theory. In this contribution, the example of Schwarzschild's early speculations about the non-Euclidean nature of physical space on cosmological scales is presented and their reflection in his reception of general relativity is discussed.

Two-Mirror Schwarzschild Aplanats: Basic Relations

NASA Astrophysics Data System (ADS)

Terebizh, V. Yu.

2005-02-01

The theory of aplanatic two-mirror telescopes developed by Karl Schwarzschild in 1905 is shown to lead to a unified description of both prefocal and postfocal systems. The class of surfaces in the ZEMAX optical program has been properly extended to ascertain the image quality in exact Schwarzschild aplanats. A comparison of Schwarzschild aplanats with approximate Ritchey-Chrétien and Gregory-Maksutov aplanatic telescopes reveals a noticeable advantage of the former at the system’s fast focal ratio.

Surface phenomena and the evolution of radiating fluid spheres in general relativity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Herrera, L.; Jimenez, J.; Esculpi, M.

1989-10-01

A method used to study the evolution of radiating spheres (Herrera, Jimenez, and Ruggeri) is extended to the case in which surface phenomena are taken into account. The equations have been integrated numerically for a model derived from the Schwarzschild interior solution, bringing out the effects of surface tension on the evolution of the spheres. 17 refs.

Spherically symmetric vacuum in covariant F (T )=T +α/2 T2+O (Tγ) gravity theory

NASA Astrophysics Data System (ADS)

DeBenedictis, Andrew; Ilijić, Saša

2016-12-01

Recently, a fully covariant version of the theory of F (T ) torsion gravity has been introduced by M. Kršśák and E. Saridakis [Classical Quantum Gravity 33, 115009 (2016)]. In covariant F (T ) gravity, the Schwarzschild solution is not a vacuum solution for F (T )≠T , and therefore determining the spherically symmetric vacuum is an important open problem. Within the covariant framework, we perturbatively solve the spherically symmetric vacuum gravitational equations around the Schwarzschild solution for the scenario with F (T )=T +(α /2 )T2 , representing the dominant terms in theories governed by Lagrangians analytic in the torsion scalar. From this, we compute the perihelion shift correction to solar system planetary orbits as well as perturbative gravitational effects near neutron stars. This allows us to set an upper bound on the magnitude of the coupling constant, α , which governs deviations from general relativity. We find the bound on this nonlinear torsion coupling constant by specifically considering the uncertainty in the perihelion shift of Mercury. We also analyze a bound from a similar comparison with the periastron orbit of the binary pulsar PSR J0045-7319 as an independent check for consistency. Setting bounds on the dominant nonlinear coupling is important in determining if other effects in the Solar System or greater universe could be attributable to nonlinear torsion.

Entropy Inequality Violations from Ultraspinning Black Holes.

PubMed

Hennigar, Robie A; Mann, Robert B; Kubizňák, David

2015-07-17

We construct a new class of rotating anti-de Sitter (AdS) black hole solutions with noncompact event horizons of finite area in any dimension and study their thermodynamics. In four dimensions these black holes are solutions to gauged supergravity. We find that their entropy exceeds the maximum implied from the conjectured reverse isoperimetric inequality, which states that for a given thermodynamic volume, the black hole entropy is maximized for Schwarzschild-AdS space. We use this result to suggest more stringent conditions under which this conjecture may hold.

Cosmological bouncing solutions in extended teleparallel gravity theories

NASA Astrophysics Data System (ADS)

de la Cruz-Dombriz, Álvaro; Farrugia, Gabriel; Said, Jackson Levi; Gómez, Diego Sáez-Chillón

2018-05-01

In the context of extended teleparallel gravity theories with a 3 +1 -dimensional Gauss-Bonnet analog term, we address the possibility of these theories reproducing several well-known cosmological bouncing scenarios in a four-dimensional Friedmann-Lemaître-Robertson-Walker geometry. We study which types of gravitational Lagrangians are capable of reconstructing bouncing solutions provided by analytical expressions for symmetric, oscillatory, superbounce, matter bounce, and singular bounce. Some of the Lagrangians discovered are analytical at the origin, having both Minkowski and Schwarzschild vacuum solutions. All these results open up the possibility for such theories to be competitive candidates of extended theories of gravity in cosmological scales.

Brane-world black hole solutions via a confining potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heydari-Fard, M.; Sepangi, H. R.; Razmi, H.

2007-09-15

Using a confining potential, we consider spherically symmetric vacuum (static black hole) solutions in a brane-world scenario. Working with a constant curvature bulk, two interesting cases/solutions are studied. A Schwarzschild-de Sitter black hole solution similar to the standard solution in the presence of a cosmological constant is obtained which confirms the idea that an extra term in the field equations on the brane can play the role of a positive cosmological constant and may be used to account for the accelerated expansion of the universe. The other solution is one in which we can have a proper potential to explainmore » the galaxy rotation curves without assuming the existence of dark matter and without working with new modified theories (modified Newtonian dynamics)« less

Conformally-flat, non-singular static metric in infinite derivative gravity

NASA Astrophysics Data System (ADS)

Buoninfante, Luca; Koshelev, Alexey S.; Lambiase, Gaetano; Marto, João; Mazumdar, Anupam

2018-06-01

In Einstein's theory of general relativity the vacuum solution yields a blackhole with a curvature singularity, where there exists a point-like source with a Dirac delta distribution which is introduced as a boundary condition in the static case. It has been known for a while that ghost-free infinite derivative theory of gravity can ameliorate such a singularity at least at the level of linear perturbation around the Minkowski background. In this paper, we will show that the Schwarzschild metric does not satisfy the boundary condition at the origin within infinite derivative theory of gravity, since a Dirac delta source is smeared out by non-local gravitational interaction. We will also show that the spacetime metric becomes conformally-flat and singularity-free within the non-local region, which can be also made devoid of an event horizon. Furthermore, the scale of non-locality ought to be as large as that of the Schwarzschild radius, in such a way that the gravitational potential in any metric has to be always bounded by one, implying that gravity remains weak from the infrared all the way up to the ultraviolet regime, in concurrence with the results obtained in [arXiv:1707.00273]. The singular Schwarzschild blackhole can now be potentially replaced by a non-singular compact object, whose core is governed by the mass and the effective scale of non-locality.

Actual Romanian research in post-newtonian dynamics

NASA Astrophysics Data System (ADS)

Mioc, V.; Stavinschi, M.

2007-05-01

We survey the recent Romanian results in the study of the two-body problem in post-Newtonian fields. Such a field is characterized, in general, by a potential of the form U(q)=|q|^{-1}+ something (small, but not compulsorily). We distinguish some classes of post-Newtonian models: relativistic (Schwarzschild, Fock, Einstein PN, Reissner-Nordström, Schwarzschild - de Sitter, etc.) and nonrelativistic (Manev, Mücket-Treder, Seeliger, gravito-elastic, etc.). Generalized models (the zonal-satellite problem, quasihomogeneous fields), as well as special cases (anisotropic Manev-type and Schwarzschild-type models, Popovici or Popovici-Manev photogravitational problem), were also tackled. The methods used in such studies are various: analytical (using mainly the theory of perturbations, but also other theories: functions of complex variable, variational calculus, etc.), geometric (qualitative approach of the theory of dynamical systems), and numerical (especially using the Poincaré-section technique). The areas of interest and the general results obtained focus on: exact or approximate analytical solutions; characteristics of local flows (especially at limit situations: collision and escape); quasiperiodic and periodic orbits; equilibria; symmetries; chaoticity; geometric description of the global flow (and physical interpretation of the phase-space structure). We emphasize some special features, which cannot be met within the Newtonian framework: black-hole effect, oscillatory collisions, radial librations, bounded orbits for nonnegative energy, existence of unstable circular motion (or unstable rest), symmetric periodic orbits within anisotropic models, etc.

Wormholes versus black holes: quasinormal ringing at early and late times

DOE Office of Scientific and Technical Information (OSTI.GOV)

Konoplya, R.A.; Zhidenko, A., E-mail: roman.konoplya@uni-tuebingen.de, E-mail: olexandr.zhydenko@ufabc.edu.br

Recently it has been argued that the phantom thin-shell wormholes matched with the Schwarzschild space-time near the Schwarzschild radius ring like Schwarzschild black holes at early times, but differently at late times [1]. Here we consider perturbations of the wormhole which was constructed without thin-shells: the Bronnikov-Ellis wormhole supported by the phantom matter and electromagnetic field. This wormhole solution is known to be stable under specific equation of state of the phantom matter. We show that if one does not use the above thin-shell matching, the wormhole, depending on the values of its parameters, either rings as the black holemore » at all times or rings differently also at all times . The wormhole's spectrum, investigated here, posses a number of distinctive features. In the final part we have considered general properties of scattering around arbitrary rotating traversable wormholes. We have found that symmetric and non-symmetric (with respect to the throat) wormholes are qualitatively different in this respect: first, superradiance is allowed only if for those non-symmetric wormholes for which the asymptotic values of the rotation parameters are different on both sides from the throat. Second, the symmetric wormholes cannot mimic effectively the ringing of a black hole at a few various dominant multipoles at the same time, so that the future observations of various events should easily tell the symmetric wormhole from a black hole.« less

Oscillations of Static Discs around Schwarzschild Black Holes: Effect of Self-Gravitation

NASA Astrophysics Data System (ADS)

Semerák, Oldřich; Žáček, Miroslav

2000-12-01

The oscillations of accretion-disc matter about roughly circular motion may produce a quasi-periodic variation in the observed signal (Ipser 1996, AAA 65.067.047). They were studied theoretically on non-gravitating, test discs, in a pseudo-Newtonian manner as well as in general relativity, both in static and in stationary fields. The present paper shows how the radial profiles of oscillation frequencies can be modified by the self-gravity of the disc. Exact superpositions of a Schwarzschild black hole with the Lemos and Letelier (1994, AAA 61.067.077) annular discs (static thin discs obtained by inversion of the first Morgan-Morgan solution) are considered to be simple (static) models of an accretion system. Both the epicyclic and perpendicular frequencies are plotted against the Schwarzschild radius, the circumferential radius, and the proper distance from the horizon. The curves indicate that in the innermost parts more massive discs are more stable with respect to horizontal perturbations, whereas they are less stable with respect to vertical perturbations. In the case of a sequence of discs interpretable as counter-rotating particles on stable time-like circular geodesics and having their inner rims just on marginally stable circular orbits, oscillations of the inner parts get faster with increasing disc mass; the maximum of the epicyclic frequency, important for trapping of the low-frequency modes near the inner radius, moves to smaller radii and becomes somewhat higher.

Gravitational perturbations and metric reconstruction: Method of extended homogeneous solutions applied to eccentric orbits on a Schwarzschild black hole

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hopper, Seth; Evans, Charles R.

2010-10-15

We calculate the gravitational perturbations produced by a small mass in eccentric orbit about a much more massive Schwarzschild black hole and use the numerically computed perturbations to solve for the metric. The calculations are initially made in the frequency domain and provide Fourier-harmonic modes for the gauge-invariant master functions that satisfy inhomogeneous versions of the Regge-Wheeler and Zerilli equations. These gravitational master equations have specific singular sources containing both delta function and derivative-of-delta function terms. We demonstrate in this paper successful application of the method of extended homogeneous solutions, developed recently by Barack, Ori, and Sago, to handle sourcemore » terms of this type. The method allows transformation back to the time domain, with exponential convergence of the partial mode sums that represent the field. This rapid convergence holds even in the region of r traversed by the point mass and includes the time-dependent location of the point mass itself. We present numerical results of mode calculations for certain orbital parameters, including highly accurate energy and angular momentum fluxes at infinity and at the black hole event horizon. We then address the issue of reconstructing the metric perturbation amplitudes from the master functions, the latter being weak solutions of a particular form to the wave equations. The spherical harmonic amplitudes that represent the metric in Regge-Wheeler gauge can themselves be viewed as weak solutions. They are in general a combination of (1) two differentiable solutions that adjoin at the instantaneous location of the point mass (a result that has order of continuity C{sup -1} typically) and (2) (in some cases) a delta function distribution term with a computable time-dependent amplitude.« less

Static axisymmetric Einstein equations in vacuum: Symmetry, new solutions, and Ricci solitons

NASA Astrophysics Data System (ADS)

Akbar, M. M.; MacCallum, M. A. H.

2015-09-01

An explicit one-parameter Lie point symmetry of the four-dimensional vacuum Einstein equations with two commuting hypersurface-orthogonal Killing vector fields is presented. The parameter takes values over all of the real line and the action of the group can be effected algebraically on any solution of the system. This enables one to construct particular one-parameter extended families of axisymmetric static solutions and cylindrical gravitational wave solutions from old ones, in a simpler way than most solution-generation techniques, including the prescription given by Ernst for this system. As examples, we obtain the families that generalize the Schwarzschild solution and the C -metric. These in effect superpose a Levi-Civita cylindrical solution on the seeds. Exploiting a correspondence between static solutions of Einstein's equations and Ricci solitons (self-similar solutions of the Ricci flow), this also enables us to construct new steady Ricci solitons.

A complete solution for GP-B's gyroscopic precession by retarded gravitational theory

NASA Astrophysics Data System (ADS)

Tang, Keyun

Mainstream physicists generally believe that Mercury’s Perihelion precession and GP-B’ gyroscopic precession are two of the strongest evidences supporting Einstein’ curved spacetime and general relativity. However, most classical literatures and textbooks (e.g. Ohanain: Gravitation and Spacetime) paint an incorrect picture of Mercury’s orbit anomaly, namely Mercury’s perihelion precessed 43 arc-seconds per century; a correct picture should be that Mercury rotated 43 arc-seconds per century more than along Newtonian theoretical orbit. The essence of Le Verrier’s and Newcomb’s observation and analysis is that the angular speed of Mercury is slightly faster than the Newtonian theoretical value. The complete explanation to Mercury’s orbit anomaly should include two factors, perihelion precession is one of two factors, in addition, the change of orbital radius will also cause a change of angular speed, which is another component of Mercury's orbital anomaly. If Schwarzschild metric is correct, then the solution of the Schwarzschild orbit equation must contain three non-ignorable items. The first corresponds to Newtonian ellipse; the second is a nonlinear perturbation with increasing amplitude, which causes the precession of orbit perihelion; this is just one part of the angular speed anomaly of Mercury; the third part is a linear perturbation, corresponding to a similar figure of the Newton's ellipse, but with a minimal radius; this makes no contribution to the perihelion precession of the Schwarzschild orbit, but makes the Schwarzschild orbital radius slightly smaller, leading to a slight increase in Mercury’s angular speed. All classical literatures of general relativity ignored this last factor, which is a gross oversight. If you correctly take all three factors into consideration, the final result is that the difference between the angles rotated along Schwarzschild’s orbit and the angle rotated along Newton’s orbit for one hundred years should be more than 130.5 arc-seconds; this means that Le Verrier’s observation on Mercury’s orbital anomaly can not be explained correctly by the Schwarzschild metric. In contrast, Mercury’s angular speed anomaly can be explained satisfactorily by the radial induction component and angular component of retarded gravitation. From the perspective of energy, the additional radial component of retarded gravitation makes the radius of Mercury’s orbit slightly smaller, i.e. some potential energy is lost. And the angular component of retarded gravitation changes the Mercury's angular momentum; this proves that the changes of Mercury’s orbit and angular speed are the results of gravitational radiation. I have found that there are similar errors in the explanation on the gyroscopic precession of GP-B, i.e. physicists only consider the contribution of the nonlinear perturbation terms and never consider the contribution of linear perturbation terms. For the precession of GP-B, the complete Schwarzschild’s solution should be about 19.8 arc-seconds per year; it is far more than the experimental results of 6.602 arc-seconds per year. I have calculated the gyroscopic precession of GP-B due to retarded gravitation, the result is 6.607 arc-seconds per year; this matches well with the experimental results. These successful explanations for both anomalies of Mercury’s orbit and the gyroscopic precession of GP -B shows that Retarded Gravitation is indeed a sound gravitational theory, and that spacetime is in fact flat, and gravity travels at the speed of light. Both Mercury’s angular speed anomaly and GP - B gyro precession were the result of the gravitational radiation!

Schwarzschild, Martin (1912-97)

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

Astrophysicist, born in Potsdam, Germany, the son of KARL SCHWARZSCHILD, left Germany, became professor at Princeton University. Working with John von Neumann, Schwarzschild used the powers of the newly developed electronic digital computers to work on the theory of stellar structure and evolution. He uncovered phenomena in red giant stars, including how they evolve off the main sequence in the H...

Spherically symmetric solutions and gravitational collapse in brane-worlds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heydari-Fard, Malihe; Sepangi, Hamid R., E-mail: heydarifard@qom.ac.ir, E-mail: hr-sepangi@sbu.ac.ir

2009-02-15

We consider spherically symmetric solutions within the context of brane-world theory without mirror symmetry or any form of junction conditions. For a constant curvature bulk, we obtain the modified Tolman-Oppenheimer-Volkoff (TOV) interior solutions in two cases where one is matched to a schwarzschild-de Sitter exterior while the other is consistent with an exterior solution whose structure can be used to explain the galaxy rotation curves without postulating dark matter. We also find the upper bound to the mass of a static brane-world star and show that the influence of the bulk effects on the interior solutions is small. Finally, wemore » investigate the gravitational collapse on the brane and show that the exterior of a collapsing star can be static in this scenario.« less

Exact Relativistic `Antigravity' Propulsion

NASA Astrophysics Data System (ADS)

Felber, Franklin S.

2006-01-01

The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.

Dirac Quasinormal Modes of Static f(R) de Sitter Black Holes

NASA Astrophysics Data System (ADS)

Ma, Hong

2018-02-01

Quasinormal modes (QNMs) for Dirac perturbations of f(R) black holes (BHs) are described in this paper, involving two types of f(R) solution: f(R) (Schwarzschild) BHs and f(R) (Maxwell) BHs. With the finite difference method, the stability of the f(R) black holes (BHs) is analysed and the threshold range of f(R) (Schwarzschild) BHs and f(R) (Maxwell) BHs is defined respectively. The results show that due to the presence of the correction factor R0, the damping rate of Dirac field decreases. Meanwhile, the influence of angular quantum number values |k| on the f(R) BHs is investigated. The results indicate that the QNMs oscillation becomes tenser and damping speed slowly decreases with |k| increasing. Furthermore, under the Dirac perturbation, the stability of f(R) solutions can be reflected in the manner of Dirac QNMs. The relationships between the QNMs and the parameters (|k|, charge Q and mass m) are discussed in massless, and massive cases, by contrast to the classical BHs. Supported by FAPESP No. 2012/08934-0, National Natural Science Foundation of China under Grant Nos. 11205254, 11178018, 11375279, 11605015, and the Natural Science Foundation Project of CQ CSTC 2011BB0052, and the Fundamental Research Funds for the Central Universities 106112016CDJXY300002 and CDJRC10300003

Bose–Einstein graviton condensate in a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Alfaro, Jorge; Espriu, Domènec; Gabbanelli, Luciano

2018-01-01

We analyze in detail a previous proposal by Dvali and Gómez that black holes could be treated as consisting of a Bose–Einstein condensate of gravitons. In order to do so we extend the Einstein–Hilbert action with a chemical potential-like term, thus placing ourselves in a grand-canonical ensemble. The form and characteristics of this chemical potential-like piece are discussed in some detail. We argue that the resulting equations of motion derived from the action could be interpreted as the Gross–Pitaevskii equation describing a graviton Bose–Einstein condensate trapped by the black hole gravitational field. After this, we proceed to expand the ensuring equations of motion up to second order around the classical Schwarzschild metric so that some non-linear terms in the metric fluctuation are kept. Next we search for solutions and, modulo some very plausible assumptions, we find out that the condensate vanishes outside the horizon but is non-zero in its interior. Inspired by a linearized approximation around the horizon we are able to find an exact solution for the mean-field wave function describing the graviton Bose–Einstein condensate in the black hole interior. After this, we can rederive some of the relations involving the number of gravitons N and the black hole characteristics along the lines suggested by Dvali and Gómez.

General Relativity During the Great War

NASA Astrophysics Data System (ADS)

Trimble, Virginia L.

2016-01-01

Einstein's (and Hilbert's) equations saw light of day in the darkness of Berlin 1915, as is well known. Moving from this highlight to less conspicuous topics, we find Karl Schwarzschild's solution of those equations (1916) followed shortly by his death. On the observational and American front, Slipher's assemblage of galaxy radial velocities, begun in 1912 with M31, continued apace. Shapley was busily moving us out of the galactic center. Also at Mt. Wilson, Charles St. John looked for gravitational redshift in the solar spectrum in 1917 without firmly detecting it. Adams demonstrated the very low luminosities of Sirius B and 40 Eri B in 1914 (but his attempt at a redshift for the former came only in 1923). Perhaps least well known is that a handful of additional critical theoretical papers date from the war years and describe the Lense-Thirring effect, the Reissner-Nordstrom solution, and a charged solution with a cosmological constant (due to the even more obscure Friedrich Kottler). Some of these came out of neutral Holland, but Kottler served both at Ypres and on the Galician front. Interesting mixes of military service and relativistic contributions are also associated with the names of Friedmann, Le Lemaître, Weyl (of the tensor), Minkowski, Hubble, Flamm, Droste, and Kretschmann. Astronomers in neutral Denmark, Holland and (until 1917) the USA facilitated transmittal of astronomical observations and other news across the battle lines so that Schwarzschild received an obituary in Nature and Moseley one in Naturwissenschaften.

The 3 + 1 decomposition of conformal Yano-Killing tensors and ‘momentary’ charges for the spin-2 field

NASA Astrophysics Data System (ADS)

Jezierski, Jacek; Migacz, Szymon

2015-02-01

The ‘fully charged’ spin-2 field solution is presented. This is an analog of the Coulomb solution in electrodynamics and represents the ‘non-waving’ part of the spin-2 field theory. Basic facts and definitions of the spin-2 field and conformal Yano-Killing tensors are introduced. Application of those two objects provides a precise definition of quasi-local gravitational charge. Next, the 3 + 1 decomposition leads to the construction of the momentary gravitational charges on the initial surface, which is applicable for Schwarzschild-like spacetimes.

Black hole solutions in mimetic Born-Infeld gravity

NASA Astrophysics Data System (ADS)

Chen, Che-Yu; Bouhmadi-López, Mariam; Chen, Pisin

2018-01-01

The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. We find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in this case, the maximal proper time for a timelike radially-infalling observer to reach the singularity is found to be infinite.

Black hole solutions in mimetic Born-Infeld gravity.

PubMed

Chen, Che-Yu; Bouhmadi-López, Mariam; Chen, Pisin

2018-01-01

The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. We find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in this case, the maximal proper time for a timelike radially-infalling observer to reach the singularity is found to be infinite.

Black hole solutions in mimetic Born-Infeld gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Che-Yu; Bouhmadi-López, Mariam; Chen, Pisin

The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. Here, we find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in this case, the maximal proper time for a timelike radially-infalling observer to reach the singularitymore » is found to be infinite.« less

Black hole solutions in mimetic Born-Infeld gravity

DOE PAGES

Chen, Che-Yu; Bouhmadi-López, Mariam; Chen, Pisin

2018-01-23

The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. Here, we find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in this case, the maximal proper time for a timelike radially-infalling observer to reach the singularitymore » is found to be infinite.« less

Asymptotically flat black holes in Horndeski theory and beyond

DOE Office of Scientific and Technical Information (OSTI.GOV)

Babichev, E.; Charmousis, C.; Lehébel, A., E-mail: eugeny.babichev@th.u-psud.fr, E-mail: christos.charmousis@th.u-psud.fr, E-mail: antoine.lehebel@th.u-psud.fr

We find spherically symmetric and static black holes in shift-symmetric Horndeski and beyond Horndeski theories. They are asymptotically flat and sourced by a non trivial static scalar field. The first class of solutions is constructed in such a way that the Noether current associated with shift symmetry vanishes, while the scalar field cannot be trivial. This in certain cases leads to hairy black hole solutions (for the quartic Horndeski Lagrangian), and in others to singular solutions (for a Gauss-Bonnet term). Additionally, we find the general spherically symmetric and static solutions for a pure quartic Lagrangian, the metric of which ismore » Schwarzschild. We show that under two requirements on the theory in question, any vacuum GR solution is also solution to the quartic theory. As an example, we show that a Kerr black hole with a non-trivial scalar field is an exact solution to these theories.« less

Quantum corrected Schwarzschild thin-shell wormhole

NASA Astrophysics Data System (ADS)

Jusufi, Kimet

2016-11-01

Recently, Ali and Khalil (Nucl Phys B, 909, 173-185, 2016), based on Bohmian quantum mechanics, derived a quantum corrected version of the Schwarzschild metric. In this paper, we construct a quantum corrected Schwarzschild thin-shell wormhole (QSTSW) and investigate the stability of this wormhole. First we compute the surface stress at the wormhole throat by applying the Darmois-Israel formalism to the modified Schwarzschild metric and show that exotic matter is required at the throat to keep the wormhole stable. We then study the stability analysis of the wormhole by considering phantom-energy for the exotic matter, generalized Chaplygin gas (GCG), and the linearized stability analysis. It is argued that quantum corrections can affect the stability domain of the wormhole.

Primordial SdS universe from a 5D vacuum: scalar field fluctuations on Schwarzschild and Hubble horizons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aguilar, José Edgar Madriz; Bellini, Mauricio, E-mail: jemadriz@fisica.ugto.mx, E-mail: mbellini@mdp.edu.ar

2010-11-01

We study scalar field fluctuations of the inflaton field in an early inflationary universe on an effective 4D Schwarzschild-de Sitter (SdS) metric, which is obtained after make a planar coordinate transformation on a 5D Ricci-flat Schwarzschild-de Sitter (SdS) static metric. We obtain the important result that the spectrum of fluctuations at zeroth order is independent of the scalar field mass M on Schwarzschild scales, while on cosmological scales it exhibits a mass dependence. However, in the first-order expansion, the spectrum depends of the inflaton mass and the amplitude is linear with the Black-Hole (BH) mass m.

Linearized Israel matching conditions for cosmological perturbations in a moving brane background

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bucher, Martin; DAMTP, University of Cambridge, Cambridge CB3 0WA; Carvalho, Carla

2005-04-15

In the Randall-Sundrum cosmological models, a (3+1)-dimensional brane subject to a Z{sub 2} orbifold symmetry is embedded in a (4+1)-dimensional bulk spacetime empty except for a negative cosmological constant. The unperturbed braneworld cosmological solutions, subject to homogeneity and isotropy in the three transverse spatial dimensions, are most simply presented by means of a moving brane description. Owing to a generalization of Birkhoff's theorem, as long as there are no perturbations violating the three-dimensional spatial homogeneity and isotropy, the bulk spacetime remains stationary and trivial. For the spatially flat case, the bulk spacetime is described by one of three bulk solutions:more » a pure AdS{sup 5} solution, an AdS{sup 5}-Schwarzschild black hole solution, or an AdS{sup 5}-Schwarzschild naked singularity solution. The brane moves on the boundary of one of these simple bulk spacetimes, its trajectory determined by the evolution of the stress-energy localized on the brane. We derive here the form of the Israel matching conditions for the linearized cosmological perturbations in this moving brane picture. These Israel matching conditions must be satisfied in any gauge. However, they are not sufficient to determine how to describe in a specific gauge the reflection of the bulk gravitational waves off the brane boundary. In this paper we adopt a fully covariant Lorentz gauge condition in the bulk and find the supplementary gauge conditions that must be imposed on the boundary to ensure that the reflected waves do not violate the Lorentz gauge condition. Compared to the form obtained from Gaussian normal coordinates, the form of the Israel matching conditions obtained here is more complex. However, the propagation of the bulk gravitons is simpler because the coordinates used for the background exploit fully the symmetry of the bulk background solution.« less

Initial data sets for the Schwarzschild spacetime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gomez-Lobo, Alfonso Garcia-Parrado; Kroon, Juan A. Valiente; School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS

2007-01-15

A characterization of initial data sets for the Schwarzschild spacetime is provided. This characterization is obtained by performing a 3+1 decomposition of a certain invariant characterization of the Schwarzschild spacetime given in terms of concomitants of the Weyl tensor. This procedure renders a set of necessary conditions--which can be written in terms of the electric and magnetic parts of the Weyl tensor and their concomitants--for an initial data set to be a Schwarzschild initial data set. Our approach also provides a formula for a static Killing initial data set candidate--a KID candidate. Sufficient conditions for an initial data set tomore » be a Schwarzschild initial data set are obtained by supplementing the necessary conditions with the requirement that the initial data set possesses a stationary Killing initial data set of the form given by our KID candidate. Thus, we obtain an algorithmic procedure of checking whether a given initial data set is Schwarzschildean or not.« less

On Light-Like Extremal Surfaces in Curved Spacetimes

NASA Astrophysics Data System (ADS)

Huang, Shou-Jun; He, Chun-Lei

2014-01-01

In this paper, we are concerned with light-like extremal surfaces in curved spacetimes. It is interesting to find that under a diffeomorphic transformation of variables, the light-like extremal surfaces can be described by a system of nonlinear geodesic equations. Particularly, we investigate the light-like extremal surfaces in Schwarzschild spacetime in detail and some new special solutions are derived systematically with aim to compare with the known results and to illustrate the method.

Three Göttingen lectures by Karl Schwarzschild, 1904-1905. (German Title: Drei Göttinger Vorlesungen Karl Schwarzschilds 1904-1905)

NASA Astrophysics Data System (ADS)

Schmidt-Kaler, Theodor

Karl Schwarzschild (1873-1916), perhaps the most eminent astronomer of his time, was professor at Göttingen University from 1901 to 1909. Three of his lectures from the years 1904 to 1906 are available in the form of copy-books written by his students Arnold Kohlschütter (1883-1969) and Max Born (1882-1970). Here, an overview of these lectures is given.

Karl Schwarzschild's investigations of `out-of-focus photometry' between 1897 and 1899 at Kuffner Observatory in Vienna

NASA Astrophysics Data System (ADS)

Habison, Peter

From 1897 to 1899 Karl Schwarzschild worked at the Kuffner Observatory in Vienna. During these years he developed new measuring techniques in the field of photographic photometry, where he studied particularly the quantitative determination of the departure from the reciprocity law during photographic exposure. This paper concentrates on Schwarzschild's early work in this field and gives an overview of his important Viennese years.

Black String and Velocity Frame Dragging

NASA Astrophysics Data System (ADS)

Lee, Jungjai; Kim, Hyeong-Chan

We investigate velocity frame dragging with the boosted Schwarzschild black string solution and the boosted Kaluza-Klein bubble solution, in which a translational symmetry along the boosted z-coordinate is implemented. The velocity frame dragging effect can be nullified by the motion of an observer using the boost symmetry along the z-coordinate if it is not compact. However, in spacetime with the compact z-coordinate, we show that the effect cannot be removed since the compactification breaks the global Lorentz boost symmetry. As a result, the comoving velocity depends on r and the momentum parameter along the z-coordinate becomes an observer independent characteristic quantity of the black string and bubble solutions. The dragging induces a spherical ergo-region around the black string.

Light deflection and Gauss-Bonnet theorem: definition of total deflection angle and its applications

NASA Astrophysics Data System (ADS)

Arakida, Hideyoshi

2018-05-01

In this paper, we re-examine the light deflection in the Schwarzschild and the Schwarzschild-de Sitter spacetime. First, supposing a static and spherically symmetric spacetime, we propose the definition of the total deflection angle α of the light ray by constructing a quadrilateral Σ^4 on the optical reference geometry M^opt determined by the optical metric \\bar{g}_{ij}. On the basis of the definition of the total deflection angle α and the Gauss-Bonnet theorem, we derive two formulas to calculate the total deflection angle α ; (1) the angular formula that uses four angles determined on the optical reference geometry M^opt or the curved (r, φ ) subspace M^sub being a slice of constant time t and (2) the integral formula on the optical reference geometry M^opt which is the areal integral of the Gaussian curvature K in the area of a quadrilateral Σ ^4 and the line integral of the geodesic curvature κ _g along the curve C_{Γ}. As the curve C_{Γ}, we introduce the unperturbed reference line that is the null geodesic Γ on the background spacetime such as the Minkowski or the de Sitter spacetime, and is obtained by projecting Γ vertically onto the curved (r, φ ) subspace M^sub. We demonstrate that the two formulas give the same total deflection angle α for the Schwarzschild and the Schwarzschild-de Sitter spacetime. In particular, in the Schwarzschild case, the result coincides with Epstein-Shapiro's formula when the source S and the receiver R of the light ray are located at infinity. In addition, in the Schwarzschild-de Sitter case, there appear order O(Lambda;m) terms in addition to the Schwarzschild-like part, while order O(Λ) terms disappear.

Opening Switch Research on a Plasma Focus VI.

DTIC Science & Technology

1988-02-26

Sausage Instability in the Plasma Focus In this section the classical Kruskal- Schwarzschild 3 theory for the sausage mode is applied to the pinch phase...on 1) the shape of the pinch, 2) axial flow of plasma, and 3) self-generated magnetic fields are also presented. The Kruskal- Schwarzschild Theory The...classical mhd theory for the m=O mode in a plasma supported by a magnetic field against gravity; this is the well-known Kruskal- Schwarzschild

Null geodesics and red-blue shifts of photons emitted from geodesic particles around a noncommutative black hole space-time

NASA Astrophysics Data System (ADS)

Kuniyal, Ravi Shankar; Uniyal, Rashmi; Biswas, Anindya; Nandan, Hemwati; Purohit, K. D.

2018-06-01

We investigate the geodesic motion of massless test particles in the background of a noncommutative geometry-inspired Schwarzschild black hole. The behavior of effective potential is analyzed in the equatorial plane and the possible motions of massless particles (i.e. photons) for different values of impact parameter are discussed accordingly. We have also calculated the frequency shift of photons in this space-time. Further, the mass parameter of a noncommutative inspired Schwarzschild black hole is computed in terms of the measurable redshift of photons emitted by massive particles moving along circular geodesics in equatorial plane. The strength of gravitational fields of noncommutative geometry-inspired Schwarzschild black hole and usual Schwarzschild black hole in General Relativity is also compared.

Spacetime completeness of non-singular black holes in conformal gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bambi, Cosimo; Rachwał, Lesław; Modesto, Leonardo, E-mail: bambi@fudan.edu.cn, E-mail: lmodesto@sustc.edu.cn, E-mail: grzerach@gmail.com

We explicitly prove that the Weyl conformal symmetry solves the black hole singularity problem, otherwise unavoidable in a generally covariant local or non-local gravitational theory. Moreover, we yield explicit examples of local and non-local theories enjoying Weyl and diffeomorphism symmetry (in short co-covariant theories). Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free spherically symmetric and axi-symmetric exact solutions for black hole spacetimes conformally equivalent to the Schwarzschild or the Kerr spacetime. We first check the absence of divergences in the Kretschmann invariant for the rescaled metrics. Afterwords, we show that the new typesmore » of black holes are geodesically complete and linked by a Newman-Janis transformation just as in standard general relativity (based on Einstein-Hilbert action). Furthermore, we argue that no massive or massless particles can reach the former Schwarzschild singularity or touch the former Kerr ring singularity in a finite amount of their proper time or of their affine parameter. Finally, we discuss the Raychaudhuri equation in a co-covariant theory and we show that the expansion parameter for congruences of both types of geodesics (for massless and massive particles) never reaches minus infinity. Actually, the null geodesics become parallel at the r =0 point in the Schwarzschild spacetime (the origin) and the focusing of geodesics is avoided. The arguments of regularity of curvature invariants, geodesic completeness, and finiteness of geodesics' expansion parameter ensure us that we are dealing with singularity-free and geodesically-complete black hole spacetimes.« less

Black holes in multi-fractional and Lorentz-violating models

NASA Astrophysics Data System (ADS)

Calcagni, Gianluca; Rodríguez Fernández, David; Ronco, Michele

2017-05-01

We study static and radially symmetric black holes in the multi-fractional theories of gravity with q-derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length ℓ _*. In the q-derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to ℓ _*. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q-derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models.

Gravity and large black holes in Randall-Sundrum II braneworlds.

PubMed

Figueras, Pau; Wiseman, Toby

2011-08-19

We show how to construct low energy solutions to the Randall-Sundrum II (RSII) model by using an associated five-dimensional anti-de Sitter space (AdS(5)) and/or four-dimensional conformal field theory (CFT(4)) problem. The RSII solution is given as a perturbation of the AdS(5)-CFT(4) solution, with the perturbation parameter being the radius of curvature of the brane metric compared to the AdS length ℓ. The brane metric is then a specific perturbation of the AdS(5)-CFT(4) boundary metric. For low curvatures the RSII solution reproduces 4D general relativity on the brane. Recently, AdS(5)-CFT(4) solutions with a 4D Schwarzschild boundary metric were numerically constructed. We modify the boundary conditions to numerically construct large RSII static black holes with radius up to ~20ℓ. For a large radius, the RSII solutions are indeed close to the associated AdS(5)-CFT(4) solution. © 2011 American Physical Society

Doppler frequency in interplanetary radar and general relativity

NASA Technical Reports Server (NTRS)

Mcvittie, G. C.

1972-01-01

The change of frequency of an interplanetary radar signal sent from the earth to another planet or to a space probe is worked out according to general relativity. The Schwarzschild spacetime is employed and its null geodesics control the motion of the signals. Exact Doppler frequency formulas are derived for one-way and two-way radar in terms of an arbitrary Schwarzschild radial coordinate. A reduction to the special relativity case is used to interpret the formulas in terms of the relative radial velocity of emitter and target. The general relativity corrections are worked out approximately for each of three possible Schwarzschild radial coordinates, and a numerical example is given. The amount of the correction is different according as one or the other of the Schwarzschild coordinates is identified with the radius vector deduced from classical celestial mechanics. The identification problem is discussed.

Black hole shadow in an expanding universe with a cosmological constant

NASA Astrophysics Data System (ADS)

Perlick, Volker; Tsupko, Oleg Yu.; Bisnovatyi-Kogan, Gennady S.

2018-05-01

We analytically investigate the influence of a cosmic expansion on the shadow of the Schwarzschild black hole. We suppose that the expansion is driven by a cosmological constant only and use the Kottler (or Schwarzschild-de Sitter) spacetime as a model for a Schwarzschild black hole embedded in a de Sitter universe. We calculate the angular radius of the shadow for an observer who is comoving with the cosmic expansion. It is found that the angular radius of the shadow shrinks to a nonzero finite value if the comoving observer approaches infinity.

Exact optics - III. Schwarzschild's spectrograph camera revised

NASA Astrophysics Data System (ADS)

Willstrop, R. V.

2004-03-01

Karl Schwarzschild identified a system of two mirrors, each defined by conic sections, free of third-order spherical aberration, coma and astigmatism, and with a flat focal surface. He considered it impractical, because the field was too restricted. This system was rediscovered as a quadratic approximation to one of Lynden-Bell's `exact optics' designs which have wider fields. Thus the `exact optics' version has a moderate but useful field, with excellent definition, suitable for a spectrograph camera. The mirrors are strongly aspheric in both the Schwarzschild design and the exact optics version.

Karl Schwarzschild and the professionalization of astrophysics. (German Title: Karl Schwarzschild und die Professionalisierung der Astrophysik)

NASA Astrophysics Data System (ADS)

Schmidt-Kaler, Theodor

Professionalization is characteristic for physics and astronomy since 1830, and forms the basis for their rapid evolution in the 20th century. Karl Schwarzschild's contributions to professionalization of astronomy are presented: the introduction of course lectures in a repeating cycle, a permanent astrophysical laboratory, a tight connection between teaching and research, simulations and suggestions for astronomy at high schools and for the training of high school teachers, an interest in international organisation, and the initiative and planning of a southern observatory.

Time-Resolved, High-Resolution, X-Ray Microscopy of In-Vitro Biological and Life Science Specimens with the Aid of Laser Plasmas

DTIC Science & Technology

1994-06-30

transmissive Fresnel lens. We have made considerable effort in the last few years to explore the potential of x-ray multilayer-coated Schwarzschild x-ray...ray mirror fabrication and efficient x-ray mirror design. A 120mm diameter, NA = 0.35, 15X Schwarzschild microscope coated with Ni/C multilayer mios for...et al 2 developed a smaller, 33mm diameter, NA - 0.28, 15X Schwarzschild microscope coated with a W/C multilayer mirror for 4.4nm, in the socalled

Hypergeometric Equation in Modeling Relativistic Isotropic Sphere

NASA Astrophysics Data System (ADS)

Thirukkanesh, S.; Ragel, F. C.

2014-04-01

We study the Einstein system of equations in static spherically symmetric spacetimes. We obtained classes of exact solutions to the Einstein system by transforming the condition for pressure isotropy to a hypergeometric equation choosing a rational form for one of the gravitational potentials. The solutions are given in simple form that is a desirable requisite to study the behavior of relativistic compact objects in detail. A physical analysis indicate that our models satisfy all the fundamental requirements of realistic star and match smoothly with the exterior Schwarzschild metric. The derived masses and densities are consistent with the previously reported experimental and theoretical studies describing strange stars. The models satisfy the standard energy conditions required by normal matter.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Afonso, V.I.; Olmo, Gonzalo J.; Rubiera-Garcia, D., E-mail: viafonso@df.ufcg.edu.br, E-mail: gonzalo.olmo@uv.es, E-mail: drgarcia@fc.ul.pt

The existence of static, spherically symmetric, self-gravitating scalar field solutions in the context of Born-Infeld gravity is explored. Upon a combination of analytical approximations and numerical methods, the equations for a free scalar field (without a potential term) are solved, verifying that the solutions recover the predictions of General Relativity far from the center but finding important new effects in the central regions. We find two classes of objects depending on the ratio between the Schwarzschild radius and a length scale associated to the Born-Infeld theory: massive solutions have a wormhole structure, with their throat at r ≈ 2 Mmore » , while for the lighter configurations the topology is Euclidean. The total energy density of these solutions exhibits a solitonic profile with a maximum peaked away from the center, and located at the throat whenever a wormhole exists. The geodesic structure and curvature invariants are analyzed for the various configurations considered.« less

A two-mass expanding exact space-time solution

NASA Astrophysics Data System (ADS)

Uzan, Jean-Philippe; Ellis, George F. R.; Larena, Julien

2011-01-01

In order to understand how locally static configurations around gravitationally bound bodies can be embedded in an expanding universe, we investigate the solutions of general relativity describing a space-time whose spatial sections have the topology of a 3-sphere with two identical masses at the poles. We show that Israel junction conditions imply that two spherically symmetric static regions around the masses cannot be glued together. If one is interested in an exterior solution, this prevents the geometry around the masses to be of the Schwarzschild type and leads to the introduction of a cosmological constant. The study of the extension of the Kottler space-time shows that there exists a non-static solution consisting of two static regions surrounding the masses that match a Kantowski-Sachs expanding region on the cosmological horizon. The comparison with a Swiss-Cheese construction is also discussed.

Schwarzschild camera

NASA Technical Reports Server (NTRS)

1980-01-01

The fabrication procedures for the primary and secondary mirrors for a Schwarzschild camera are summarized. The achieved wave front for the telescope was 1/2 wave at .63 microns. Interferograms of the two mirrors as a system are given and the mounting procedures are outlined.

Self-gravitating black hole scalar wigs

NASA Astrophysics Data System (ADS)

Barranco, Juan; Bernal, Argelia; Degollado, Juan Carlos; Diez-Tejedor, Alberto; Megevand, Miguel; Núñez, Darío; Sarbach, Olivier

2017-07-01

It has long been known that no static, spherically symmetric, asymptotically flat Klein-Gordon scalar field configuration surrounding a nonrotating black hole can exist in general relativity. In a series of previous papers, we proved that, at the effective level, this no-hair theorem can be circumvented by relaxing the staticity assumption: for appropriate model parameters, there are quasibound scalar field configurations living on a fixed Schwarzschild background which, although not being strictly static, have a larger lifetime than the age of the universe. This situation arises when the mass of the scalar field distribution is much smaller than the black hole mass, and following the analogies with the hair in the literature we dubbed these long-lived field configurations wigs. Here we extend our previous work to include the gravitational backreaction produced by the scalar wigs. We derive new approximate solutions of the spherically symmetric Einstein-Klein-Gordon system which represent self-gravitating scalar wigs surrounding black holes. These configurations interpolate between boson star configurations and Schwarzschild black holes dressed with the long-lived scalar test field distributions discussed in previous papers. Nonlinear numerical evolutions of initial data sets extracted from our approximate solutions support the validity of our approach. Arbitrarily large lifetimes are still possible, although for the parameter space that we analyze in this paper they seem to decay faster than the quasibound states. Finally, we speculate about the possibility that these configurations could describe the innermost regions of dark matter halos.

Accretion of a relativistic, collisionless kinetic gas into a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Rioseco, Paola; Sarbach, Olivier

2017-05-01

We provide a systematic study for the accretion of a collisionless, relativistic kinetic gas into a nonrotating black hole. To this end, we first solve the relativistic Liouville equation on a Schwarzschild background spacetime. The most general solution for the distribution function is given in terms of appropriate symplectic coordinates on the cotangent bundle, and the associated observables, including the particle current density and stress energy-momentum tensor, are determined. Next, we explore the case where the flow is steady-state and spherically symmetric. Assuming that in the asymptotic region the gas is described by an equilibrium distribution function, we determine the relevant parameters of the accretion flow as a function of the particle density and the temperature of the gas at infinity. In particular, we find that in the low temperature limit the tangential pressure at the horizon is about an order of magnitude larger than the radial one, showing explicitly that a collisionless gas, despite exerting kinetic pressure, behaves very differently than an isotropic perfect fluid, and providing a partial explanation for the known fact that the accretion rate is much lower than in the hydrodynamic case of Bondi-Michel accretion. Finally, we establish the asymptotic stability of the steady-state spherical flows by proving pointwise convergence results which show that a large class of (possibly nonstationary and nonspherical) initial conditions for the distribution function lead to solutions of the Liouville equation which relax in time to a steady-state, spherically symmetric configuration.

New wrinkles on black hole perturbations: Numerical treatment of acoustic and gravitational waves

NASA Astrophysics Data System (ADS)

Tenyotkin, Valery

2009-06-01

This thesis develops two main topics. A full relativistic calculation of quasinormal modes of an acoustic black hole is carried out. The acoustic black hole is formed by a perfect, inviscid, relativistic, ideal gas that is spherically accreting onto a Schwarzschild black hole. The second major part is the calculation of sourceless vector (electromagnetic) and tensor (gravitational) covariant field evolution equations for perturbations on a Schwarzschild background using the relatively recent [Special characters omitted.] decomposition method. Scattering calculations are carried out in Schwarzschild coordinates for electromagnetic and gravitational cases as validation of the method and the derived equations.

Exact Harmonic Metric for a Uniformly Moving Schwarzschild Black Hole

NASA Astrophysics Data System (ADS)

He, Guan-Sheng; Lin, Wen-Bin

2014-02-01

The harmonic metric for Schwarzschild black hole with a uniform velocity is presented. In the limit of weak field and low velocity, this metric reduces to the post-Newtonian approximation for one moving point mass. As an application, we derive the dynamics of particle and photon in the weak-field limit for the moving Schwarzschild black hole with an arbitrary velocity. It is found that the relativistic motion of gravitational source can induce an additional centripetal force on the test particle, which may be comparable to or even larger than the conventional Newtonian gravitational force.

Black holes thermodynamics in a new kind of noncommutative geometry

NASA Astrophysics Data System (ADS)

Faizal, Mir; Amorim, R. G. G.; Ulhoa, S. C.

Motivated by the energy-dependent metric in gravity’s rainbow, we will propose a new kind of energy-dependent noncommutative geometry. It will be demonstrated that like gravity’s rainbow, this new noncommutative geometry is described by an energy-dependent metric. We will analyze the effect of this noncommutative deformation on the Schwarzschild black holes and Kerr black holes. We will perform our analysis by relating the commutative and this new energy-dependent noncommutative metrics using an energy-dependent Moyal star product. We will also analyze the thermodynamics of these new noncommutative black hole solutions. We will explicitly derive expression for the corrected entropy and temperature for these black hole solutions. It will be demonstrated that, for these deformed solutions, black remnants cannot form. This is because these corrections increase rather than reduce the temperature of the black holes.

Nonlinear Thermal Instability in Compressible Viscous Flows Without Heat Conductivity

NASA Astrophysics Data System (ADS)

Jiang, Fei

2018-04-01

We investigate the thermal instability of a smooth equilibrium state, in which the density function satisfies Schwarzschild's (instability) condition, to a compressible heat-conducting viscous flow without heat conductivity in the presence of a uniform gravitational field in a three-dimensional bounded domain. We show that the equilibrium state is linearly unstable by a modified variational method. Then, based on the constructed linearly unstable solutions and a local well-posedness result of classical solutions to the original nonlinear problem, we further construct the initial data of linearly unstable solutions to be the one of the original nonlinear problem, and establish an appropriate energy estimate of Gronwall-type. With the help of the established energy estimate, we finally show that the equilibrium state is nonlinearly unstable in the sense of Hadamard by a careful bootstrap instability argument.

A qualitative study of the complete set of solutions of the differential equation of motion of a test particle in the equatorial plane of the Kerr gravitational field

NASA Technical Reports Server (NTRS)

Montgomery, H. E.; Chan, F. K.

1973-01-01

A study is made of the mathematical solution of the differential equation of motion of a test particle in the equatorial plane of the Kerr gravitational field, using S (Schwarzschild-like) coordinates. A qualitative solution of this equation leads to the conclusion that there can only be 25 different types of orbits. For each value of a, the results are presented in a master diagram for which h and e are the parameters. A master diagram divides the h, e parameter space into regions such that at each point within one of these regions the types of admissible orbits are qualitatively the same. A pictorial representation of the physical orbits in the r, phi plane is also given.

Solitons and black holes in non-Abelian Einstein-Born-Infeld theory

NASA Astrophysics Data System (ADS)

Dyadichev, V. V.; Gal'tsov, D. V.

2000-08-01

Recently it was shown that the Born-Infeld modification of the quadratic Yang-Mills action gives rise to classical particle-like solutions in the flat space which have a striking similarity with the Bartnik-McKinnon solutions obtained within the gravity coupled Yang-Mills theory. We show that both families of solutions are continuously related within the framework of the Einstein-Born-Infeld theory via interpolating sequences of parameters. We also investigate an internal structure of the associated black holes and find that the Born-Infeld non-linearity changes drastically the black hole interior typical for the usual quadratic Yang-Mills theory. In the latter case a generic solution exhibits violent metric oscillations near the singularity. In the Born-Infeld case the generic interior solution is smooth, the metric tends to the standard Schwarzschild type singularity, and we did not observe internal horizons. Smoothing of the `violent' EYM singularity may be interpreted as a result of non-gravitational quantum effects.

The enhancement of quantum entanglement under an open Dirac system with the Hawking effect in Schwarzschild space-time

NASA Astrophysics Data System (ADS)

Sun, Wen-Yang; Wang, Dong; Fang, Bao-Long; Shi, Jia-Dong; Ye, Liu

2018-06-01

In this letter, we mainly investigate how to enhance the damaged quantum entanglement under an open Dirac system with the Hawking effect within Schwarzschild space-time. We consider that particle A held by Alice undergoes generalized amplitude damping noise in a flat space-time, and that another particle B by Bob entangled with A is under a Schwarzschild space-time. Subsequently, we put forward a physical scheme to recover the damaged quantum entanglement by prior weak measurement on subsystem A before the interaction with the decoherence noise followed by post-measurement filtering operation. The results indicate that our scheme can effectively recover the damaged quantum entanglement affected by the Hawking effect and the noisy channel. Thus, our work might be beneficial to understand the dynamic behavior of the quantum state and recover the damaged quantum entanglement with open Dirac systems under the Hawking effect in the background of a Schwarzschild black hole.

Hyperboloidal evolution of test fields in three spatial dimensions

NASA Astrophysics Data System (ADS)

Zenginoǧlu, Anıl; Kidder, Lawrence E.

2010-06-01

We present the numerical implementation of a clean solution to the outer boundary and radiation extraction problems within the 3+1 formalism for hyperbolic partial differential equations on a given background. Our approach is based on compactification at null infinity in hyperboloidal scri fixing coordinates. We report numerical tests for the particular example of a scalar wave equation on Minkowski and Schwarzschild backgrounds. We address issues related to the implementation of the hyperboloidal approach for the Einstein equations, such as nonlinear source functions, matching, and evaluation of formally singular terms at null infinity.

Black holes in multi-fractional and Lorentz-violating models.

PubMed

Calcagni, Gianluca; Rodríguez Fernández, David; Ronco, Michele

2017-01-01

We study static and radially symmetric black holes in the multi-fractional theories of gravity with q -derivatives and with weighted derivatives, frameworks where the spacetime dimension varies with the probed scale and geometry is characterized by at least one fundamental length [Formula: see text]. In the q -derivatives scenario, one finds a tiny shift of the event horizon. Schwarzschild black holes can present an additional ring singularity, not present in general relativity, whose radius is proportional to [Formula: see text]. In the multi-fractional theory with weighted derivatives, there is no such deformation, but non-trivial geometric features generate a cosmological-constant term, leading to a de Sitter-Schwarzschild black hole. For both scenarios, we compute the Hawking temperature and comment on the resulting black-hole thermodynamics. In the case with q -derivatives, black holes can be hotter than usual and possess an additional ring singularity, while in the case with weighted derivatives they have a de Sitter hair of purely geometric origin, which may lead to a solution of the cosmological constant problem similar to that in unimodular gravity. Finally, we compare our findings with other Lorentz-violating models.

One-loop quantum gravity repulsion in the early Universe.

PubMed

Broda, Bogusław

2011-03-11

Perturbative quantum gravity formalism is applied to compute the lowest order corrections to the classical spatially flat cosmological Friedmann-Lemaître-Robertson-Walker solution (for the radiation). The presented approach is analogous to the approach applied to compute quantum corrections to the Coulomb potential in electrodynamics, or rather to the approach applied to compute quantum corrections to the Schwarzschild solution in gravity. In the framework of the standard perturbative quantum gravity, it is shown that the corrections to the classical deceleration, coming from the one-loop graviton vacuum polarization (self-energy), have (UV cutoff free) opposite to the classical repulsive properties which are not negligible in the very early Universe. The repulsive "quantum forces" resemble those known from loop quantum cosmology.

Generalized quasitopological gravity

NASA Astrophysics Data System (ADS)

Hennigar, Robie A.; KubizÅák, David; Mann, Robert B.

2017-05-01

We construct the most general, to cubic order in curvature, theory of gravity whose (most general) static spherically symmetric vacuum solutions are fully described by a single field equation. The theory possesses the following remarkable properties: (i) It has a well-defined Einstein gravity limit, (ii) it admits "Schwarzschild-like" solutions characterized by a single metric function, (iii) on maximally symmetric backgrounds it propagates the same degrees of freedom as Einstein's gravity, and (iv) Lovelock and quasitopological gravities, as well as the recently developed Einsteinian cubic gravity [Bueno and Cano Phys. Rev. D 94, 104005 (2016)., 10.1103/PhysRevD.94.104005] in four dimensions, are recovered as special cases. We perform a brief analysis of asymptotically flat black holes in this theory and study their thermodynamics.

A new length scale for quantum gravity: A resolution of the black hole information loss paradox

NASA Astrophysics Data System (ADS)

Singh, Tejinder P.

We show why and how Compton wavelength and Schwarzschild radius should be combined into one single new length scale, which we call the Compton-Schwarzschild length. Doing so offers a resolution of the black hole information loss paradox, and suggests Planck mass remnant black holes as candidates for dark matter. It also compels us to introduce torsion, and identify the Dirac field with a complex torsion field. Dirac equation and Einstein equations, are shown to be mutually dual limiting cases of an underlying gravitation theory which involves the Compton-Schwarzschild length scale, and includes a complex torsion field.

The Schwarzschild effect of the dosimetry film Kodak EDR 2.

PubMed

Djouguela, A; Kollhoff, R; Rubach, A; Harder, D; Poppe, B

2005-11-07

The magnitude of the Schwarzschild effect or failure of the reciprocity law has been experimentally investigated for the dosimetry film EDR 2 from Kodak. When the dose rate applied to achieve a given dose was reduced by a factor of 12, the net optical density was reduced by up to 5%. The clinical importance of this effect is negligible as long as the films are calibrated at a value of the dose rate approximately representative of the dose rates occurring in the target volume, but in target regions of strongly reduced dose rate the Schwarzschild effect should be allowed for by a correction of the net optical density.

Astronomical Observations by Speckle Interferometry.

DTIC Science & Technology

1986-06-12

commonly -been noted [Heintz (101)] that it was Karl *, Schwarzchild who iui 1895 [ Schwarzschild (190)] made the first measure- ments of binary stars...J. Lett 163. Michelson, A A, Pease. F. G. 1921. Ap. 280: L23 J. 53: 249 190. Schwarzschild . K. 1896. Astron. Nadir. 164. Morgan. B. L., lieddoes. 1

On the existence of black holes in distorted Schwarzschild spacetime using marginally trapped surfaces

NASA Astrophysics Data System (ADS)

Pilkington, Terry

The classical definition of a black hole in terms of an event horizon relies on global properties of the spacetime. Realistic black holes have matter distributions surrounding them, which negates the asymptotic flatness needed for an event horizon. Using the (quasi-)local concept of marginally trapped surfaces, we investigate the Schwarzschild spacetime distorted by an axisymmetric matter distribution. We determine that it is possible to locate a future outer trapping horizon for a given foliation within certain value ranges of multipole moments. Furthermore, we show that there are no marginally trapped surfaces for arbitrary values of the multipole moment magnitudes. KEYWORDS: SCHWARZSCHILD; BLACK HOLE; DISTORTED SPACETIME; MARGINALLY TRAPPED SURFACE; FUTURE OUTER TRAPPING HORIZON

The 100th birthday of the conic constant and Schwarzschild's revolutionary papers in optics

NASA Astrophysics Data System (ADS)

Rakich, Andrew

2005-08-01

In 1905 Karl Schwarzschild published three papers on optics, two of which revolutionized the field of reflecting telescope optics. In his first paper he developed a full theory of the aberrations of reflecting telescopes, generalizing the Eikonal of Bruns to take into account systems with an infinite long conjugate. In the second paper Schwarzschild applied his formulation to a masterful analysis of 2 mirror anastigmatic systems, along the way discovering the so called Ritchey-Chretien aplanat, 18 years Ritchey and Chretien's announcement. Numerous other innovations are given in what must be seen as being among the most important papers on the aberrations of optical systems ever written.

Particle dynamics in the original Schwarzschild metric

NASA Astrophysics Data System (ADS)

Fimin, N. N.; Chechetkin, V. M.

2016-04-01

The properties of the original Schwarzschild metric for a point gravitating mass are considered. The laws of motion in the corresponding space-time are established, and the transition from the Schwarzschildmetric to the metric of a "dusty universe" are studied. The dynamics of a system of particles in thr post-Newtonian approximation are analyzed.

Dirac perturbations on Schwarzschild-anti-de Sitter spacetimes: Generic boundary conditions and new quasinormal modes

NASA Astrophysics Data System (ADS)

Wang, Mengjie; Herdeiro, Carlos; Jing, Jiliang

2017-11-01

We study Dirac quasinormal modes of Schwarzschild-anti-de Sitter (Schwarzschild-AdS) black holes, following the generic principle for allowed boundary conditions proposed in [M. Wang, C. Herdeiro, and M. O. P. Sampaio, Phys. Rev. D 92, 124006 (2015)., 10.1103/PhysRevD.92.124006]. After deriving the equations of motion for Dirac fields on the aforementioned background, we impose vanishing energy flux boundary conditions to solve these equations. We find a set of two Robin boundary conditions are allowed. These two boundary conditions are used to calculate Dirac normal modes on empty AdS and quasinormal modes on Schwarzschild-AdS black holes. In the former case, we recover the known normal modes of empty AdS; in the latter case, the two sets of Robin boundary conditions lead to two different branches of quasinormal modes. The impact on these modes of the black hole size, the angular momentum quantum number and the overtone number are discussed. Our results show that vanishing energy flux boundary conditions are a robust principle, applicable not only to bosonic fields but also to fermionic fields.

Scalar perturbations of nonsingular nonrotating black holes in conformal gravity

NASA Astrophysics Data System (ADS)

Toshmatov, Bobir; Bambi, Cosimo; Ahmedov, Bobomurat; Stuchlík, Zdeněk; Schee, Jan

2017-09-01

We study scalar and electromagnetic perturbations of a family of nonsingular nonrotating black hole spacetimes that are solutions in a large class of conformally invariant theories of gravity. The effective potential for scalar perturbations depends on the exact form of the scaling factor. Electromagnetic perturbations do not feel the scaling factor, and the corresponding quasinormal mode spectrum is the same as in the Schwarzschild metric. We find that these black hole metrics are stable under scalar and electromagnetic perturbations. Assuming that the quasinormal mode spectrum for scalar perturbations is not too different from that for gravitational perturbations, we can expect that the calculation of the quasinormal mode spectrum and the observation with gravitational wave detectors of quasinormal modes from astrophysical black holes can constrain the scaling factor and test these solutions.

Static models with conformal symmetry

NASA Astrophysics Data System (ADS)

Manjonjo, A. M.; Maharaj, S. D.; Moopanar, S.

2018-02-01

We study static spherically symmetric spacetimes with a spherical conformal symmetry and a nonstatic conformal factor associated with the conformal Killing field. With these assumptions we find an explicit relationship relating two metric components of the metric tensor field. This leads to the general solution of the Einstein field equations with a conformal symmetry in a static spherically symmetric spacetime. For perfect fluids we can find all metrics explicitly and show that the models always admit a barotropic equation of state. Contained within this class of spacetimes are the well known metrics of (interior) Schwarzschild, Tolman, Kuchowicz, Korkina and Orlyanskii, Patwardhan and Vaidya, and Buchdahl and Land. The isothermal metric of Saslaw et al also admits a conformal symmetry. For imperfect fluids an infinite family of exact solutions to the field equations can be generated.

Membrane paradigm of black holes in Chern-Simons modified gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Tian-Yi; Wang, Towe, E-mail: zhaotianyi5566@foxmail.com, E-mail: twang@phy.ecnu.edu.cn

2016-06-01

The membrane paradigm of black hole is studied in the Chern-Simons modified gravity. Derived with the action principle a la Parikh-Wilczek, the stress tensor of membrane manifests a rich structure arising from the Chern-Simons term. The membrane stress tensor, if related to the bulk stress tensor in a special form, obeys the low-dimensional fluid continuity equation and the Navier-Stokes equation. This paradigm is applied to spherically symmetric static geometries, and in particular, the Schwarzschild black hole, which is a solution of a large class of dynamical Chern-Simons gravity.

Universally stable black holes

NASA Astrophysics Data System (ADS)

Bueno, Pablo; Cano, Pablo A.

We argue that, when certain higher-curvature corrections are added to the four-dimensional Einstein-Hilbert action, black holes become stable below certain mass. We show this to be the case for an infinite family of ghost-free theories involving terms of arbitrarily high order in curvature. The thermodynamic behavior of the new black holes is universal for arbitrary values of the couplings, with the only exception of the Schwarzschild solution itself, which is recovered when all the couplings are set to zero. For this class of theories, the issue of non-unitary evolution is inexistent, as black holes never evaporate completely.

A quantum analogy to the classical gravitomagnetic clock effect

NASA Astrophysics Data System (ADS)

Faruque, S. B.

2018-06-01

We present an approximation to the solution of Dirac equation in Schwarzschild field found through the use of Foldy-Wouthuysen Hamiltonian. We solve the equation for the positive energy states and found the frequencies by which the states oscillate. Difference of the periods of oscillation of the two states with two different total angular momentum quantum number j has an analogical form of the classical clock effect found in general relativity. But unlike the term that appears as clock effect in classical physics, here the term is quantized. Thus, we find a quantum analogue of the classical gravitomagnetic clock effect.

Regge calculus and observations. II. Further applications.

NASA Astrophysics Data System (ADS)

Williams, Ruth M.; Ellis, G. F. R.

1984-11-01

The method, developed in an earlier paper, for tracing geodesies of particles and light rays through Regge calculus space-times, is applied to a number of problems in the Schwarzschild geometry. It is possible to obtain accurate predictions of light bending by taking sufficiently small Regge blocks. Calculations of perihelion precession, Thomas precession, and the distortion of a ball of fluid moving on a geodesic can also show good agreement with the analytic solution. However difficulties arise in obtaining accurate predictions for general orbits in these space-times. Applications to other problems in general relativity are discussed briefly.

Holographic dark energy from fluid/gravity duality constraint by cosmological observations

NASA Astrophysics Data System (ADS)

Pourhassan, Behnam; Bonilla, Alexander; Faizal, Mir; Abreu, Everton M. C.

2018-06-01

In this paper, we obtain a holographic model of dark energy using the fluid/gravity duality. This model will be dual to a higher dimensional Schwarzschild black hole, and we would use fluid/gravity duality to relate to the parameters of this black hole to such a cosmological model. We will also analyze the thermodynamics of such a solution, and discuss the stability model. Finally, we use cosmological data to constraint the parametric space of this dark energy model. Thus, we will use observational data to perform cosmography for this holographic model based on fluid/gravity duality.

Noether's stars in f (R) gravity

NASA Astrophysics Data System (ADS)

De Laurentis, Mariafelicia

2018-05-01

The Noether Symmetry Approach can be used to construct spherically symmetric solutions in f (R) gravity. Specifically, the Noether conserved quantity is related to the gravitational mass and a gravitational radius that reduces to the Schwarzschild radius in the limit f (R) → R. We show that it is possible to construct the M- R relation for neutron stars depending on the Noether conserved quantity and the associated gravitational radius. This approach enables the recovery of extreme massive stars that could not be stable in the standard Tolman-Oppenheimer-Volkoff based on General Relativity. Examples are given for some power law f (R) gravity models.

Radiatively driven relativistic jets in Schwarzschild space-time

NASA Astrophysics Data System (ADS)

Vyas, Mukesh K.; Chattopadhyay, Indranil

2018-06-01

Context. Aims: We carry out a general relativistic study of radiatively driven conical fluid jets around non-rotating black holes and investigate the effects and significance of radiative acceleration, as well as radiation drag. Methods: We apply relativistic equations of motion in curved space-time around a Schwarzschild black hole for axis-symmetric one-dimensional jet in steady state, plying through the radiation field of the accretion disc. Radiative moments are computed using information of curved space-time. Slopes of physical variables at the sonic points are found using L'Hôpital's rule and employing Runge-Kutta's fourth order method to solve equations of motion. The analysis is carried out using the relativistic equation of state of the jet fluid. Results: The terminal speed of the jet depends on how much thermal energy is converted into jet momentum and how much radiation momentum is deposited onto the jet. Many classes of jet solutions with single sonic points, multiple sonic points, as well as those having radiation driven internal shocks are obtained. Variation of all flow variables along the jet-axis has been studied. Highly energetic electron-proton jets can be accelerated by intense radiation to terminal Lorentz factors γT 3. Moderate terminal speed vT 0.5 is obtained for moderately luminous discs. Lepton dominated jets may achieve γT 10. Conclusions: Thermal driving of the jet itself and radiation driving by accretion disc photons produce a wide-ranging jet solutions starting from moderately strong jets to the relativistic ones. Interplay of intensity, the nature of the radiation field, and the energetics of the jet result in a variety of jet solutions. We show that radiation field is able to induce steady shocks in jets, one of the criteria to explain high-energy power-law emission observed in spectra of some of the astrophysical objects.

Validity of black hole complementarity in the BTZ black hole

NASA Astrophysics Data System (ADS)

Gim, Yongwan; Kim, Wontae

2018-01-01

Based on the gedanken experiment for black hole complementarity in the Schwarzschild black hole, we calculate the energy required to duplicate information in the BTZ black hole under the assumption of absorbing boundary condition and its dual solution of the black string, respectively, in order to justify the validity of the no-cloning theorem in quantum mechanics. For the BTZ black hole, the required energy for the duplication of information can be made fairly small, whereas for the black string it exceeds the total mass of the black string, although they are related to each other under the dual transformation. So, the duplication of information might be possible in the BTZ black hole in contrast to the case of the black string, so that the no-cloning theorem could be violated for the former case. To save the duplication of information for the BTZ black hole, we perform an improved gedanken experiment by using the local thermodynamic quantities near the horizon rather than those defined at infinity, and show that the no-cloning theorem could be made valid even in the BTZ black hole. We also discuss how this local treatment for the no-cloning theorem can be applied to the black string as well as the Schwarzschild black hole innocuously.

Touching Ghosts: Observing Free Fall from an Infalling Frame of Reference into a Schwarzschild Black Hole

ERIC Educational Resources Information Center

Augousti, A. T.; Gawelczyk, M.; Siwek, A.; Radosz, A.

2012-01-01

The problem of communication between observers in the vicinity of a black hole in a Schwarzschild metric is considered. The classic example of an infalling observer Alice and a static distant mother station (MS) is extended to include a second infalling observer Bob, who follows Alice in falling towards the event horizon. Kruskal coordinates are…

Conventional and modified Schwarzschild objective for EUV lithography: design relations

NASA Astrophysics Data System (ADS)

Bollanti, S.; di Lazzaro, P.; Flora, F.; Mezi, L.; Murra, D.; Torre, A.

2006-12-01

The design criteria of a Schwarzschild-type optical system are reviewed in relation to its use as an imaging system in an extreme ultraviolet lithography setup. Both the conventional and the modified reductor imaging configurations are considered, and the respective performances, as far as the geometrical resolution in the image plane is concerned, are compared. In this connection, a formal relation defining the modified configuration is elaborated, refining a rather naïve definition presented in an earlier work. The dependence of the geometrical resolution on the image-space numerical aperture for a given magnification is investigated in detail for both configurations. So, the advantages of the modified configuration with respect to the conventional one are clearly evidenced. The results of a semi-analytical procedure are compared with those obtained from a numerical simulation performed by an optical design program. The Schwarzschild objective based system under implementation at the ENEA Frascati Center within the context of the Italian FIRB project for EUV lithography has been used as a model. Best-fit functions accounting for the behaviour of the system parameters vs. the numerical aperture are reported; they can be a useful guide for the design of Schwarzschild objective type optical systems.

First order perturbations of the Einstein-Straus and Oppenheimer-Snyder models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mars, Marc; Mena, Filipe C.; Vera, Rauel

We derive the linearly perturbed matching conditions between a Schwarzschild spacetime region with stationary and axially symmetric perturbations and a Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime with arbitrary perturbations. The matching hypersurface is also perturbed arbitrarily and, in all cases, the perturbations are decomposed into scalars using the Hodge operator on the sphere. This allows us to write down the matching conditions in a compact way. In particular, we find that the existence of a perturbed (rotating, stationary, and vacuum) Schwarzschild cavity in a perturbed FLRW universe forces the cosmological perturbations to satisfy constraints that link rotational and gravitational wave perturbations. We alsomore » prove that if the perturbation on the FLRW side vanishes identically, then the vacuole must be perturbatively static and hence Schwarzschild. By the dual nature of the problem, the first result translates into links between rotational and gravitational wave perturbations on a perturbed Oppenheimer-Snyder model, where the perturbed FLRW dust collapses in a perturbed Schwarzschild environment which rotates in equilibrium. The second result implies, in particular, that no region described by FLRW can be a source of the Kerr metric.« less

Schwarzschild-de Sitter spacetimes, McVittie coordinates, and trumpet geometries

NASA Astrophysics Data System (ADS)

Dennison, Kenneth A.; Baumgarte, Thomas W.

2017-12-01

Trumpet geometries play an important role in numerical simulations of black hole spacetimes, which are usually performed under the assumption of asymptotic flatness. Our Universe is not asymptotically flat, however, which has motivated numerical studies of black holes in asymptotically de Sitter spacetimes. We derive analytical expressions for trumpet geometries in Schwarzschild-de Sitter spacetimes by first generalizing the static maximal trumpet slicing of the Schwarzschild spacetime to static constant mean curvature trumpet slicings of Schwarzschild-de Sitter spacetimes. We then switch to a comoving isotropic radial coordinate which results in a coordinate system analogous to McVittie coordinates. At large distances from the black hole the resulting metric asymptotes to a Friedmann-Lemaître-Robertson-Walker metric with an exponentially-expanding scale factor. While McVittie coordinates have another asymptotically de Sitter end as the radial coordinate goes to zero, so that they generalize the notion of a "wormhole" geometry, our new coordinates approach a horizon-penetrating trumpet geometry in the same limit. Our analytical expressions clarify the role of time-dependence, boundary conditions and coordinate conditions for trumpet slices in a cosmological context, and provide a useful test for black hole simulations in asymptotically de Sitter spacetimes.

Komar energy and Smarr formula for noncommutative inspired Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Banerjee, Rabin; Gangopadhyay, Sunandan

2011-11-01

We calculate the Komar energy E for a noncommutative inspired Schwarzschild black hole. A deformation from the conventional identity E = 2 ST H is found in the next to leading order computation in the noncommutative parameter θ (i.e. {{O}(sqrt{θ}e^{-M^2/θ})}) which is also consistent with the fact that the area law now breaks down. This deformation yields a nonvanishing Komar energy at the extremal point T H = 0 of these black holes. We then work out the Smarr formula, clearly elaborating the differences from the standard result M = 2 ST H , where the mass ( M) of the black hole is identified with the asymptotic limit of the Komar energy. Similar conclusions are also shown to hold for a deSitter-Schwarzschild geometry.

Space–time and spatial geodesic orbits in Schwarzschild geometry

NASA Astrophysics Data System (ADS)

Resca, Lorenzo

2018-05-01

Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit equations for a proper spatial submanifold of Schwarzschild metric at any given coordinate-time correspond to an unphysical gravitational repulsion in the non-relativistic limit. This demonstrates at a basic level the centrality and critical role of relativistic time and its intimate pseudo-Riemannian connection with space. Correspondingly, a commonly popularised depiction of geodesic orbits of planets as resulting from the curvature of space produced by the Sun, represented as a rubber sheet dipped in the middle by the weighing of that massive body, is mistaken and misleading for the essence of relativity, even in the non-relativistic limit.

a Virtual Trip to the Schwarzschild-De Sitter Black Hole

NASA Astrophysics Data System (ADS)

Bakala, Pavel; Hledík, Stanislav; Stuchlík, Zdenĕk; Truparová, Kamila; Čermák, Petr

2008-09-01

We developed realistic fully general relativistic computer code for simulation of optical projection in a strong, spherically symmetric gravitational field. Standard theoretical analysis of optical projection for an observer in the vicinity of a Schwarzschild black hole is extended to black hole spacetimes with a repulsive cosmological constant, i.e, Schwarzschild-de Sitter (SdS) spacetimes. Influence of the cosmological constant is investigated for static observers and observers radially free-falling from static radius. Simulation includes effects of gravitational lensing, multiple images, Doppler and gravitational frequency shift, as well as the amplification of intensity. The code generates images of static observers sky and a movie simulations for radially free-falling observers. Techniques of parallel programming are applied to get high performance and fast run of the simulation code.

On the proof of the C 0-inextendibility of the Schwarzschild spacetime

NASA Astrophysics Data System (ADS)

Sbierski, Jan

2018-02-01

This article presents a streamlined version of the author’s original proof of the C 0-inextendibility of the maximal analytic Schwarzschild spacetime. Firstly, we deviate from the original proof by using the result, recently established in collaboration with Galloway and Ling, that given a C 0-extension of a globally hyperbolic spacetime, one can find a timelike geodesic that leaves this spacetime. This result much simplifies the proof of the inextendibility through the exterior region of the Schwarzschild spacetime. Secondly, we give a more flexible and shorter argument for the inextendibility through the interior region. Furthermore, we present a small new structural result for the boundary of a globally hyperbolic spacetime within a C 0-extension which serves as a new and simpler starting point for the proof.

Black holes in vector-tensor theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heisenberg, Lavinia; Kase, Ryotaro; Tsujikawa, Shinji

We study static and spherically symmetric black hole (BH) solutions in second-order generalized Proca theories with nonminimal vector field derivative couplings to the Ricci scalar, the Einstein tensor, and the double dual Riemann tensor. We find concrete Lagrangians which give rise to exact BH solutions by imposing two conditions of the two identical metric components and the constant norm of the vector field. These exact solutions are described by either Reissner-Nordström (RN), stealth Schwarzschild, or extremal RN solutions with a non-trivial longitudinal mode of the vector field. We then numerically construct BH solutions without imposing these conditions. For cubic andmore » quartic Lagrangians with power-law couplings which encompass vector Galileons as the specific cases, we show the existence of BH solutions with the difference between two non-trivial metric components. The quintic-order power-law couplings do not give rise to non-trivial BH solutions regular throughout the horizon exterior. The sixth-order and intrinsic vector-mode couplings can lead to BH solutions with a secondary hair. For all the solutions, the vector field is regular at least at the future or past horizon. The deviation from General Relativity induced by the Proca hair can be potentially tested by future measurements of gravitational waves in the nonlinear regime of gravity.« less

Relativistic stars in degenerate higher-order scalar-tensor theories after GW170817

NASA Astrophysics Data System (ADS)

Kobayashi, Tsutomu; Hiramatsu, Takashi

2018-05-01

We study relativistic stars in degenerate higher-order scalar-tensor theories that evade the constraint on the speed of gravitational waves imposed by GW170817. It is shown that the exterior metric is given by the usual Schwarzschild solution if the lower order Horndeski terms are ignored in the Lagrangian and a shift symmetry is assumed. However, this class of theories exhibits partial breaking of Vainshtein screening in the stellar interior and thus modifies the structure of a star. Employing a simple concrete model, we show that for high-density stars the mass-radius relation is altered significantly even if the parameters are chosen so that only a tiny correction is expected in the Newtonian regime. We also find that, depending on the parameters, there is a maximum central density above which solutions cease to exist.

Gravastars with higher dimensional spacetimes

NASA Astrophysics Data System (ADS)

Ghosh, Shounak; Ray, Saibal; Rahaman, Farook; Guha, B. K.

2018-07-01

We present a new model of gravastar in the higher dimensional Einsteinian spacetime including Einstein's cosmological constant Λ. Following Mazur and Mottola (2001, 2004) we design the star with three specific regions, as follows: (I) Interior region, (II) Intermediate thin spherical shell and (III) Exterior region. The pressure within the interior region is equal to the negative matter density which provides a repulsive force over the shell. This thin shell is formed by ultra relativistic plasma, where the pressure is directly proportional to the matter-energy density which does counter balance the repulsive force from the interior whereas the exterior region is completely vacuum assumed to be de Sitter spacetime which can be described by the generalized Schwarzschild solution. With this specification we find out a set of exact non-singular and stable solutions of the gravastar which seems physically very interesting and reasonable.

Solar Observations on Magneto-Convection

DTIC Science & Technology

1989-05-31

Technical Library National Solar Observatory Sunspot, NM 88349 Karl - Schwarzschild -Strasse 1 8046 Garching bei Mundhen Solar Observations On Magneto...Schmidt, Hermann-Ulrich Schmidt, Hans-Christoph Thomas (eds.) Max-Planck-Institut fir Physik und Astrophysik Institut fiur Astrophysik Karl ... Schwarzschild -St-. 1 D-8046 Garching, FklG 14TIS CRiA.&l DTIC TA. U~Jar,iou8:ed B ......... ... Distribution I -- Availability COcý----- Avail and or Dist special

Black holes in six-dimensional conformal gravity

NASA Astrophysics Data System (ADS)

Lü, H.; Pang, Yi; Pope, C. N.

2013-05-01

We study conformally invariant theories of gravity in six dimensions. In four dimensions, there is a unique such theory that is polynomial in the curvature and its derivatives, namely, Weyl-squared, and furthermore all solutions of Einstein gravity are also solutions of the conformal theory. By contrast, in six dimensions there are three independent conformally invariant polynomial terms one could consider. There is a unique linear combination (up to overall scale) for which Einstein metrics are also solutions, and this specific theory forms the focus of our attention in this paper. We reduce the equations of motion for the most general spherically symmetric black hole to a single fifth-order differential equation. We obtain the general solution in the form of an infinite series, characterized by five independent parameters, and we show how a finite three-parameter truncation reduces to the already known Schwarzschild-AdS metric and its conformal scaling. We derive general results for the thermodynamics and the first law for the full five-parameter solutions. We also investigate solutions in extended theories coupled to conformally invariant matter, and in addition we derive some general results for conserved charges in cubic-curvature theories in arbitrary dimensions.

Behavior of a spin-1/2 massive charged particle in Schwarzschild immersed in an electromagnetic universe

NASA Astrophysics Data System (ADS)

Al-Badawi, A.

2018-02-01

The Dirac equation is considered in a spacetime that represents a Schwarzschild metric coupled to a uniform external electromagnetic field. Due to the presence of electromagnetic field from the surroundings, the interaction with the spin-1/2 massive charged particle is considered. The equations of the spin-1/2 massive charged particle are separated into radial and angular equations by adopting the Newman-Penrose formalism. The angular equations obtained are similar to the Schwarzschild geometry. For the radial equations we manage to obtain the one dimensional Schrödinger-type wave equations with effective potentials. Finally, we study the behavior of the potentials by plotting them as a function of radial distance and expose the effect of the external parameter, charge and the frequency of the particle on them.

Thermodynamic phase transition of a black hole in rainbow gravity

NASA Astrophysics Data System (ADS)

Feng, Zhong-Wen; Yang, Shu-Zheng

2017-09-01

In this letter, using the rainbow functions that were proposed by Magueijo and Smolin, we investigate the thermodynamics and the phase transition of rainbow Schwarzschild black hole. First, we calculate the rainbow gravity corrected Hawking temperature. From this modification, we then derive the local temperature, free energy, and other thermodynamic quantities in an isothermal cavity. Finally, we analyze the critical behavior, thermodynamic stability, and phase transition of the rainbow Schwarzschild black hole. The results show that the rainbow gravity can stop the Hawking radiation in the final stages of black holes' evolution and lead to the remnants of black holes. Furthermore, one can observe that the rainbow Schwarzschild black hole has one first-order phase transition, two second-order phase transitions, and three Hawking-Page-type phase transitions in the framework of rainbow gravity theory.

Turbulence and Laminar Structures: Can They Co-Exist?

NASA Technical Reports Server (NTRS)

Canuto, V. M.

2000-01-01

Schwarzschild first suggested that the laminar structures observed in the high Reynolds number Re = UL/nu approx. = (10(exp 12)) solar photosphere are the result of turbulence rather than a proof of its absence. He reasoned that since turbulence generates large turbulent viscosities nu(sub t) much greater than nu, the "effective" Reynolds number Re = UL/nu(sub t) approx. = O(1). Schwarzschild's argument is, however, incomplete for it assumes that the entire role of the non-linear interactions is to "enhance" viscosity. While this is not true in general, we present a proof of how and why it may occur, thus completing Schwarzschild's argument. We further discuss the fact that the same model non-local turbulence models have been shown to reproduce LES data for a variety of flows pertaining to astrophysics, geophysics and laboratory situations (at a fraction of the time).

Imprints from the global cosmological expansion to the local spacetime dynamics.

PubMed

Fahr, Hans J; Siewert, Mark

2008-05-01

We study the general relativistic spacetime metrics surrounding massive cosmological objects, such as suns, stars, galaxies or galaxy clusters. The question addressed here is the transition of local, object-related spacetime metrics into the global, cosmological Robertson-Walker metrics. We demonstrate that the answer often quoted for this problem from the literature, the so-called Einstein-Straus vacuole, which connects a static outer Schwarzschild solution with the time-dependent Robertson-Walker universe, is inadequate to describe the local spacetime of a gravitationally bound system. Thus, we derive here an alternative model describing such bound systems by a metrics more closely tied to the fundamental problem of structure formation in the early universe and obtain a multitude of solutions characterising the time-dependence of a local scale parameter. As we can show, a specific solution out of this multitude is able to, as a by-product, surprisingly enough, explain the presently much discussed phenomenon of the PIONEER anomaly.

Global solutions to the electrodynamic two-body problem on a straight line

NASA Astrophysics Data System (ADS)

Bauer, G.; Deckert, D.-A.; Dürr, D.; Hinrichs, G.

2017-06-01

The classical electrodynamic two-body problem has been a long standing open problem in mathematics. For motion constrained to the straight line, the interaction is similar to that of the two-body problem of classical gravitation. The additional complication is the presence of unbounded state-dependent delays in the Coulomb forces due to the finiteness of the speed of light. This circumstance renders the notion of local solutions meaningless, and therefore, straightforward ODE techniques cannot be applied. Here, we study the time-symmetric case, i.e., the Fokker-Schwarzschild-Tetrode (FST) equations, comprising both advanced and retarded delays. We extend the technique developed in Deckert and Hinrichs (J Differ Equ 260:6900-6929, 2016), where existence of FST solutions was proven on the half line, to ensure global existence—a result that had been obtained by Bauer (Ein Existenzsatz für die Wheeler-Feynman-Elektrodynamik, Herbert Utz Verlag, München, 1997). Due to the novel technique, the presented proof is shorter and more transparent but also relies on the idea to employ asymptotic data to characterize solutions.

X ray microscope assembly and alignment support and advanced x ray microscope design and analysis

NASA Technical Reports Server (NTRS)

Shealy, David L.

1991-01-01

Considerable efforts have been devoted recently to the design, analysis, fabrication, and testing of spherical Schwarzschild microscopes for soft x ray application in microscopy and projection lithography. The spherical Schwarzschild microscope consists of two concentric spherical mirrors configured such that the third order spherical aberration and coma are zero. Since multilayers are used on the mirror substrates for x ray applications, it is desirable to have only two reflecting surfaces in a microscope. In order to reduce microscope aberrations and increase the field of view, generalized mirror surface profiles have been considered in this investigation. Based on incoherent and sine wave modulation transfer function (MTF) calculations, the object plane resolution of a microscope has been analyzed as a function of the object height and numerical aperture (NA) of the primary for several spherical Schwarzschild, conic, and aspherical head reflecting two mirror microscope configurations.

Gauge invariant perturbations of the Schwarzschild spacetime

NASA Astrophysics Data System (ADS)

Thompson, Jonathan E.; Chen, Hector; Whiting, Bernard F.

2017-09-01

Beginning with the pioneering work of Regge and Wheeler (1957 Phys. Rev. 108 1063), there have been many studies of perturbations away from the Schwarzschild spacetime background. In particular several authors Moncrief (1974 Ann. Phys. 88 323), Sachs (1964 Relativity, Groups and Topology (New York: Gordon and Breach)) and Brizuela et al (2007 Phys. Rev. D 76 024004) have investigated gauge invariant quantities of the Regge-Wheeler (RW) formalism. Steven Detweiler also investigated perturbations of Schwarzschild in his own formalism, introducing his own gauge choice which he denoted the ‘easy (EZ) gauge’, and which he was in the process of adapting for use in the second-order self-force problem. We present here a compilation of some of his working results, arising from notes for which there seems to have been no manuscript in preparation. In particular, we outline Detweiler’s formalism, list the gauge invariant quantities he used, and explain the process by which he found them.

Design and analysis of a fast, two-mirror soft-x-ray microscope

NASA Technical Reports Server (NTRS)

Shealy, D. L.; Wang, C.; Jiang, W.; Jin, L.; Hoover, R. B.

1992-01-01

During the past several years, a number of investigators have addressed the design, analysis, fabrication, and testing of spherical Schwarzschild microscopes for soft-x-ray applications using multilayer coatings. Some of these systems have demonstrated diffraction limited resolution for small numerical apertures. Rigorously aplanatic, two-aspherical mirror Head microscopes can provide near diffraction limited resolution for very large numerical apertures. The relationships between the numerical aperture, mirror radii and diameters, magnifications, and total system length for Schwarzschild microscope configurations are summarized. Also, an analysis of the characteristics of the Head-Schwarzschild surfaces will be reported. The numerical surface data predicted by the Head equations were fit by a variety of functions and analyzed by conventional optical design codes. Efforts have been made to determine whether current optical substrate and multilayer coating technologies will permit construction of a very fast Head microscope which can provide resolution approaching that of the wavelength of the incident radiation.

Editor's note: Reviews in Modern Astronomy 27

NASA Astrophysics Data System (ADS)

Berlepsch, Regina v.

2015-06-01

In order to make the scientific events of the meetings of the Astronomische Gese llschaft (AG) more international and bring them to the attention of the worldwide astronomical community, it was decided to devote the Reviews in Modern Astronomy} to the outcomes of the large annual fall meetings of the AG. In particular, it emphasized the Karl Schwarzschild Lectures, the Ludwig Biermann Award Lectures, the invited reviews, and the highlight contributions on recent progress and achievements from leading scientists. The most prestigious of them, the Karl Schwarzschild Lectures, constitutes a special series of reviews by outstanding scientists who have been awarded the Karl Schwarzschild Medal during the fall meeting of the AG. At the same time, excellent young astronomers are honored by the Ludwig Biermann Award. In 2010 the ``Doctoral Thesis Award'' was established to honor the most outstanding Doctoral Thesis of the past year.

Temporal and spatial foliations of spacetimes.

NASA Astrophysics Data System (ADS)

Herold, H.

For the solution of initial-value problems in numerical relativity usually the (3+1) splitting of Einstein's equations is employed. An important part of this splitting is the choice of the temporal gauge condition. In order to estimate the quality of time-evolution schemes, different time slicings of given well-known spherically symmetric spacetimes have been studied. Besides the maximal slicing condition the harmonic slicing prescription has been used to calculate temporal foliations of the Schwarzschild and the Oppenheimer-Snyder spacetime. Additionally, the author has studied a recently proposed, geometrically motivated spatial gauge condition, which is defined by considering the foliations of the three-dimensional space-like hypersurfaces by 2-surfaces of constant mean extrinsic curvature. Apart from the equations for the shift vector, which can be derived for this gauge condition, he has investigated such spatial foliations for well-known stationary axially symmetric spacetimes, namely for the Kerr metric and for numerically determined solutions for rapidly rotating neutron stars.

Brane - Anti-Brane Democracy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rajaraman, Arvind

2003-06-02

We suggest a duality invariant formula for the entropy and temperature of nonextreme black holes in supersymmetric string theory. The entropy is given in terms of the duality invariant parameter of the deviation from extremality and 56 SU(8) covariant central charges. It interpolates between the entropies of Schwarzschild solution and extremal solutions with various amount of unbroken supersymmetries and therefore serves for classification of black holes in supersymmetric string theories. We introduce the second auxiliary 56 via E(7) symmetric constraint. The symmetric and antisymmetric combinations of these two multiplets are related via moduli to the corresponding two fundamental representations ofmore » E(7): brane and anti-brane ''numbers.'' Using the CPT as well as C symmetry of the entropy formula and duality one can explain the mysterious simplicity of the non-extreme black hole area formula in terms of branes and anti-branes.« less

Stability of Black Holes and the Speed of Gravitational Waves within Self-Tuning Cosmological Models

NASA Astrophysics Data System (ADS)

Babichev, Eugeny; Charmousis, Christos; Esposito-Farèse, Gilles; Lehébel, Antoine

2018-06-01

The gravitational wave event GW170817 together with its electromagnetic counterparts constrains the speed of gravity to be extremely close to that of light. We first show, on the example of an exact Schwarzschild-de Sitter solution of a specific beyond-Horndeski theory, that imposing the strict equality of these speeds in the asymptotic homogeneous Universe suffices to guarantee so even in the vicinity of the black hole, where large curvature and scalar-field gradients are present. We also find that the solution is stable in a range of the model parameters. We finally show that an infinite class of beyond-Horndeski models satisfying the equality of gravity and light speeds still provides an elegant self-tuning: the very large bare cosmological constant entering the Lagrangian is almost perfectly counterbalanced by the energy-momentum tensor of the scalar field, yielding a tiny observable effective cosmological constant.

Black hole hair formation in shift-symmetric generalised scalar-tensor gravity

NASA Astrophysics Data System (ADS)

Benkel, Robert; Sotiriou, Thomas P.; Witek, Helvi

2017-03-01

A linear coupling between a scalar field and the Gauss-Bonnet invariant is the only known interaction term between a scalar and the metric that: respects shift symmetry; does not lead to higher order equations; inevitably introduces black hole hair in asymptotically flat, 4-dimensional spacetimes. Here we focus on the simplest theory that includes such a term and we explore the dynamical formation of scalar hair. In particular, we work in the decoupling limit that neglects the backreaction of the scalar onto the metric and evolve the scalar configuration numerically in the background of a Schwarzschild black hole and a collapsing dust star described by the Oppenheimer-Snyder solution. For all types of initial data that we consider, the scalar relaxes at late times to the known, static, analytic configuration that is associated with a hairy, spherically symmetric black hole. This suggests that the corresponding black hole solutions are indeed endpoints of collapse.

Design and analysis of aspherical multilayer imaging X-ray microscope

NASA Technical Reports Server (NTRS)

Shealy, David L.; Jiang, WU; Hoover, Richard B.

1991-01-01

Spherical Schwarzschild microscopes for soft X-ray applications in microscopy and projection lithography employ two concentric spherical mirrors that are configured such that the third-order spherical aberration and coma are zero. Based on incoherent, sine-wave MTF calculations, the object-plane resolution of a magnification-factor-20 microscope is presently analyzed as a function of object height and numerical aperture of the primary for several spherical Schwarzschild, conic, and aspherical two-mirror microscope configurations.

Aspects of neutrino oscillation in alternative gravity theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chakraborty, Sumanta, E-mail: sumantac.physics@gmail.com

2015-10-01

Neutrino spin and flavour oscillation in curved spacetime have been studied for the most general static spherically symmetric configuration. Having exploited the spherical symmetry we have confined ourselves to the equatorial plane in order to determine the spin and flavour oscillation frequency in this general set-up. Using the symmetry properties we have derived spin oscillation frequency for neutrino moving along a geodesic or in a circular orbit. Starting from the expression of neutrino spin oscillation frequency we have shown that even in this general context, in high energy limit the spin oscillation frequency for neutrino moving along circular orbit vanishes.more » We have verified previous results along this line by transforming to Schwarzschild coordinates under appropriate limit. This finally lends itself to the probability of neutrino helicity flip which turns out to be non-zero. While for neutrino flavour oscillation we have derived general results for oscillation phase, which subsequently have been applied to three different gravity theories. One, of them appears as low-energy approximation to string theory, where we have an additional field, namely, dilaton field coupled to Maxwell field tensor. This yields a realization of Reissner-Nordström solution in string theory at low-energy. Next one corresponds to generalization of Schwarzschild solution by introduction of quadratic curvature terms of all possible form to the Einstein-Hilbert action. Finally, we have also discussed regular black hole solutions. In all these cases the flavour oscillation probabilities can be determined for solar neutrinos and thus can be used to put bounds on the parameters of these gravity theories. While for spin oscillation probability, we have considered two cases, Gauss-Bonnet term added to the Einstein-Hilbert action and the f(R) gravity theory. In both these cases we could impose bounds on the parameters which are consistent with previous considerations. In a nutshell, in this work we have presented both spin and flavour oscillation frequency of neutrino in most general static spherically symmetric spacetime, encompassing a vast class of solutions, which when applied to three such instances in alternative theories for flavour oscillation and two alternative theories for spin oscillation put bounds on the parameters of these theories. Implications are also discussed.« less

Equatorial Geodesics Around the Magnetars

NASA Astrophysics Data System (ADS)

Alfradique, Viviane A. P.; Troconis, Orlenys N.; Negreiros, Rodrigo P.

Neutron stars manifest themselves as different classes of astrophysical sources that are associated to distinct phenomenology. Here we focus our attention on magnetars (or strongly magnetized neutron stars) that are associated to Soft Gamma Repeaters and Anomalous X-ray Pulsars. The magnetic field on surface of these objects, reaches values greater than 1015 G. Under intense magnetic fields, relativistic effects begin to be decisive for the definition of the structure and evolution of these objects. We are tempted to question ourselves to how strengths fields affect the structure of neutron star. In this work, our objective is study and compare two solutions of Einstein-Maxwell equations: the Bonnor solution, which is an analytical solution that describe the exterior spacetime for a massive compact object which has a magnetic field that is characterize as a dipole field and a complete solution that describe the interior and exterior spacetime for the same source found by numerical methods). For this, we describe the geodesic equations generated by such solutions. Our results show that the orbits generated by the Bonnor solution are the same as described by numerical solution. Also, show that the inclusion of magnetic fields with values up to 1017G in the center of the star does not modify sharply the particle orbits described around this star, so the use of Schwarzschild solution for the description of these orbits is a reasonable approximation.

Mass inflation and chaotic behaviour inside hairy black holes

NASA Astrophysics Data System (ADS)

Breitenlohner, Peter; Lavrelashvili, George; Maison, Dieter

1998-07-01

We analyze the interior geometry of static, spherically symmetric black holes of the Einstein-Yang-Mills-Higgs theory. Generically the solutions exhibit a behaviour that may be described as ``mass inflation'', although with a remarkable difference between the cases with and without a Higgs field. Without Higgs field the YM field induces a kind of cyclic behaviour leading to repeated cycles of mass inflation - taking the form of violent explosions - interrupted by quiescent periods and subsequent approaches to an almost Cauchy horizon. With the Higgs field no such cycles occur in the asymptotic behaviour. In addition there are non-generic families with a Schwarzschild and a Reissner-Nordstrøm type singularity at r=0, respectively.

Quasi-normal modes from non-commutative matrix dynamics

NASA Astrophysics Data System (ADS)

Aprile, Francesco; Sanfilippo, Francesco

2017-09-01

We explore similarities between the process of relaxation in the BMN matrix model and the physics of black holes in AdS/CFT. Focusing on Dyson-fluid solutions of the matrix model, we perform numerical simulations of the real time dynamics of the system. By quenching the equilibrium distribution we study quasi-normal oscillations of scalar single trace observables, we isolate the lowest quasi-normal mode, and we determine its frequencies as function of the energy. Considering the BMN matrix model as a truncation of N=4 SYM, we also compute the frequencies of the quasi-normal modes of the dual scalar fields in the AdS5-Schwarzschild background. We compare the results, and we finda surprising similarity.

Gravitational field of global monopole within the Eddington-inspired Born-Infeld theory of gravity

NASA Astrophysics Data System (ADS)

Lambaga, Reyhan D.; Ramadhan, Handhika S.

2018-06-01

Within the framework of the recent Eddington-inspired Born-Infeld (EiBI) theory we study gravitational field around an SO(3) global monopole. The solution also suffers from the deficit solid angle as in the Barriola-Vilenkin metric but shows a distinct feature that cannot be transformed away unless in the vanishing EiBI coupling constant, κ . When seen as a black hole eating up a global monopole, the corresponding Schwarzschild horizon is shrunk by κ . The deficit solid angle makes the space is globally not Euclidean, and to first order in κ (weak-field limit) the deflection angle of light is smaller than its Barriola-Vilenkin counterpart.

General Relativity

NASA Astrophysics Data System (ADS)

Hobson, M. P.; Efstathiou, G. P.; Lasenby, A. N.

2006-02-01

1. The spacetime of special relativity; 2. Manifolds and coordinates; 3. Vector calculus on manifolds; 4. Tensor calculus on manifolds; 5. Special relativity revisited; 6. Electromagnetism; 7. The equivalence principle and spacetime curvature; 8. The gravitational field equations; 9. The Schwarzschild geometry; 10. Experimental tests of general relativity; 11. Schwarzschild black holes; 12. Further spherically-symmetric geometries; 13. The Kerr geometry; 14. The Friedmann-Robertson-Walker geometry; 15. Cosmological models; 16. Inflationary cosmology; 17. Linearised general relativity; 18. Gravitational waves; 19. A variational approach to general relativity.

Over the horizon: Distinguishing the Schwarzschild spacetime and the R P3 spacetime using an Unruh-DeWitt detector

NASA Astrophysics Data System (ADS)

Ng, Keith K.; Mann, Robert B.; Martín-Martínez, Eduardo

2017-10-01

The RP3 geon and the Schwarzschild black hole are two black hole spacetimes which differ only behind the event horizon. We show that the thermal Hawking radiation emanating from the two black holes contains nontrivial correlations, that these correlations contain information about their interiors, and demonstrate that a particle detector can recover these correlations. In this manner, a simple particle detector can determine the structure behind the event horizon of an eternal black hole.

Dirac Particles' Hawking Radiation from a Schwarzschild Black Hole

NASA Astrophysics Data System (ADS)

He, Xiao-Kai; Liu, Wen-Biao

2007-08-01

Considering energy conservation and the backreaction of particles to spacetime, we investigate the massless/massive Dirac particles' Hawking radiation from a Schwarzschild black hole. The exact expression of the emission rate near the horizon is obtained and the result indicates that Hawking radiation spectrum is not purely thermal. The result obtained is consistent with the results obtained before. It satisfies the underlying unitary theory and offers a possible mechanism to explain the information loss paradox. Whereas the improved Damour-Ruffini method is more concise and understandable.

Schwarzschild black holes can wear scalar wigs.

PubMed

Barranco, Juan; Bernal, Argelia; Degollado, Juan Carlos; Diez-Tejedor, Alberto; Megevand, Miguel; Alcubierre, Miguel; Núñez, Darío; Sarbach, Olivier

2012-08-24

We study the evolution of a massive scalar field surrounding a Schwarzschild black hole and find configurations that can survive for arbitrarily long times, provided the black hole or the scalar field mass is small enough. In particular, both ultralight scalar field dark matter around supermassive black holes and axionlike scalar fields around primordial black holes can survive for cosmological times. Moreover, these results are quite generic in the sense that fairly arbitrary initial data evolve, at late times, as a combination of those long-lived configurations.

Thermodynamic phase transition in the rainbow Schwarzschild black hole

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gim, Yongwan; Kim, Wontae, E-mail: yongwan89@sogang.ac.kr, E-mail: wtkim@sogang.ac.kr

2014-10-01

We study the thermodynamic phase transition in the rainbow Schwarzschild black hole where the metric depends on the energy of the test particle. Identifying the black hole temperature with the energy from the modified dispersion relation, we obtain the modified entropy and thermodynamic energy along with the modified local temperature in the cavity to provide well defined black hole states. It is found that apart from the conventional critical temperature related to Hawking-Page phase transition there appears an additional critical temperature which is of relevance to the existence of a locally stable tiny black hole; however, the off-shell free energymore » tells us that this black hole should eventually tunnel into the stable large black hole. Finally, we discuss the reason why the temperature near the horizon is finite in the rainbow black hole by employing the running gravitational coupling constant, whereas it is divergent near the horizon in the ordinary Schwarzschild black hole.« less

Proper temperature of the Schwarzschild AdS black hole revisited

NASA Astrophysics Data System (ADS)

Eune, Myungseok; Kim, Wontae

2017-10-01

The Unruh temperature calculated by using the global embedding of the Schwarzschild AdS spacetime into the Minkowski spacetime was identified with the local proper temperature; however, it became imaginary in a certain region outside the event horizon. So, the temperature was assumed to be zero of non-thermal radiation for that region. In this work, we revisit this issue in an exactly soluble two-dimensional Schwarzschild AdS black hole and present an alternative resolution to this problem in terms of the Tolman's procedure. However, the process appears to be non-trivial in the sense that the original procedure assuming the traceless energy-momentum tensor should be extended in such a way that it should cover the non-vanishing case of the energy-momentum tensor in the presence of the trace anomaly. Consequently, we show that the proper temperature turns out to be real everywhere outside the event horizon without any imaginary value, in particular, it vanishes at both the horizon and the asymptotic infinity.

Wormholes minimally violating the null energy condition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bouhmadi-López, Mariam; Lobo, Francisco S N; Martín-Moruno, Prado, E-mail: mariam.bouhmadi@ehu.es, E-mail: fslobo@fc.ul.pt, E-mail: pmmoruno@fc.ul.pt

2014-11-01

We consider novel wormhole solutions supported by a matter content that minimally violates the null energy condition. More specifically, we consider an equation of state in which the sum of the energy density and radial pressure is proportional to a constant with a value smaller than that of the inverse area characterising the system, i.e., the area of the wormhole mouth. This approach is motivated by a recently proposed cosmological event, denoted {sup t}he little sibling of the big rip{sup ,} where the Hubble rate and the scale factor blow up but the cosmic derivative of the Hubble rate doesmore » not [1]. By using the cut-and-paste approach, we match interior spherically symmetric wormhole solutions to an exterior Schwarzschild geometry, and analyse the stability of the thin-shell to linearized spherically symmetric perturbations around static solutions, by choosing suitable properties for the exotic material residing on the junction interface radius. Furthermore, we also consider an inhomogeneous generalization of the equation of state considered above and analyse the respective stability regions. In particular, we obtain a specific wormhole solution with an asymptotic behaviour corresponding to a global monopole.« less

Extended DBI massive gravity with generalized fiducial metric

NASA Astrophysics Data System (ADS)

Chullaphan, Tossaporn; Tannukij, Lunchakorn; Wongjun, Pitayuth

2015-06-01

We consider an extended model of DBI massive gravity by generalizing the fiducial metric to be an induced metric on the brane corresponding to a domain wall moving in five-dimensional Schwarzschild-Anti-de Sitter spacetime. The model admits all solutions of FLRW metric including flat, closed and open geometries while the original one does not. The background solutions can be divided into two branches namely self-accelerating branch and normal branch. For the self-accelerating branch, the graviton mass plays the role of cosmological constant to drive the late-time acceleration of the universe. It is found that the number degrees of freedom of gravitational sector is not correct similar to the original DBI massive gravity. There are only two propagating degrees of freedom from tensor modes. For normal branch, we restrict our attention to a particular class of the solutions which provides an accelerated expansion of the universe. It is found that the number of degrees of freedom in the model is correct. However, at least one of them is ghost degree of freedom which always present at small scale implying that the theory is not stable.

Time delay and magnification centroid due to gravitational lensing by black holes and naked singularities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Virbhadra, K. S.; Keeton, C. R.; Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, NJ 08854

We model the massive dark object at the center of the Galaxy as a Schwarzschild black hole as well as Janis-Newman-Winicour naked singularities, characterized by the mass and scalar charge parameters, and study gravitational lensing (particularly time delay, magnification centroid, and total magnification) by them. We find that the lensing features are qualitatively similar (though quantitatively different) for Schwarzschild black holes, weakly naked, and marginally strongly naked singularities. However, the lensing characteristics of strongly naked singularities are qualitatively very different from those due to Schwarzschild black holes. The images produced by Schwarzschild black hole lenses and weakly naked and marginallymore » strongly naked singularity lenses always have positive time delays. On the other hand, strongly naked singularity lenses can give rise to images with positive, zero, or negative time delays. In particular, for a large angular source position the direct image (the outermost image on the same side as the source) due to strongly naked singularity lensing always has a negative time delay. We also found that the scalar field decreases the time delay and increases the total magnification of images; this result could have important implications for cosmology. As the Janis-Newman-Winicour metric also describes the exterior gravitational field of a scalar star, naked singularities as well as scalar star lenses, if these exist in nature, will serve as more efficient cosmic telescopes than regular gravitational lenses.« less

Schwarzschild black hole encircled by a rotating thin disc: Properties of perturbative solution

NASA Astrophysics Data System (ADS)

Kotlařík, P.; Semerák, O.; Čížek, P.

2018-04-01

Will [Astrophys. J. 191, 521 (1974), 10.1086/152992] solved the perturbation of a Schwarzschild black hole due to a slowly rotating light concentric thin ring, using Green's functions expressed as infinite-sum expansions in multipoles and in the small mass and rotational parameters. In a previous paper [P. Čížek and O. Semerák, Astrophys. J. Suppl. Ser. 232, 14 (2017), 10.3847/1538-4365/aa876b], we expressed the Green functions in closed form containing elliptic integrals, leaving just summation over the mass expansion. Such a form is more practical for numerical evaluation, but mainly for generalizing the problem to extended sources where the Green functions have to be integrated over the source. We exemplified the method by computing explicitly the first-order perturbation due to a slowly rotating thin disc lying between two finite radii. After finding basic parameters of the system—mass and angular momentum of the black hole and of the disc—we now add further properties, namely those which reveal how the disc gravity influences geometry of the black-hole horizon and those of circular equatorial geodesics (specifically, radii of the photon, marginally bound and marginally stable orbits). We also realize that, in the linear order, no ergosphere occurs and the central singularity remains pointlike, and check the implications of natural physical requirements (energy conditions and subluminal restriction on orbital speed) for the single-stream as well as counter-rotating double-stream interpretations of the disc.

Codimension-2 Brane Black Holes

NASA Astrophysics Data System (ADS)

Zamorano, Nelson; Arias, Cesar; Ordenes, Ariel; Guzman, Francisco

2012-03-01

We analyze the geometry associated to a six dimensional solution of the Einstein's equations. It describes a Schwarzschild de-Sitter black hole on a 3-brane, surrounded by a two dimensional compact bulk. A four dimensional effective cosmological constant and a Planck mass are matched to their six dimensional counterpart. Deviation from Newton's law are computed in both of the solutions found. To learn about the geometry of the bulk, we study the geodesics in this sector. At least, in our opinion, there are some features of these solutions that makes worth to pursue this analysis. The singularity associated to the warped bulk is controlled by the mass M of the black hole. It vanishes if we set M=0. In the same context, it makes an interesting problem to study the Gregory-Laflamme instability in this context [1]. Another feature is the rugby ball type of geometry exhibited by these solutions [2]. They end up in two conical singularities at its respective poles. The branes are located precisely at the poles. Besides, a Wick's rotation generates a connection between different solutions. [4pt] [1] R. Gregory and R. Laflamme, Phys. Rev Lett., 70,2837 (1993)[0pt] [2] S. M. Carroll and M. M. Guica, arXiv:hep-th/0302067

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sanchez-Monroy, J.A., E-mail: antosan@gmail.com; Quimbay, C.J., E-mail: cjquimbayh@unal.edu.co; Centro Internacional de Fisica, Bogota D.C.

In the context of a semiclassical approach where vectorial gauge fields can be considered as classical fields, we obtain exact static solutions of the SU(N) Yang-Mills equations in an (n+1)-dimensional curved space-time, for the cases n=1,2,3. As an application of the results obtained for the case n=3, we consider the solutions for the anti-de Sitter and Schwarzschild metrics. We show that these solutions have a confining behavior and can be considered as a first step in the study of the corrections of the spectra of quarkonia in a curved background. Since the solutions that we find in this work aremore » valid also for the group U(1), the case n=2 is a description of the (2+1) electrodynamics in the presence of a point charge. For this case, the solution has a confining behavior and can be considered as an application of the planar electrodynamics in a curved space-time. Finally we find that the solution for the case n=1 is invariant under a parity transformation and has the form of a linear confining solution. - Highlights: Black-Right-Pointing-Pointer We study exact static confining solutions of the SU(N) Yang-Mills equations in an (n+1)-dimensional curved space-time. Black-Right-Pointing-Pointer The solutions found are a first step in the study of the corrections on the spectra of quarkonia in a curved background. Black-Right-Pointing-Pointer A expression for the confinement potential in low dimensionality is found.« less

Throat quantization of the Schwarzschild-Tangherlini(-AdS) black hole

NASA Astrophysics Data System (ADS)

Maeda, Hideki

2018-01-01

By the throat quantization pioneered by Louko and Mäkelä, we derive the mass and area/entropy spectra for the Schwarzschild-Tangherlini-type asymptotically flat or AdS vacuum black hole in arbitrary dimensions. Using the WKB approximation for black holes with large mass, we show that area/entropy is equally spaced for asymptotically flat black holes, while mass is equally spaced for asymptotically AdS black holes. Exact spectra can be obtained for toroidal AdS black holes in arbitrary dimensions including the three-dimensional BTZ black hole.

Numerical simulation of electromagnetic waves in Schwarzschild space-time by finite difference time domain method and Green function method

NASA Astrophysics Data System (ADS)

Jia, Shouqing; La, Dongsheng; Ma, Xuelian

2018-04-01

The finite difference time domain (FDTD) algorithm and Green function algorithm are implemented into the numerical simulation of electromagnetic waves in Schwarzschild space-time. FDTD method in curved space-time is developed by filling the flat space-time with an equivalent medium. Green function in curved space-time is obtained by solving transport equations. Simulation results validate both the FDTD code and Green function code. The methods developed in this paper offer a tool to solve electromagnetic scattering problems.

Schwarzschild fuzzball and explicitly unitary Hawking radiation

NASA Astrophysics Data System (ADS)

Zeng, Ding-fang

2018-05-01

We provide a fuzzball picture for Schwarzschild black holes, in which matters and energy consisting the hole are not positioned on the central point exclusively but oscillate around there in a serial of eigen-modes, each of which features a special level of binding degrees and are quantum mechanically possible to be measured outside the horizon. By listing these modes explicitly for holes as large as 6Mpl, we find that their number increases exponentially with the area. Basing on these results, we construct a simple but explicitly unitary formulation of Hawking radiations.

Half Century of Black-Hole Theory: From Physicists' Purgatory to Mathematicians' Paradise

NASA Astrophysics Data System (ADS)

Carter, Brandon

2006-06-01

Although implicit in the discovery of the Schwarzschild solution 40 years earlier, the issues raised by the theory of what are now known as black holes were so unsettling to physicists of Einstein's generation that the subject remained in a state of semiclandestine gestation until his demise. That turning point — just half a century after Einstein's original foundation of relativity theory, and just half a century ago today — can be considered to mark the birth of black hole theory as a subject of systematic development by physicists of a new and less inhibited generation, whose enthusastic investigations have revealed structures of unforeseen mathematical beauty, even though questions about the physical significance of the concomitant singularities remain controversial.

Strong-field gravitational-wave emission in Schwarzschild and Kerr geometries: some general considerations

NASA Astrophysics Data System (ADS)

Rodríguez, J. F.; Rueda, J. A.; Ruffini, R.

2018-01-01

We have used the perturbations of the exact solutions of the Einstein equations to estimate the relativistic wave emission of a test particle orbiting around a black hole. We show how the hamiltonian equations of motion of a test particle augmented with the radiation-reaction force can establish a priori constraints on the possible phenomena occurring in the merger of compact objects. The dynamical evolution consists of a helicoidal sequence of quasi-circular orbits, induced by the radiation-reaction and the background spacetime. Near the innermost stable circular orbit the evolution is followed by a smooth transition and finally plunges geodesically into the black hole horizon. This analysis gives physical insight of the merger of two equal masses objects.

Accretion onto a higher dimensional black hole

NASA Astrophysics Data System (ADS)

John, Anslyn J.; Ghosh, Sushant G.; Maharaj, Sunil D.

2013-11-01

We examine the steady-state spherically symmetric accretion of relativistic fluids, with a polytropic equation of state, onto a higher-dimensional Schwarzschild black hole. The mass accretion rate, critical radius, and flow parameters are determined and compared with results obtained in standard four dimensions. The accretion rate, M˙, is an explicit function of the black hole mass, M, as well as the gas boundary conditions and the dimensionality, D, of the spacetime. We also find the asymptotic compression ratios and temperature profiles below the accretion radius and at the event horizon. This analysis is a generalization of Michel’s solution to higher dimensions and of the Newtonian expressions of Giddings and Mangano, which consider the accretion of TeV black holes.

The algebraic-hyperbolic approach to the linearized gravitational constraints on a Minkowski background

NASA Astrophysics Data System (ADS)

Winicour, Jeffrey

2017-08-01

An algebraic-hyperbolic method for solving the Hamiltonian and momentum constraints has recently been shown to be well posed for general nonlinear perturbations of the initial data for a Schwarzschild black hole. This is a new approach to solving the constraints of Einstein’s equations which does not involve elliptic equations and has potential importance for the construction of binary black hole data. In order to shed light on the underpinnings of this approach, we consider its application to obtain solutions of the constraints for linearized perturbations of Minkowski space. In that case, we find the surprising result that there are no suitable Cauchy hypersurfaces in Minkowski space for which the linearized algebraic-hyperbolic constraint problem is well posed.

Symmetry operators and decoupled equations for linear fields on black hole spacetimes

NASA Astrophysics Data System (ADS)

Araneda, Bernardo

2017-02-01

In the class of vacuum Petrov type D spacetimes with cosmological constant, which includes the Kerr-(A)dS black hole as a particular case, we find a set of four-dimensional operators that, when composed off shell with the Dirac, Maxwell and linearized gravity equations, give a system of equations for spin weighted scalars associated with the linear fields, that decouple on shell. Using these operator relations we give compact reconstruction formulae for solutions of the original spinor and tensor field equations in terms of solutions of the decoupled scalar equations. We also analyze the role of Killing spinors and Killing-Yano tensors in the spin weight zero equations and, in the case of spherical symmetry, we compare our four-dimensional formulation with the standard 2  +  2 decomposition and particularize to the Schwarzschild-(A)dS black hole. Our results uncover a pattern that generalizes a number of previous results on Teukolsky-like equations and Debye potentials for higher spin fields.

On HPM approximation for the perihelion precession angle in general relativity

NASA Astrophysics Data System (ADS)

Shchigolev, Victor; Bezbatko, Dmitrii

2017-03-01

In this paper, the homotopy perturbation method (HPM) is applied for calculating the perihelion precession angle of planetary orbits in General Relativity. The HPM is quite efficient and is practically well suited for use in many astrophysical and cosmological problems. For our purpose, we applied HPM to the approximate solutions for the orbits in order to calculate the perihelion shift. On the basis of the main idea of HPM, we construct the appropriate homotopy that leads to the problem of solving the set of linear algebraic equations. As a result, we obtain a simple formula for the angle of precession avoiding any restrictions on the smallness of physical parameters. First of all, we consider the simple examples of the Schwarzschild metric and the Reissner - Nordström spacetime of a charged star for which the approximate geodesics solutions are known. Furthermore, the implementation of HPM has allowed us to readily obtain the precession angle for the orbits in the gravitational field of Kiselev black hole.

The Euler-Poisson-Darboux equation for relativists

NASA Astrophysics Data System (ADS)

Stewart, John M.

2009-09-01

The Euler-Poisson-Darboux (EPD) equation is the simplest linear hyperbolic equation in two independent variables whose coefficients exhibit singularities, and as such must be of interest as a paradigm to relativists. Sadly it receives scant treatment in the textbooks. The first half of this review is didactic in nature. It discusses in the simplest terms possible the nature of solutions of the EPD equation for the timelike and spacelike singularity cases. Also covered is the Riemann representation of solutions of the characteristic initial value problem, which is hard to find in the literature. The second half examines a few of the possible applications, ranging from explicit computation of the leading terms in the far-field backscatter from predominantly outgoing radiation in a Schwarzschild space-time, to computing explicitly the leading terms in the matter-induced singularities in plane symmetric space-times. There are of course many other applications and the aim of this article is to encourage relativists to investigate this underrated paradigm.

Gesammelte Werke / Collected Works

NASA Astrophysics Data System (ADS)

Schwarzschild, Karl; Voigt, Hans-Heinrich

Der bekannte Astronom Karl Schwarzschild (1873-1916) gilt als der Begründer der Astrophysik und als hervorragender Forscher mit einer erstaunlichen Bandbreite seiner Interessen. Arbeiten zur Himmelsmechanik, Elektrodynamik und Relativitätstheorie weisen ihn als vorzüglichen Mathematiker und Physiker auf der Höhe seiner Zeit aus. Untersuchungen zur Photographischen Photometrie, Optik und Spektroskopie zeigen den versierten Beobachter, der sein Meßinstrumentarium beherrscht, und schließlich arbeitete Schwarzschild als Astrophysiker an Sternatmosphären, Kometen, Struktur und Dynamik von Sternsystemen. Die in seinem kurzen Leben entstandene Fülle an wissenschaftlichen Arbeiten ist in drei Bänden der Gesamtausgabe gesammelt, ergänzt durch biographisches Material, Annotationen von Fachleuten und einen Essay des Nobelpreisträgers S. Chandrasekhar. The well-known astronomer Karl Schwarzschild (1873-1916) is regarded as the founder of astrophysics and as an exceptionally talented researcher whose interests spanned a remarkably broad spectrum. His work on celestial mechanics, electrodynamics, and relativity theory demonstrates his great abilities as a mathematician and physicist who significantly influenced the science of his times. His investigations of photographic photometry, optics, and spectroscopy display his strengths as an observer who knew his instruments. But above all Schwarzschild pursued questions of astrophysics, addressing in particular stellar atmospheres, comets, and the structure and dynamics of stellar systems. The host of scientific works that he authored in his short life is now collected in the form of this three-volume complete works; it is supplemented by biographical material, notes from some of todays experts, and an essay by the Nobel Laureate S. Chandrasekhar.

Fabrication of nanoscale patterns in lithium fluoride crystal using a 13.5 nm Schwarzschild objective and a laser produced plasma source.

PubMed

Wang, Xin; Mu, Baozhong; Jiang, Li; Zhu, Jingtao; Yi, Shengzhen; Wang, Zhanshan; He, Pengfei

2011-12-01

Lithium fluoride (LiF) crystal is a radiation sensitive material widely used as EUV and soft x-ray detector. The LiF-based detector has high resolution, in principle limited by the point defect size, large field of view, and wide dynamic range. Using LiF crystal as an imaging detector, a resolution of 900 nm was achieved by a projection imaging of test meshes with a Schwarzschild objective operating at 13.5 nm. In addition, by imaging of a pinhole illuminated by the plasma, an EUV spot of 1.5 μm diameter in the image plane of the objective was generated, which accomplished direct writing of color centers with resolution of 800 nm. In order to avoid sample damage and contamination due to the influence of huge debris flux produced by the plasma source, a spherical normal-incidence condenser was used to collect EUV radiation. Together with a description of experimental results, the development of the Schwarzschild objective, the influence of condenser on energy density and the alignment of the imaging system are also reported.

(Non-adiabatic) string creation on nice slices in Schwarzschild black holes

NASA Astrophysics Data System (ADS)

Puhm, Andrea; Rojas, Francisco; Ugajin, Tomonori

2017-04-01

Nice slices have played a pivotal role in the discussion of the black hole information paradox as they avoid regions of strong spacetime curvature and yet smoothly cut through the infalling matter and the outgoing Hawking radiation, thus, justifying the use of low energy field theory. To avoid information loss it has been argued recently, however, that local effective field theory has to break down at the horizon. To assess the extent of this breakdown in a UV complete framework we study string-theoretic effects on nice slices in Schwarzschild black holes. Our purpose is two-fold. First, we use nice slices to address various open questions and caveats of [1] where it was argued that boost-enhanced non-adiabatic string-theoretic effects at the horizon could provide a dynamical mechanism for the firewall. Second, we identify two non-adiabatic effects on nice slices in Schwarzschild black holes: pair production of open strings near the horizon enhanced by the presence of the infinite tower of highly excited string states and a late-time non-adiabatic effect intrinsic to nice slices.

Hawking radiation spectra for scalar fields by a higher-dimensional Schwarzschild-de Sitter black hole

NASA Astrophysics Data System (ADS)

Pappas, T.; Kanti, P.; Pappas, N.

2016-07-01

In this work, we study the propagation of scalar fields in the gravitational background of a higher-dimensional Schwarzschild-de Sitter black hole as well as on the projected-on-the-brane four-dimensional background. The scalar fields have also a nonminimal coupling to the corresponding, bulk or brane, scalar curvature. We perform a comprehensive study by deriving exact numerical results for the greybody factors, and study their profile in terms of particle and spacetime properties. We then proceed to derive the Hawking radiation spectra for a higher-dimensional Schwarzschild-de Sitter black hole, and we study both bulk and brane channels. We demonstrate that the nonminimal field coupling, which creates an effective mass term for the fields, suppresses the energy emission rates while the cosmological constant assumes a dual role. By computing the relative energy rates and the total emissivity ratio for bulk and brane emission, we demonstrate that the combined effect of a large number of extra dimensions and value of the field coupling gives to the bulk channel the clear domination in the bulk-brane energy balance.

(Non-adiabatic) string creation on nice slices in Schwarzschild black holes

DOE PAGES

Puhm, Andrea; Rojas, Francisco; Ugajin, Tomonori

2017-04-27

Nice slices have played a pivotal role in the discussion of the black hole information paradox as they avoid regions of strong spacetime curvature and yet smoothly cut through the infalling matter and the outgoing Hawking radiation, thus, justifying the use of low energy field theory. To avoid information loss it has been argued recently, however, that local effective field theory has to break down at the horizon. To assess the extent of this breakdown in a UV complete framework we study string-theoretic effects on nice slices in Schwarzschild black holes. Here, our purpose is two-fold. First, we use nicemore » slices to address various open questions and caveats of [1] where it was argued that boost-enhanced non-adiabatic string-theoretic effects at the horizon could provide a dynamical mechanism for the firewall. Second, we identify two non-adiabatic effects on nice slices in Schwarzschild black holes: pair production of open strings near the horizon enhanced by the presence of the infinite tower of highly excited string states and a late-time non-adiabatic effect intrinsic to nice slices.« less

(Non-adiabatic) string creation on nice slices in Schwarzschild black holes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Puhm, Andrea; Rojas, Francisco; Ugajin, Tomonori

Nice slices have played a pivotal role in the discussion of the black hole information paradox as they avoid regions of strong spacetime curvature and yet smoothly cut through the infalling matter and the outgoing Hawking radiation, thus, justifying the use of low energy field theory. To avoid information loss it has been argued recently, however, that local effective field theory has to break down at the horizon. To assess the extent of this breakdown in a UV complete framework we study string-theoretic effects on nice slices in Schwarzschild black holes. Here, our purpose is two-fold. First, we use nicemore » slices to address various open questions and caveats of [1] where it was argued that boost-enhanced non-adiabatic string-theoretic effects at the horizon could provide a dynamical mechanism for the firewall. Second, we identify two non-adiabatic effects on nice slices in Schwarzschild black holes: pair production of open strings near the horizon enhanced by the presence of the infinite tower of highly excited string states and a late-time non-adiabatic effect intrinsic to nice slices.« less

A generalized sine condition and performance comparison of Wolter type II and Wolter-Schwarzschild extreme ultraviolet telescopes

NASA Technical Reports Server (NTRS)

Saha, T. T.

1984-01-01

An equation similar to the Abbe sine condition is derived for a Wolter type II telescope. This equation and the sine condition are then combined to produce a so called generalized sine condition. Using the law of reflection, Fermat's principle, the generalized sine condition, and simple geometry the surface equations for a Wolter type II telescope and an equivalent Wolter-Schwarzschild telescope are calculated. The performances of the telescopes are compared in terms of rms blur circle radius at the Gaussian focal plane and at best focus.

Higher dimensional Taub-NUT spaces and applications

NASA Astrophysics Data System (ADS)

Stelea, Cristian Ionut

In the first part of this thesis we discuss classes of new exact NUT-charged solutions in four dimensions and higher, while in the remainder of the thesis we make a study of their properties and their possible applications. Specifically, in four dimensions we construct new families of axisymmetric vacuum solutions using a solution-generating technique based on the hidden SL(2,R) symmetry of the effective action. In particular, using the Schwarzschild solution as a seed we obtain the Zipoy-Voorhees generalisation of the Taub-NUT solution and of the Eguchi-Hanson soliton. Using the C-metric as a seed, we obtain and study the accelerating versions of all the above solutions. In higher dimensions we present new classes of NUT-charged spaces, generalising the previously known even-dimensional solutions to odd and even dimensions, as well as to spaces with multiple NUT-parameters. We also find the most general form of the odd-dimensional Eguchi-Hanson solitons. We use such solutions to investigate the thermodynamic properties of NUT-charged spaces in (A)dS backgrounds. These have been shown to yield counter-examples to some of the conjectures advanced in the still elusive dS/CFT paradigm (such as the maximal mass conjecture and Bousso's entropic N-bound). One important application of NUT-charged spaces is to construct higher dimensional generalisations of Kaluza-Klein magnetic monopoles, generalising the known 5-dimensional Kaluza-Klein soliton. Another interesting application involves a study of time-dependent higher-dimensional bubbles-of-nothing generated from NUT-charged solutions. We use them to test the AdS/CFT conjecture as well as to generate, by using stringy Hopf-dualities, new interesting time-dependent solutions in string theory. Finally, we construct and study new NUT-charged solutions in higher-dimensional Einstein-Maxwell theories, generalising the known Reissner-Nordstrom solutions.

On the global Casimir effect in the Schwarzschild spacetime

NASA Astrophysics Data System (ADS)

Muniz, C. R.; Tahim, M. O.; Cunha, M. S.; Vieira, H. S.

2018-01-01

In this paper we study the vacuum quantum fluctuations of the stationary modes of an uncharged scalar field with mass m around a Schwarzschild black hole with mass M, at zero and non-zero temperatures. The procedure consists of calculating the energy eigenvalues starting from the exact solutions found for the dynamics of the scalar field, considering a frequency cutoff in which the particle is not absorbed by the black hole. From this result, we obtain the exterior contributions for the vacuum energy associated to the stationary states of the scalar field, by considering the half-summing of the levels of energy and taking into account the respective degeneracies, in order to better capture the nontrivial topology of the black hole spacetime. Then we use the Riemann's zeta function to regularize the vacuum energy thus found. Such a regularized quantity is the Casimir energy, whose analytic computation we show to yield a convergent series. The Casimir energy obtained does not take into account any boundaries artificially imposed on the system, just the nontrivial spacetime topology associated to the source and its singularity. We suggest that this latter manifests itself through the vacuum tension calculated on the event horizon. We also investigate the problem by considering the thermal corrections via Helmholtz free energy calculation, computing the Casimir internal energy, the corresponding tension on the event horizon, the Casimir entropy, and the thermal capacity of the regularized quantum vacuum, analyzing their behavior at low and high temperatures, pointing out the thermodynamic instability of the system in the considered regime, i.e. mMll 1.

On the consistency of the Oppenheimer-Snyder solution for a dust star. Reply to Marshall's criticism

NASA Astrophysics Data System (ADS)

Zakir, Zahid

2018-02-01

The recent alternative to the Oppenheimer-Snyder (OS) solution for a dust star proposed by Marshall in the paper "Gravitational collapse without black holes" (Astrophys. Space Sci. 342:329, 2012) is analyzed. It is shown that this proposal leads to a non-diagonal metric, with which the Einstein equations become practically unsolvable. Any ansatz proposed as their exact solution turns out to be arbitrary and may be unlimited number of the such solutions. This is due to the fact that an auxiliary function y(R,r), introduced by OS as t=M(y), is unambiguously fixed by the diagonality condition and the matching on the surface, and thus in the non-diagonal case it remains arbitrary. It is also shown that the OS solution, as a description in terms of the Schwarzschild coordinates, leads to a frozen star (or frozar) picture not only for the surface, asymptotically freezing outside the gravitational radius, but for interior layers too which also freeze near their own asymptotes. At most of the inner region these asymptotes are located almost equidistantly and only for layers initially close to the surface they become denser. The reason for the such densifying is not "a gravitational repulsion", but their later freezing and higher spatial contractions, while they remain be uniform and free falling in the comoving frames.

Michel accretion of a polytropic fluid with adiabatic index \\gamma \\gt 5/3: global flows versus homoclinic orbits

NASA Astrophysics Data System (ADS)

Chaverra, Eliana; Mach, Patryk; Sarbach, Olivier

2016-05-01

We analyze the properties of a polytropic fluid that is radially accreted into a Schwarzschild black hole. The case where the adiabatic index γ lies in the range of 1\\lt γ ≤slant 5/3 has been treated in previous work. In this article, we analyze the complementary range of 5/3\\lt γ ≤slant 2. To this purpose, the problem is cast into an appropriate Hamiltonian dynamical system, whose phase flow is analyzed. While, for 1\\lt γ ≤slant 5/3, the solutions are always characterized by the presence of a unique critical saddle point, we show that, when 5/3\\lt γ ≤slant 2, an additional critical point might appear, which is a center point. For the parametrization used in this paper, we prove that, whenever this additional critical point appears, there is a homoclinic orbit. Solutions corresponding to homoclinic orbits differ from standard transonic solutions with vanishing asymptotic velocities in two aspects: they are local (i.e., they cannot be continued to arbitrarily large radii); the dependence of the density or the value of the velocity on the radius is not monotonic.

The Black Hole in the Most Massive Ultracompact Dwarf Galaxy M59-UCD3

NASA Astrophysics Data System (ADS)

Ahn, Christopher P.; Seth, Anil C.; Cappellari, Michele; Krajnović, Davor; Strader, Jay; Voggel, Karina T.; Walsh, Jonelle L.; Bahramian, Arash; Baumgardt, Holger; Brodie, Jean; Chilingarian, Igor; Chomiuk, Laura; den Brok, Mark; Frank, Matthias; Hilker, Michael; McDermid, Richard M.; Mieske, Steffen; Neumayer, Nadine; Nguyen, Dieu D.; Pechetti, Renuka; Romanowsky, Aaron J.; Spitler, Lee

2018-05-01

We examine the internal properties of the most massive ultracompact dwarf galaxy (UCD), M59-UCD3, by combining adaptive-optics-assisted near-IR integral field spectroscopy from Gemini/NIFS and Hubble Space Telescope (HST) imaging. We use the multiband HST imaging to create a mass model that suggests and accounts for the presence of multiple stellar populations and structural components. We combine these mass models with kinematics measurements from Gemini/NIFS to find a best-fit stellar mass-to-light ratio (M/L) and black hole (BH) mass using Jeans anisotropic models (JAMs), axisymmetric Schwarzschild models, and triaxial Schwarzschild models. The best-fit parameters in the JAM and axisymmetric Schwarzschild models have BHs between 2.5 and 5.9 million solar masses. The triaxial Schwarzschild models point toward a similar BH mass but show a minimum χ 2 at a BH mass of ∼0. Models with a BH in all three techniques provide better fits to the central V rms profiles, and thus we estimate the BH mass to be {4.2}-1.7+2.1× {10}6 M ⊙ (estimated 1σ uncertainties). We also present deep radio imaging of M59-UCD3 and two other UCDs in Virgo with dynamical BH mass measurements, and we compare these to X-ray measurements to check for consistency with the fundamental plane of BH accretion. We detect faint radio emission in M59cO but find only upper limits for M60-UCD1 and M59-UCD3 despite X-ray detections in both these sources. The BH mass and nuclear light profile of M59-UCD3 suggest that it is the tidally stripped remnant of a ∼109–1010 M ⊙ galaxy.

Infinite derivative gravity: non-singular cosmology & blackhole solutions

NASA Astrophysics Data System (ADS)

Mazumdar, A.

Both Einstein’s theory of General Relativity and Newton’s theory of gravity possess a short distance and small time scale catastrophe. The blackhole singularity and cosmological Big Bang singularity problems highlight that current theories of gravity are incomplete description at early times and small distances. I will discuss how one can potentially resolve these fundamental problems at a classical level and quantum level. In particular, I will discuss infinite derivative theories of gravity, where gravitational interactions become weaker in the ultraviolet, and therefore resolving some of the classical singularities, such as Big Bang and Schwarzschild singularity for compact non-singular objects with mass up to 1025 grams. In this lecture, I will discuss quantum aspects of infinite derivative gravity and discuss few aspects which can make the theory asymptotically free in the UV.

Scalar resonant frequencies and Hawking effect of an f ( R ) global monopole

NASA Astrophysics Data System (ADS)

Vieira, H. S.; Morais Graça, J. P.; Bezerra, V. B.

2017-09-01

Massive scalar fields are considered in the gravitational field produced by a Schwarzschild black hole with a global monopole in f(R) gravity. The exact solution of the radial part of the Klein-Gordon equation in this background is obtained and is given in terms of the general Heun functions. We apply the properties of the general Heun functions to study the Hawking radiation and the resonant frequencies of scalar particles. H.S.V. is funded by the Brazilian research agencies CNPq (research Project No. 140612/2014-9) and CAPES (PDSE Process No. 88881.133092/2016-01). J.P.M.G. is funded by the CNPq through the research Project No. 150565/2016-0. V.B.B. is partially supported by the CNPq through the research Project No. 304553/2010-7

Charges in gravitational fields: From Fermi, via Hanni-Ruffini-Wheeler, to the 'electric Meissner effect'

NASA Astrophysics Data System (ADS)

Ruffini, R.

2004-07-01

Recent developments in obtaining a detailed model for gamma-ray bursts have shown the need for a deeper understanding of phenomena described by solutions of the Einstein-Maxwell equations, reviving interest in the behavior of charges close to a black hole. In particular a drastic difference has been found between the lines of force of a charged test particle in the fields of Schwarzschild and Reissner-Nordström black holes. This difference characterizes a general relativistic effect for the electric field of a charged test particle around a (charged) Reissner-Nordström black hole similar to the “Meissner effect” for a magnetic field around a superconductor. These new results are related to earlier work by Fermi and Hanni-Ruffini-Wheeler.

An exact solution to the Einstein-Maxwell equations representing a nonspherical, highly charged object

NASA Astrophysics Data System (ADS)

Menon, Govind K.

The Reissner-Nordstrom solution possesses a naked singularity when e2 > m2, where m is the mass and e is the net charge of the system. Also, the singularity at r = 0 is repulsive (i.e., no timelike geodesics (neutral particles) can reach the singularity). These unusual properties of the Reissner-Nordstrom geometry are considered as an accident resulting from the highly symmetric nature of the space-time. Here we wish to generalize the condition of spherical symmetry to axial symmetry and to probe into the issues of naked singularity and gravitational repulsion. To do this, we must construct a nonspherical solution to the Einstein-Maxwell set of equations in the event that e2 > m2. The Erez-Rosen extension of the vacuum Schwarzschild solution to the non-spherical case gave one of the first physically significant solutions of the Einstein field equations. Nonvacuum extensions of the Erez-Rosen solution representing a non-spherical mass containing a very high net charge (i.e., when e2 > m2) will be discussed. The special case of spherical symmetry, as would be expected, results in the Reissner-Nordstrom solution. The search for the physical singularities involves the calculation of a nontrivial scalar constructed from the Riemann curvature tensor. As it turns out, the resulting geometry does indeed possess a naked singularity. In addition, the space-time also entertains gravitational repulsion. However, unlike the Reissner-Nordstrom solution, it has been found that all timelike geodesics are not necessarily repelled from the origin.

Large N phase transitions and the fate of small Schwarzschild-AdS black holes

NASA Astrophysics Data System (ADS)

Yaffe, Laurence G.

2018-01-01

Sufficiently small Schwarzschild-AdS black holes in asymptotically global AdS5×S5 spacetime are known to become dynamically unstable toward deformation of the internal S5 geometry. The resulting evolution of such an unstable black hole is related, via holography, to the dynamics of supercooled plasma which has reached the limit of metastability in maximally supersymmetric large-N Yang-Mills theory on R ×S3. Puzzles related to the resulting dynamical evolution are discussed, with a key issue involving differences between the large-N limit in the dual field theory and typical large volume thermodynamic limits.

Hawking radiation, Unruh radiation, and the equivalence principle.

PubMed

Singleton, Douglas; Wilburn, Steve

2011-08-19

We compare the response function of an Unruh-DeWitt detector for different space-times and different vacua and show that there is a detailed violation of the equivalence principle. In particular comparing the response of an accelerating detector to a detector at rest in a Schwarzschild space-time we find that both detectors register thermal radiation, but for a given, equivalent acceleration the fixed detector in the Schwarzschild space-time measures a higher temperature. This allows one to locally distinguish the two cases. As one approaches the horizon the two temperatures have the same limit so that the equivalence principle is restored at the horizon. © 2011 American Physical Society

Effective temperatures and radiation spectra for a higher-dimensional Schwarzschild-de Sitter black hole

NASA Astrophysics Data System (ADS)

Kanti, P.; Pappas, T.

2017-07-01

The absence of a true thermodynamical equilibrium for an observer located in the causal area of a Schwarzschild-de Sitter spacetime has repeatedly raised the question of the correct definition of its temperature. In this work, we consider five different temperatures for a higher-dimensional Schwarzschild-de Sitter black hole: the bare T0, the normalized TBH, and three effective ones given in terms of both the black-hole and cosmological horizon temperatures. We find that these five temperatures exhibit similarities but also significant differences in their behavior as the number of extra dimensions and the value of the cosmological constant are varied. We then investigate their effect on the energy emission spectra of Hawking radiation. We demonstrate that the radiation spectra for the normalized temperature TBH—proposed by Bousso and Hawking over twenty years ago—leads to the dominant emission curve, while the other temperatures either support a significant emission rate only in a specific Λ regime or have their emission rates globally suppressed. Finally, we compute the bulk-over-brane emissivity ratio and show that the use of different temperatures may lead to different conclusions regarding the brane or bulk dominance.

Advection-dominated Inflow/Outflows from Evaporating Accretion Disks.

PubMed

Turolla; Dullemond

2000-03-01

In this Letter we investigate the properties of advection-dominated accretion flows (ADAFs) fed by the evaporation of a Shakura-Sunyaev accretion disk (SSD). In our picture, the ADAF fills the central cavity evacuated by the SSD and extends beyond the transition radius into a coronal region. We find that, because of global angular momentum conservation, a significant fraction of the hot gas flows away from the black hole, forming a transsonic wind, unless the injection rate depends only weakly on radius (if r2sigma&d2;~r-xi, xi<1&solm0;2). The Bernoulli number of the inflowing gas is negative if the transition radius is less, similar100 Schwarzschild radii, so matter falling into the hole is gravitationally bound. The ratio of inflowing to outflowing mass is approximately 1/2, so in these solutions the accretion rate is of the same order as in standard ADAFs and much larger than in advection-dominated inflow/outflow models. The possible relevance of evaporation-fed solutions to accretion flows in black hole X-ray binaries is briefly discussed.

Numerical 3+1 General Relativistic Magnetohydrodynamics: A Local Characteristic Approach

NASA Astrophysics Data System (ADS)

Antón, Luis; Zanotti, Olindo; Miralles, Juan A.; Martí, José M.; Ibáñez, José M.; Font, José A.; Pons, José A.

2006-01-01

We present a general procedure to solve numerically the general relativistic magnetohydrodynamics (GRMHD) equations within the framework of the 3+1 formalism. The work reported here extends our previous investigation in general relativistic hydrodynamics (Banyuls et al. 1997) where magnetic fields were not considered. The GRMHD equations are written in conservative form to exploit their hyperbolic character in the solution procedure. All theoretical ingredients necessary to build up high-resolution shock-capturing schemes based on the solution of local Riemann problems (i.e., Godunov-type schemes) are described. In particular, we use a renormalized set of regular eigenvectors of the flux Jacobians of the relativistic MHD equations. In addition, the paper describes a procedure based on the equivalence principle of general relativity that allows the use of Riemann solvers designed for special relativistic MHD in GRMHD. Our formulation and numerical methodology are assessed by performing various test simulations recently considered by different authors. These include magnetized shock tubes, spherical accretion onto a Schwarzschild black hole, equatorial accretion onto a Kerr black hole, and magnetized thick disks accreting onto a black hole and subject to the magnetorotational instability.

General theories of linear gravitational perturbations to a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Tattersall, Oliver J.; Ferreira, Pedro G.; Lagos, Macarena

2018-02-01

We use the covariant formulation proposed by Tattersall, Lagos, and Ferreira [Phys. Rev. D 96, 064011 (2017), 10.1103/PhysRevD.96.064011] to analyze the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasinormal modes of perturbed black holes may be affected by modifications to general relativity. We restrict ourselves to single-tensor, scalar-tensor and vector-tensor diffeomorphism-invariant gravity models in a Schwarzschild black hole background. We show explicitly the full covariant form of the quadratic actions in such cases, which allow us to then analyze odd parity (axial) and even parity (polar) perturbations simultaneously in a straightforward manner.

Accretion onto a noncommutative-inspired Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Gangopadhyay, Sunandan; Paik, Biplab; Mandal, Rituparna

2018-05-01

In this paper, we investigate the problem of ordinary baryonic matter accretion onto the noncommutative (NC) geometry-inspired Schwarzschild black hole. The fundamental equations governing the spherically symmetric steady state matter accretion are deduced. These equations are seen to be modified due to the presence of noncommutativity. The matter accretion rate is computed and is found to increase rapidly with the increase in strength of the NC parameter. The sonic radius reduces while the sound speed at the sonic point increases with the increase in the strength of noncommutativity. The profile of the thermal environment is finally investigated below the sonic radius and at the event horizon and is found to be affected by noncommutativity.

Probing quantum entanglement in the Schwarzschild space-time beyond the single-mode approximation

NASA Astrophysics Data System (ADS)

He, Juan; Ding, Zhi-Yong; Ye, Liu

2018-05-01

In this paper, we deduce the vacuum structure for Dirac fields in the background of Schwarzschild space-time beyond the single-mode approximation and discuss the performance of quantum entanglement between particle and antiparticle modes of a Dirac field with Hawking effect. It is shown that Hawking radiation does not always destroy the physically accessible entanglement, and entanglement amplification may happen in some cases. This striking result is different from that of the single-mode approximation, which holds that the Hawking radiation can only destroy entanglement. Lastly, we analyze the physically accessible entanglement relation outside the event horizon and demonstrate that the monogamy inequality is constantly established regardless of the choice of given parameters.

Hot spaghetti: Viscous gravitational collapse

NASA Astrophysics Data System (ADS)

Müller, Berndt; Schäfer, Andreas

2018-02-01

We explore the fate of matter falling into a macroscopic Schwarzschild black hole for the simplified case of a radially collapsing thin spherical shell for which the back reaction of the geometry can be neglected. We treat the internal dynamics of the in-falling matter in the framework of viscous relativistic hydrodynamics and calculate how the internal temperature of the collapsing matter evolves as it falls toward the Schwarzschild singularity. We find that viscous hydrodynamics fails when either the dissipative radial pressure exceeds the thermal pressure and the total radial pressure becomes negative, or the time scale of variation of the tidal forces acting on the collapsing matter becomes shorter than the characteristic hydrodynamic response time.

Interior volume of (1 + D)-dimensional Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Bhaumik, Nilanjandev; Majhi, Bibhas Ranjan

2018-01-01

We calculate the maximum interior volume, enclosed by the event horizon, of a (1 + D)-dimensional Schwarzschild black hole. Taking into account the mass change due to Hawking radiation, we show that the volume increases towards the end of the evaporation. This fact is not new as it has been observed earlier for four-dimensional case. The interesting point we observe is that this increase rate decreases towards the higher value of space dimensions D; i.e. it is a decelerated expansion of volume with the increase of spatial dimensions. This implies that for a sufficiently large D, the maximum interior volume does not change. The possible implications of these results are also discussed.

Spacetime can be neither discrete nor continuous

NASA Astrophysics Data System (ADS)

Corda, Christian

2018-04-01

We show that our recent Bohr-like approach to black hole (BH) quantum physics implies that spacetime quantization could be energy-dependent. Thus, in a certain sense, spacetime can be neither discrete nor continuous. Our approach also permits to show that the “volume quantum” of the Schwarzschild spacetime increases with increasing energy during BH evaporation and arrives at a maximum value when the Planck scale is reached and the generalized uncertainty principle (GUP) prevents the total BH evaporation. Remarkably, this result does not depend on the BH original mass. The interesting consequence is that the behavior of BH evaporation should be the same for all Schwarzschild BHs when the Planck scale is approached.

Aplanatic Two-Surface Systems: The Optics Of Our Grandfathers

NASA Astrophysics Data System (ADS)

Krautter, Martin

1986-10-01

Karl Schwarzschild (1873 - 1916)1 has set up the 2-mirror systems as a 2-parameter mani-fold. He constructed them for primary aplanatism with conic section surfaces, and for finite aplanatism with numerically determined surfaces of revolution. Developing from the still older 2-paraboloid telescopes, conceived by Marin Mersenne, the systems since designed fill three domains of existence. The grazing incidence systems too (the Wolter-Schwarz-schild systems) have their loci on this map. Martin Linnemann (born 1880), student of Karl Schwarzschild, designed the first lenses, made aplanatic with two general surfaces of revolution2. For later authors remained only to vary image scale to non-zero values, and to adapt the design method to computer use.

Scattering of massless fermions by Schwarzschild and Reissner-Nordström black holes

NASA Astrophysics Data System (ADS)

Sporea, Ciprian A.

2017-12-01

We study the scattering of massless Dirac fermions by Schwarzschild and Reissner-Nordström black holes. This is done by applying partial wave analysis to the scattering modes obtained after solving the massless Dirac equation in the asymptotic regions of the two black hole geometries. We successfully obtain analytic phase shifts, with the help of which the scattering cross section is computed. The glory and spiral scattering phenomena are shown to be present, as in the case of massive fermion scattering by black holes. Supported by a grant of the Ministry of National Education and Scientific Research, RDI Programme for Space Technology and Advanced Research - STAR, project number 181/20.07.2017

The Effect of Hawking Radation on Fermion Re-Inflation of a Schwartszchild Kugelblitz

NASA Astrophysics Data System (ADS)

Lee, J. S.

The implementation of laser-created subatomic black holes (Schwarzschild Kugelblitzes or SKs) as propulsive and power sources for interstellar starships has been presented in the literature [l]. SKs with life expectancies of only several years resulting from petawatt Hawking Radiation suggest the appeal of a mechanism to "re-inflate" the SK. This paper calculates the absorption cross-sections and absorption probabilities of attometer Schwarzschild Kugelblitzes, and demonstrates the need for incoming inflating particles to have an energy in the TeV-PeV range. The interaction between collimated re-inflating fermions and the instantaneous spectrum of Hawking radiation, and the challenges associated with subnuclear-scale beam collimation are examined.

Tunneling from the past horizon

NASA Astrophysics Data System (ADS)

Kang, Subeom; Yeom, Dong-han

2018-04-01

We investigate a tunneling and emission process of a thin-shell from a Schwarzschild black hole, where the shell was initially located beyond the Einstein-Rosen bridge and finally appears at the right side of the Penrose diagram. In order to obtain such a solution, we should assume that the areal radius of the black hole horizon increases after the tunneling. Hence, there is a parameter range such that the tunneling rate is exponentially enhanced, rather than suppressed. We may have two interpretations regarding this. First, such a tunneling process from the past horizon is improbable by physical reasons; second, such a tunneling is possible in principle, but in order to obtain a stable Einstein-Rosen bridge, one needs to restrict the parameter spaces. If such a process is allowed, this can be a nonperturbative contribution to Einstein-Rosen bridges as well as eternal black holes.

Effect of the cosmological constant on halo size

NASA Astrophysics Data System (ADS)

Kulchoakrungsun, Ekapob; Lam, Adrian; Lowe, David A.

2018-04-01

In this work, we consider the effect of the cosmological constant on galactic halo size. As a model, we study the general relativistic derivation of orbits in the Schwarzschild-de Sitter metric. We find that there exists a length scale rΛ corresponding to a maximum size of a circular orbit of a test mass in a gravitationally bound system, which is the geometric mean of the cosmological horizon size squared and the Schwarzschild radius. This agrees well with the size of a galactic halo when the effects of dark matter are included. The size of larger structures such as galactic clusters and superclusters are also well-approximated by this scale. This model provides a simplified approach to computing the size of such structures without the usual detailed dynamical models. Some of the more detailed approaches that appear in the literature are reviewed, and we find the length scales agree to within a factor of order one. Finally, we note the length scale associated with the effects of MOND or Verlinde’s emergent gravity, which offer explanations of the flattening of galaxy rotation curves without invoking dark matter, may be expressed as the geometric mean of the cosmological horizon size and the Schwarzschild radius, which is typically 100 times smaller than rΛ.

Astronomy from Olbers to Schwarzschild. (German Title: Astronomie von Olbers bis Schwarzschild)

NASA Astrophysics Data System (ADS)

Dick, Wolfgang R.; Hamel, Jürgen

This issue comprises talks presented 2000 September 18 at the colloquium ``International relations in astronomy'' it is supplemented by additional articles about this topic. The foundation of the international ``Vereinigte Astronomische Gesellschaft'', which took place in 1800 in Bremen, prompted us to investigate the development of astronomy in German-speaking regions, and its international relations during the 19th century. We investigate the activities of famous astronomers like W. Olbers, J.E. Bode, F.X. von Zach, J.H. Schroeter, H.C. Schumacher and K. Schwarzschild, as well as those of their less famous professional colleagues like J.G. Schrader and L. de Ball. The geographical spectrum extends from Bremen and Lilienthal over Kiel, Gotha and Dresden to Copenhagen, Vienna and Chile. Among the topics are: telescope construction, including telescopes made by Herschel, the rediscovery of the minor planet Ceres 1801/02, the Berlin ``Astronomisches Jahrbuch'', the foundation of the ``Astronomische Nachrichten'', the evolution from the ``Vereinigte Astronomische Gesellschaft'' to the present-day ``Astronomische Gesellschaft'', the research at the Kuffner Observatory in Vienna, the professionalization in astronomy, and the attempts of many countries to establish a southern observatory in Chile. A listing of astronomical monuments in Lilienthal and Bremen concludes the book. All papers are written in German with English abstracts.

Perturbation of a Schwarzschild Black Hole Due to a Rotating Thin Disk

DOE Office of Scientific and Technical Information (OSTI.GOV)

Čížek, P.; Semerák, O., E-mail: oldrich.semerak@mff.cuni.cz

Will, in 1974, treated the perturbation of a Schwarzschild black hole due to a slowly rotating, light, concentric thin ring by solving the perturbation equations in terms of a multipole expansion of the mass-and-rotation perturbation series. In the Schwarzschild background, his approach can be generalized to perturbation by a thin disk (which is more relevant astrophysically), but, due to rather bad convergence properties, the resulting expansions are not suitable for specific (numerical) computations. However, we show that Green’s functions, represented by Will’s result, can be expressed in closed form (without multipole expansion), which is more useful. In particular, they canmore » be integrated out over the source (a thin disk in our case) to yield good converging series both for the gravitational potential and for the dragging angular velocity. The procedure is demonstrated, in the first perturbation order, on the simplest case of a constant-density disk, including the physical interpretation of the results in terms of a one-component perfect fluid or a two-component dust in a circular orbit about the central black hole. Free parameters are chosen in such a way that the resulting black hole has zero angular momentum but non-zero angular velocity, as it is just carried along by the dragging effect of the disk.« less

Line Emission from an Accretion Disk Around a Rotating Black Hole: Toward a Measurement of Frame Dragging

NASA Technical Reports Server (NTRS)

Bromley, Benjamin C.; Chen, Kaiyou; Miller, Warner A.

1997-01-01

Line emission from an accretion disk and a corotating hot spot about a rotating black hole are considered for possible signatures of the frame-dragging effect. We explicitly compare integrated line profiles from a geometrically thin disk about a Schwarzschild and an extreme Kerr black hole, and show that the line profile differences are small if the inner radius of the disk is near or above the Schwarzschild stable-orbit limit of radius 6GM/sq c. However, if the inner disk radius extends below this limit, as is Possible in the extreme Kerr spacetime, then differences can become significant, especially if the disk emissivity is stronger near the inner regions. We demonstrate that the first three moments of a line profile define a three-dimensional space in which the presence of material at small radii becomes quantitatively evident in broad classes of disk models. In the context of the simple, thin disk paradigm, this moment-mapping scheme suggests formally that the iron line detected by the Advanced Satellite,for Cosmology and Astrophysics mission from MCG --6-30-15 (Tanaka et al.) is approximately 3 times more likely to originate from a disk about a rotating black hole than from a Schwarzschild system. A statistically significant detection of black hole rotation in this way may be achieved after only modest improvements in the quality of data. We also consider light curves and frequency shifts in line emission as a function of time for corotating hot spots in extreme Kerr and Schwarzschild geometries. The frequency-shift profile is a valuable measure of orbital parameters and might possibly be used to detect frame dragging even at radii approaching 6GM/sq c if the inclination angle of the orbital plane is large. The light curve from a hot spot shows differences as well, although these too are pronounced only at large inclination angles.

Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field

NASA Astrophysics Data System (ADS)

Karagiorgos, A.; Pailas, T.; Dimakis, N.; Terzis, Petros A.; Christodoulakis, T.

2018-03-01

We consider a Bianchi type III axisymmetric geometry in the presence of an electromagnetic field. A first result at the classical level is that the symmetry of the geometry need not be applied on the electromagnetic tensor Fμν the algebraic restrictions, implied by the Einstein field equations to the stress energy tensor Tμν, suffice to reduce the general Fμν to the appropriate form. The classical solution thus found contains a time dependent electric and a constant magnetic charge. The solution is also reachable from the corresponding mini-superspace action, which is strikingly similar to the Reissner-Nordstr{öm one. This points to a connection between the black hole geometry and the cosmological solution here found, which is the analog of the known correlation between the Schwarzschild and the Kantowski-Sachs metrics. The configuration space is drastically modified by the presence of the magnetic charge from a 3D flat to a 3D pp wave geometry. We map the emerging linear and quadratic classical integrals of motion, to quantum observables. Along with the Wheeler-DeWitt equation these observables provide unique, up to constants, wave functions. The employment of a Bohmian interpretation of these quantum states results in deterministic (semi-classical) geometries most of which are singularity free.

Integrability in conformally coupled gravity: Taub-NUT spacetimes and rotating black holes

NASA Astrophysics Data System (ADS)

Bardoux, Yannis; Caldarelli, Marco M.; Charmousis, Christos

2014-05-01

We consider four dimensional stationary and axially symmetric spacetimes for conformally coupled scalar-tensor theories. We show that, in analogy to the Lewis-Papapetrou problem in General Relativity (GR), the theory at hand can be recast in an analogous integrable form. We give the relevant rod formalism, introduced by Weyl for vacuum GR, explicitly giving the rod structure of the black hole of Bocharova et al. and Bekenstein (BBMB), in complete analogy to the Schwarzschild solution. The additional scalar field is shown to play the role of an extra Weyl potential. We then employ the Ernst method as a concrete solution generating example to obtain the Taub-NUT version of the BBMB hairy black hole. The solution is easily extended to include a cosmological constant. We show that the anti-de Sitter hyperbolic version of this solution is free of closed timelike curves that plague usual Taub-NUT metrics, and thus consists of a rotating, asymptotically locally anti-de Sitter black hole. This stationary solution has no curvature singularities whatsoever in the conformal frame, and the NUT charge is shown here to regularize the central curvature singularity of the corresponding static black hole. Given our findings we discuss the anti-de Sitter hyperbolic version of Taub-NUT in four dimensions, and show that the curvature singularity of the NUT-less solution is now replaced by a neighbouring chronological singularity screened by horizons. We argue that the properties of this rotating black hole are very similar to those of the rotating BTZ black hole in three dimensions.

ROTATING ACCRETION FLOWS: FROM INFINITY TO THE BLACK HOLE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Jason; Ostriker, Jeremiah; Sunyaev, Rashid, E-mail: jgli@astro.princeton.edu

2013-04-20

Accretion onto a supermassive black hole of a rotating inflow is a particularly difficult problem to study because of the wide range of length scales involved. There have been broadly utilized analytic and numerical treatments of the global properties of accretion flows, but detailed numerical simulations are required to address certain critical aspects. We use the ZEUS code to run hydrodynamical simulations of rotating, axisymmetric accretion flows with Bremsstrahlung cooling, considering solutions for which the centrifugal balance radius significantly exceeds the Schwarzschild radius, with and without viscous angular momentum transport. Infalling gas is followed from well beyond the Bondi radiusmore » down to the vicinity of the black hole. We produce a continuum of solutions with respect to the single parameter M-dot{sub B}/ M-dot{sub Edd}, and there is a sharp transition between two general classes of solutions at an Eddington ratio of M-dot{sub B}/M-dot{sub Edd}{approx}few Multiplication-Sign 10{sup -2}. Our high inflow solutions are very similar to the standard Shakura and Sunyaev results. But our low inflow results are to zeroth order the stationary Papaloizou and Pringle solution, which has no accretion. To next order in the small, assumed viscosity they show circulation, with disk and conical wind outflows almost balancing inflow. These solutions are characterized by hot, vertically extended disks, and net accretion proceeds at an extremely low rate, only of order {alpha} times the inflow rate. Our simulations have converged with respect to spatial resolution and temporal duration, and they do not depend strongly on our choice of boundary conditions.« less

A sensitive EUV Schwarzschild microscope for plasma studies with sub-micrometer resolution

DOE PAGES

Zastrau, U.; Rodel, C.; Nakatsutsumi, M.; ...

2018-02-05

We present an extreme ultraviolet (EUV) microscope using a Schwarzschild objective which is optimized for single-shot sub-micrometer imaging of laser-plasma targets. The microscope has been designed and constructed for imaging the scattering from an EUV-heated solid-density hydrogen jet. Here, imaging of a cryogenic hydrogen target was demonstrated using single pulses of the free-electron laser in Hamburg (FLASH) free-electron laser at a wavelength of 13.5 nm. In a single exposure, we observe a hydrogen jet with ice fragments with a spatial resolution in the sub-micrometer range. In situ EUV imaging is expected to enable novel experimental capabilities for warm dense mattermore » studies of micrometer-sized samples in laser-plasma experiments.« less

Optical Design for a Survey X-Ray Telescope

NASA Technical Reports Server (NTRS)

Saha, Timo T.; Zhang, William W.; McClelland, Ryan S.

2014-01-01

Optical design trades are underway at the Goddard Space Flight Center to define a telescope for an x-ray survey mission. Top-level science objectives of the mission include the study of x-ray transients, surveying and long-term monitoring of compact objects in nearby galaxies, as well as both deep and wide-field x-ray surveys. In this paper we consider Wolter, Wolter-Schwarzschild, and modified Wolter-Schwarzschild telescope designs as basic building blocks for the tightly nested survey telescope. Design principles and dominating aberrations of individual telescopes and nested telescopes are discussed and we compare the off-axis optical performance at 1.0 KeV and 4.0 KeV across a 1.0-degree full field-of-view.

A sensitive EUV Schwarzschild microscope for plasma studies with sub-micrometer resolution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zastrau, U.; Rodel, C.; Nakatsutsumi, M.

We present an extreme ultraviolet (EUV) microscope using a Schwarzschild objective which is optimized for single-shot sub-micrometer imaging of laser-plasma targets. The microscope has been designed and constructed for imaging the scattering from an EUV-heated solid-density hydrogen jet. Here, imaging of a cryogenic hydrogen target was demonstrated using single pulses of the free-electron laser in Hamburg (FLASH) free-electron laser at a wavelength of 13.5 nm. In a single exposure, we observe a hydrogen jet with ice fragments with a spatial resolution in the sub-micrometer range. In situ EUV imaging is expected to enable novel experimental capabilities for warm dense mattermore » studies of micrometer-sized samples in laser-plasma experiments.« less

Design and analysis of multilayer x ray/XUV microscope

NASA Technical Reports Server (NTRS)

Shealy, David L.

1990-01-01

The design and analysis of a large number of normal incidence multilayer x ray microscopes based on the spherical mirror Schwarzschild configuration is examined. Design equations for the spherical mirror Schwarzschild microscopes are summarized and used to evaluate mirror parameters for microscopes with magnifications ranging from 2 to 50x. Ray tracing and diffraction analyses are carried out for many microscope configurations to determine image resolution as a function of system parameters. The results are summarized in three publication included herein. A preliminary study of advanced reflecting microscope configurations, where aspherics are used in place of the spherical microscope mirror elements, has indicated that the aspherical elements will improve off-axis image resolution and increase the effective field of view.

Coordinate Families for the Schwarzschild Geometry Based on Radial Timelike Geodesics

NASA Technical Reports Server (NTRS)

Finch, Tehani K.

2015-01-01

We explore the connections between various coordinate systems associated with observersmoving inwardly along radial geodesics in the Schwarzschild geometry. Painleve-Gullstrand (PG) time is adapted to freely falling observers dropped from rest from infinity; Lake-Martel-Poisson (LMP) time coordinates are adapted to observers who start at infinity with non-zero initial inward velocity; Gautreau-Hoffmann time coordinates are adapted to observers dropped from rest from a finite distance from the black hole horizon.We construct from these an LMP family and a proper-time family of time coordinates, the intersection of which is PG time. We demonstrate that these coordinate families are distinct, but related, one-parameter generalizations of PG time, and show linkage to Lemaître coordinates as well.

Accretion of a symmetry-breaking scalar field by a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Traykova, Dina; Braden, Jonathan; Peiris, Hiranya V.

2018-01-01

We simulate the behaviour of a Higgs-like field in the vicinity of a Schwarzschild black hole using a highly accurate numerical framework. We consider both the limit of the zero-temperature Higgs potential and a toy model for the time-dependent evolution of the potential when immersed in a slowly cooling radiation bath. Through these numerical investigations, we aim to improve our understanding of the non-equilibrium dynamics of a symmetry-breaking field (such as the Higgs) in the vicinity of a compact object such as a black hole. Understanding this dynamics may suggest new approaches for studying properties of scalar fields using black holes as a laboratory. This article is part of the Theo Murphy meeting issue `Higgs Cosmology'.

Energy levels of a scalar particle in a static gravitational field close to the black hole limit

NASA Astrophysics Data System (ADS)

Gossel, G. H.; Berengut, J. C.; Flambaum, V. V.

2011-10-01

The bound-state energy levels of a scalar particle in the gravitational field of finite-sized objects with interiors described by the Florides and Schwarzschild metrics are found. For these metrics, bound states with zero energy (where the binding energy is equal to the rest mass of the scalar particle) only exist when a singularity occurs in the metric. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides metric the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the center. Moreover, the energy spectrum is shown to become quasi-continuous as the metric becomes singular.

Relativistic self-similar dynamic gravitational collapses of a quasi-spherical general polytropic magnetofluid

NASA Astrophysics Data System (ADS)

Lou, Yu-Qing; Xia, Yu-Kai

2017-05-01

We study magnetohydrodynamic (MHD) self-similar collapses and void evolution, with or without shocks, of a general polytropic quasi-spherical magnetofluid permeated by random transverse magnetic fields under the Paczynski-Wiita gravity that captures essential general relativistic effects of a Schwarzschild black hole (BH) with a growing mass. Based on the derived set of non-linear MHD ordinary differential equations, we obtain various asymptotic MHD solutions, the geometric and analytical properties of the magnetosonic critical curve (MSCC) and MHD shock jump conditions. Novel asymptotic MHD solution behaviours near the rim of central expanding voids are derived analytically. By exploring numerical global MHD solutions, we identify allowable boundary conditions at large radii that accommodate a smooth solution and show that a reasonable amount of magnetization significantly increases the mass accretion rate in the expansion-wave-collapse solution scenario. We also construct the counterparts of envelope-expansion-core-collapse solutions that cross the MSCC twice, which are found to be closely paired with a sequence of global smooth solutions satisfying a novel type of central MHD behaviours. MHD shocks with static outer and various inner flow profiles are also examined. Astrophysical applications include dynamic core collapses of magnetized massive stars and compact objects as well as formation of supermassive, hypermassive, dark matter and mixed matter BHs in the Universe, including the early Universe. Such gigantic BHs can be detected in X-ray/gamma-ray sources, quasars, ultraluminous infrared galaxies or extremely luminous infrared galaxies and dark matter overwhelmingly dominated elliptical galaxies as well as massive dark matter halos, etc. Gravitational waves and electromagnetic wave emissions in broad band (including e.g., gamma-ray bursts and fast radio bursts) can result from this type of dynamic collapses of forming BHs involving magnetized media.

Optical Analysis of an Ultra-High resolution Two-Mirror Soft X-Ray Microscope

NASA Technical Reports Server (NTRS)

Shealy, David L.; Wang, Cheng; Hoover, Richard B.

1994-01-01

This work has summarized for a Schwarzschild microscope some relationships between numerical aperture (NA), magnification, diameter of the primary mirror, radius of curvature of the secondary mirror, and the total length of the microscope. To achieve resolutions better than a spherical Schwarzschild microscope of 3.3 Lambda for a perfectly aligned and fabricated system. it is necessary to use aspherical surfaces to control higher-order aberrations. For an NA of 0.35, the aspherical Head microscope provides diffraction limited resolution of 1.4 Lambda where the aspherical surfaces differ from the best fit spherical surface by approximately 1 micrometer. However, the angle of incidence varies significantly over the primary and the secondary mirrors, which will require graded multilayer coatings to operate near peak reflectivities. For higher numerical apertures, the variation of the angle of incidence over the secondary mirror surface becomes a serious problem which must be solved before multilayer coatings can be used for this application. Tolerance analysis of the spherical Schwarzschild microscope has shown that water window operations will require 2-3 times tighter tolerances to achieve a similar performance for operations with 130 A radiation. Surface contour errors have been shown to have a significant impact on the MTF and must be controlled to a peak-to-valley variation of 50-100 A and a frequency of 8 periods over the surface of a mirror.

Quantum dynamics in phase space: Moyal trajectories 2

NASA Astrophysics Data System (ADS)

Braunss, G.

2013-01-01

Continuing a previous paper [G. Braunss, J. Phys. A: Math. Theor. 43, 025302 (2010), 10.1088/1751-8113/43/2/025302] where we had calculated ℏ2-approximations of quantum phase space viz. Moyal trajectories of examples with one and two degrees of freedom, we present in this paper the calculation of ℏ2-approximations for four examples: a two-dimensional Toda chain, the radially symmetric Schwarzschild field, and two examples with three degrees of freedom, the latter being the nonrelativistic spherically Coulomb potential and the relativistic cylinder symmetrical Coulomb potential with a magnetic field H. We show in particular that an ℏ2-approximation of the nonrelativistic Coulomb field has no singularity at the origin (r = 0) whereas the classical trajectories are singular at r = 0. In the third example, we show in particular that for an arbitrary function γ(H, z) the expression β ≡ pz + γ(H, z) is classically (ℏ = 0) a constant of motion, whereas for ℏ ≠ 0 this holds only if γ(H, z) is an arbitrary polynomial of second order in z. This statement is shown to extend correspondingly to a cylinder symmetrical Schwarzschild field with a magnetic field. We exhibit in detail a number of properties of the radially symmetric Schwarzschild field. We exhibit finally the problems of the nonintegrable Hénon-Heiles Hamiltonian and give a short review of the regular Hilbert space representation of Moyal operators.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adamek, Julian; Daverio, David; Durrer, Ruth

We present a new N-body code, gevolution , for the evolution of large scale structure in the Universe. Our code is based on a weak field expansion of General Relativity and calculates all six metric degrees of freedom in Poisson gauge. N-body particles are evolved by solving the geodesic equation which we write in terms of a canonical momentum such that it remains valid also for relativistic particles. We validate the code by considering the Schwarzschild solution and, in the Newtonian limit, by comparing with the Newtonian N-body codes Gadget-2 and RAMSES . We then proceed with a simulation ofmore » large scale structure in a Universe with massive neutrinos where we study the gravitational slip induced by the neutrino shear stress. The code can be extended to include different kinds of dark energy or modified gravity models and going beyond the usually adopted quasi-static approximation. Our code is publicly available.« less

Strange quintessence star in Krori-Barua spacetime

NASA Astrophysics Data System (ADS)

Bhar, Piyali

2015-04-01

In the present paper a new model of a compact star is obtained by utilizing the Krori-Barua (KB) ansatz [Krori and Barua in J. Phys. A, Math. Gen. 8:508, 1975] in the presence of a quintessence field characterized by a parameter ω q with . The obtained model of strange stars is singularity free and satisfies all the physical requirements. Our model is stable as well as it is in static equilibrium. The numerical values of the mass of the strange stars 4U1820-30 (radius=10 km), SAX J1808.4-3658(SS1) (radius=7.07 km) and Her X-1 (radius=7.7 km) calculated from our model are very close to the standard data. The interior solution is matched to the exterior Schwarzschild spacetime in the presence of a thin shell where a negative surface pressure is needed to keep the thin shell from collapsing.

Superrotation charge and supertranslation hair on black holes

DOE PAGES

Hawking, Stephen W.; Perry, Malcolm J.; Strominger, Andrew

2017-05-31

It is shown that black hole spacetimes in classical Einstein gravity are characterized by, in addition to their ADM mass M, momentummore » $$\\vec{P}$$, angular momentum $$\\vec{J}$$ and boost charge $$\\vec{/k}$$ , an infinite head of supertranslation hair. Furthermore, the distinct black holes are distinguished by classical superrotation charges measured at infinity. Solutions with supertranslation hair are diffeomorphic to the Schwarzschild spacetime, but the diffeomorphisms are part of the BMS subgroup and act nontrivially on the physical phase space. It is shown that a black hole can be supertranslated by throwing in an asymmetric shock wave. We derive a leading-order Bondi-gauge expression for the linearized horizon supertranslation charge and shown to generate, via the Dirac bracket, supertranslations on the linearized phase space of gravitational excitations of the horizon. The considerations of this paper are largely classical augmented by comments on their implications for the quantum theory.« less

Superrotation charge and supertranslation hair on black holes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hawking, Stephen W.; Perry, Malcolm J.; Strominger, Andrew

It is shown that black hole spacetimes in classical Einstein gravity are characterized by, in addition to their ADM mass M, momentummore » $$\\vec{P}$$, angular momentum $$\\vec{J}$$ and boost charge $$\\vec{/k}$$ , an infinite head of supertranslation hair. Furthermore, the distinct black holes are distinguished by classical superrotation charges measured at infinity. Solutions with supertranslation hair are diffeomorphic to the Schwarzschild spacetime, but the diffeomorphisms are part of the BMS subgroup and act nontrivially on the physical phase space. It is shown that a black hole can be supertranslated by throwing in an asymmetric shock wave. We derive a leading-order Bondi-gauge expression for the linearized horizon supertranslation charge and shown to generate, via the Dirac bracket, supertranslations on the linearized phase space of gravitational excitations of the horizon. The considerations of this paper are largely classical augmented by comments on their implications for the quantum theory.« less

Hawking radiation power equations for black holes

NASA Astrophysics Data System (ADS)

Mistry, Ravi; Upadhyay, Sudhaker; Ali, Ahmed Farag; Faizal, Mir

2017-10-01

We derive the Hawking radiation power equations for black holes in asymptotically flat, asymptotically Anti-de Sitter (AdS) and asymptotically de Sitter (dS) black holes. This is done by using the greybody factor for these black holes. We observe that the radiation power equation for asymptotically flat black holes, corresponding to greybody factor at low frequency, depends on both the Hawking temperature and the horizon radius. However, for the greybody factors at asymptotic frequency, it only depends on the Hawking temperature. We also obtain the power equation for asymptotically AdS black holes both below and above the critical frequency. The radiation power equation for at asymptotic frequency is same for both Schwarzschild AdS and Reissner-Nordström AdS solutions and only depends on the Hawking temperature. We also discuss the power equation for asymptotically dS black holes at low frequency, for both even or odd dimensions.

Standing shocks in magnetized dissipative accretion flow around black holes

NASA Astrophysics Data System (ADS)

Sarkar, Biplob; Das, Santabrata

2018-02-01

We explore the global structure of the accretion flow around a Schwarzschild black hole where the accretion disc is threaded by toroidal magnetic fields. The accretion flow is optically thin and advection dominated. The synchrotron radiation is considered to be the active cooling mechanism in the flow. With this, we obtain the global transonic accretion solutions and show that centrifugal barrier in the rotating magnetized accretion flow causes a discontinuous transition of the flow variables in the form of shock waves. The shock properties and the dynamics of the post-shock corona are affected by the flow parameters such as viscosity, cooling rate and strength of the magnetic fields. The shock properties are investigated against these flow parameters. We further show that for a given set of boundary parameters at the outer edge of the disc, accretion flow around a black hole admits shock when the flow parameters are tuned for a considerable range.

Brane Physics in M-theory

NASA Astrophysics Data System (ADS)

Argurio, Riccardo

1998-07-01

The thesis begins with an introduction to M-theory (at a graduate student's level), starting from perturbative string theory and proceeding to dualities, D-branes and finally Matrix theory. The following chapter treats, in a self-contained way, of general classical p-brane solutions. Black and extremal branes are reviewed, along with their semi-classical thermodynamics. We then focus on intersecting extremal branes, the intersection rules being derived both with and without the explicit use of supersymmetry. The last three chapters comprise more advanced aspects of brane physics, such as the dynamics of open branes, the little theories on the world-volume of branes and how the four dimensional Schwarzschild black hole can be mapped to an extremal configuration of branes, thus allowing for a statistical interpretation of its entropy. The original results were already reported in hep-th/9701042, hep-th/9704190, hep-th/9710027 and hep-th/9801053.

The Advanced Gamma-ray Imaging System (AGIS): Telescope Optical System Designs

NASA Astrophysics Data System (ADS)

Vassiliev, Vladimir; Buckley, Jim; Falcone, Abe; Fegan, Steven; Finley, John; Gaurino, Victor; Hanna, David; Kaaret, Philip; Konopelko, Alex; Krawczynski, Henric; Romani, Roger; Weekes, Trevor

2008-04-01

AGIS is a conceptual design for a future ground-based gamma-ray observatory based on an array of ˜100 imaging atmospheric Cherenkov telescopes (IACTs) with a sensitivity to gamma-rays in the energy range 40 GeV-100 TeV. The anticipated improvement of AGIS sensitivity, angular resolution, and reliability of operation imposes demanding technological and cost requirements on the design of the IACTs. In this submission we focus on the optical system (OS) of the AGIS telescopes and consider options which include traditional Davies-Cotton and the other prime- focus telescope designs, as well as a novel two-mirror aplanatic OS originally proposed by Schwarzschild. Emerging new mirror production technologies based on replication processes such as cold and hot glass slumping, cured CFRP, and electroforming provide new opportunities for cost effective solutions for the design of the OS. We evaluate the capabilities of these mirror fabrication methods for the AGIS project.

The Advanced Gamma-ray Imaging System (AGIS): Telescope Optical System Designs

NASA Astrophysics Data System (ADS)

Hanna, David S.; Buckley, J. H.; Falcone, A.; Fegan, S.; Finley, J.; Guarino, V.; Kaaret, P.; Krawczynski, H.; Krennrich, F.; Konopelko, A.; Romani, R.; Vassilliev, V.; Optical System Working Group; AGIS Collaboration

2008-03-01

The concept of a future ground-based gamma-ray observatory, AGIS, in the energy range 20 GeV-200 TeV is based on an array of 50-200 imaging atmospheric Cherenkov telescopes (IACTs). The anticipated improvement of AGIS sensitivity, angular resolution, and reliability of operation imposes demanding technological and cost requirements on the design of IACTs. In this submission we will focus on the optical system (OS) of AGIS telescopes and consider options which include traditional Davies-Cotton and the other prime-focus telescope designs, as well as the novel two-mirror aplanatic OS originally proposed by Schwarzschild. The emerging new mirror production technologies based on replication processes, such as cold and hot glass slumping, cured CFRP, and electroforming, provide new opportunities for cost effective solutions for the design of the OS. We initially evaluate capabilities of these mirror fabrication methods for the AGIS project.

Geometrothermodynamics for black holes and de Sitter space

NASA Astrophysics Data System (ADS)

Kurihara, Yoshimasa

2018-02-01

A general method to extract thermodynamic quantities from solutions of the Einstein equation is developed. In 1994, Wald established that the entropy of a black hole could be identified as a Noether charge associated with a Killing vector of a global space-time (pseudo-Riemann) manifold. We reconstruct Wald's method using geometrical language, e.g., via differential forms defined on the local space-time (Minkowski) manifold. Concurrently, the abstract thermodynamics are also reconstructed using geometrical terminology, which is parallel to general relativity. The correspondence between the thermodynamics and general relativity can be seen clearly by comparing the two expressions. This comparison requires a modification of Wald's method. The new method is applied to Schwarzschild, Kerr, and Kerr-Newman black holes and de Sitter space. The results are consistent with previous results obtained using various independent methods. This strongly supports the validity of the area theorem for black holes.

Superrotation charge and supertranslation hair on black holes

NASA Astrophysics Data System (ADS)

Hawking, Stephen W.; Perry, Malcolm J.; Strominger, Andrew

2017-05-01

It is shown that black hole spacetimes in classical Einstein gravity are characterized by, in addition to their ADM mass M, momentum \\overrightarrow{P} , angular momentum \\overrightarrow{J} and boost charge \\overrightarrow{K} , an infinite head of supertranslation hair. The distinct black holes are distinguished by classical superrotation charges measured at infinity. Solutions with super-translation hair are diffeomorphic to the Schwarzschild spacetime, but the diffeomorphisms are part of the BMS subgroup and act nontrivially on the physical phase space. It is shown that a black hole can be supertranslated by throwing in an asymmetric shock wave. A leading-order Bondi-gauge expression is derived for the linearized horizon supertranslation charge and shown to generate, via the Dirac bracket, supertranslations on the linearized phase space of gravitational excitations of the horizon. The considerations of this paper are largely classical augmented by comments on their implications for the quantum theory.

Black hole perturbations in vector-tensor theories: the odd-mode analysis

NASA Astrophysics Data System (ADS)

Kase, Ryotaro; Minamitsuji, Masato; Tsujikawa, Shinji; Zhang, Ying-li

2018-02-01

In generalized Proca theories with vector-field derivative couplings, a bunch of hairy black hole solutions have been derived on a static and spherically symmetric background. In this paper, we formulate the odd-parity black hole perturbations in generalized Proca theories by expanding the corresponding action up to second order and investigate whether or not black holes with vector hair suffer ghost or Laplacian instabilities. We show that the models with cubic couplings G3(X), where X=‑AμAμ/2 with a vector field Aμ, do not provide any additional stability condition as in General Relativity. On the other hand, the exact charged stealth Schwarzschild solution with a nonvanishing longitudinal vector component A1, which originates from the coupling to the Einstein tensor GμνAμ Aν equivalent to the quartic coupling G4(X) containing a linear function of X, is unstable in the vicinity of the event horizon. The same instability problem also persists for hairy black holes arising from general quartic power-law couplings G4(X) ⊃ β4 Xn with the nonvanishing A1, while the other branch with A1=0 can be consistent with conditions for the absence of ghost and Laplacian instabilities. We also discuss the case of other exact and numerical black hole solutions associated with intrinsic vector-field derivative couplings and show that there exists a wide range of parameter spaces in which the solutions suffer neither ghost nor Laplacian instabilities against odd-parity perturbations.

Correction of Cardy–Verlinde formula for Fermions and Bosons with modified dispersion relation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sadatian, S. Davood, E-mail: sd-sadatian@um.ac.ir; Dareyni, H.

Cardy–Verlinde formula links the entropy of conformal symmetry field to the total energy and its Casimir energy in a D-dimensional space. To correct black hole thermodynamics, modified dispersion relation can be used which is proposed as a general feature of quantum gravity approaches. In this paper, the thermodynamics of Schwarzschild four-dimensional black hole is corrected using the modified dispersion relation for Fermions and Bosons. Finally, using modified thermodynamics of Schwarzschild four-dimensional black hole, generalization for Cardy–Verlinde formula is obtained. - Highlights: • The modified Cardy–Verlinde formula obtained using MDR for Fermions and Bosons. • The modified entropy of the blackmore » hole used to correct the Cardy–Verlinde formula. • The modified entropy of the CFT has been obtained.« less

Coordinate Families for the Schwarzschild Geometry Based on Radial Timelike Geodesics

NASA Technical Reports Server (NTRS)

Finch, Tehani K.

2015-01-01

We explore the connections between various coordinate systems associated with observers moving inwardly along radial geodesics in the Schwarzschild geometry. Painleve-Gullstrand (PG) time is adapted to freely falling observers dropped from rest from in nity; Lake-Martel-Poisson (LMP) time coordinates are adapted to observers who start at in nity with non-zero initial inward velocity; Gautreau-Ho mann (GH) time coordinates are adapted to observers dropped from rest from a nite distance from the black hole horizon. We construct from these an LMP family and a propertime family of time coordinates, the intersection of which is PG time. We demonstrate that these coordinate families are distinct, but related, one-parameter generalizations of PG time, and show linkage to Lema^tre coordinates as well.

Schwarzschild-de Sitter spacetime: The role of temperature in the emission of Hawking radiation

NASA Astrophysics Data System (ADS)

Pappas, Thomas; Kanti, Panagiota

2017-12-01

We consider a Schwarzschild-de Sitter (SdS) black hole, and focus on the emission of massless scalar fields either minimally or non-minimally coupled to gravity. We use six different temperatures, two black-hole and four effective ones for the SdS spacetime, as the question of the proper temperature for such a background is still debated in the literature. We study their profiles under the variation of the cosmological constant, and derive the corresponding Hawking radiation spectra. We demonstrate that only few of these temperatures may support significant emission of radiation. We finally compute the total emissivities for each temperature, and show that the non-minimal coupling constant of the scalar field to gravity also affects the relative magnitudes of the energy emission rates.

Light on curved backgrounds

NASA Astrophysics Data System (ADS)

Batic, D.; Nelson, S.; Nowakowski, M.

2015-05-01

We consider the motion of light on different spacetime manifolds by calculating the deflection angle, lensing properties and by probing into the possibility of bound states. The metrics in which we examine the light motion include, among other items, a general relativistic dark matter metric, a dirty black hole, and a worm hole metric, the last two inspired by noncommutative geometry. The lensing in a holographic screen metric is discussed in detail. We study also the bending of light around naked singularities like, e.g., the Janis-Newman-Winicour metric and include other cases. A generic property of light behavior in these exotic metrics is pointed out. For the standard metric like the Schwarzschild and Schwarzschild-de Sitter cases, we improve the accuracy of the lensing results for the weak and strong regimes.

Radiation reaction force on a particle in Schwarzschild spacetime

NASA Astrophysics Data System (ADS)

Tripathi, Swapnil; Wiseman, Alan

2007-04-01

The mathematical modelling of the radiation reaction force experienced by a particle in curved spacetime is very important for calculations of the templates used in detection of gravitational waves with LIGO, LISA etc. In particular, extreme mass ratio inspirals are strong candidates for gravitational wave detection with LISA. We model these systems as a particle in Schwarzschild spacetime, and use the Quinn Wald axioms to regularize the self force. Mode by mode expansion techniques are used for calculating the selfforce. Recent progress in this work is being reported in this talkootnotetextA. G. Wiseman, Phys. Rev. D 61 (2000) arXiv.org:gr-qc/084014 ootnotetextT.C. Quinn, Phys. Rev. D 62 (2000) arXiv.org:gr- qc/064029 ootnotetextT.C. Quinn, R.M. Wald Phys. Rev. D 56 (1997) 3381

Boosted Schwarzschild metrics from a Kerr–Schild perspective

NASA Astrophysics Data System (ADS)

Mädler, Thomas; Winicour, Jeffrey

2018-02-01

The Kerr–Schild version of the Schwarzschild metric contains a Minkowski background which provides a definition of a boosted black hole. There are two Kerr–Schild versions corresponding to ingoing or outgoing principle null directions. We show that the two corresponding Minkowski backgrounds and their associated boosts have an unexpected difference. We analyze this difference and discuss the implications in the nonlinear regime for the gravitational memory effect resulting from the ejection of massive particles from an isolated system. We show that the nonlinear effect agrees with the linearized result based upon the retarded Green function only if the velocity of the ejected particle corresponds to a boost symmetry of the ingoing Minkowski background. A boost with respect to the outgoing Minkowski background is inconsistent with the absence of ingoing radiation from past null infinity.

Scalar self-force on eccentric geodesics in Schwarzschild spacetime: A time-domain computation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haas, Roland

2007-06-15

We calculate the self-force acting on a particle with scalar charge moving on a generic geodesic around a Schwarzschild black hole. This calculation requires an accurate computation of the retarded scalar field produced by the moving charge; this is done numerically with the help of a fourth-order convergent finite-difference scheme formulated in the time domain. The calculation also requires a regularization procedure, because the retarded field is singular on the particle's world line; this is handled mode-by-mode via the mode-sum regularization scheme first introduced by Barack and Ori. This paper presents the numerical method, various numerical tests, and a samplemore » of results for mildly eccentric orbits as well as ''zoom-whirl'' orbits.« less

Accretion of a symmetry-breaking scalar field by a Schwarzschild black hole.

PubMed

Traykova, Dina; Braden, Jonathan; Peiris, Hiranya V

2018-03-06

We simulate the behaviour of a Higgs-like field in the vicinity of a Schwarzschild black hole using a highly accurate numerical framework. We consider both the limit of the zero-temperature Higgs potential and a toy model for the time-dependent evolution of the potential when immersed in a slowly cooling radiation bath. Through these numerical investigations, we aim to improve our understanding of the non-equilibrium dynamics of a symmetry-breaking field (such as the Higgs) in the vicinity of a compact object such as a black hole. Understanding this dynamics may suggest new approaches for studying properties of scalar fields using black holes as a laboratory.This article is part of the Theo Murphy meeting issue 'Higgs Cosmology'. © 2018 The Author(s).

Introduction to Some Fundamental Concepts of General Relativity and to Their Required Use in Some Modern Timekeeping Systems

DTIC Science & Technology

1981-12-01

t e d Riemann Curvature Wnsor and R i s the Curva ture ~ c 2 l ) a r . I n 1917, Karl Schwarzschi ld s o l v e d t h e s e e q u a t i o n...tu re of time a l o n e . I t is t h e Schwarzschild met r ic t h a t leads t o the famous concept n f t h e black h o l e . This is a...01 Well, it can: 2 m - I - - - - - 0 r c 2 Figure 2 4 One calls t h i s va lue of r t h e Schwarzschild b d l u s and o f t e n

Imaging Schwarzschild multilayer X-ray microscope

NASA Technical Reports Server (NTRS)

Hoover, Richard B.; Baker, Phillip C.; Shealy, David L.; Core, David B.; Walker, Arthur B. C., Jr.; Barbee, Troy W., Jr.; Kerstetter, Ted

1993-01-01

We have designed, analyzed, fabricated, and tested Schwarzschild multilayer X-ray microscopes. These instruments use flow-polished Zerodur mirror substrates which have been coated with multilayers optimized for maximum reflectivity at normal incidence at 135 A. They are being developed as prototypes for the Water Window Imaging X-Ray Microscope. Ultrasmooth mirror sets of hemlite grade sapphire have been fabricated and they are now being coated with multilayers to reflect soft X-rays at 38 A, within the biologically important 'water window'. In this paper, we discuss the fabrication of the microscope optics and structural components as well as the mounting of the optics and assembly of the microscopes. We also describe the optical alignment, interferometric and visible light testing of the microscopes, present interferometrically measured performance data, and provide the first results of optical imaging tests.

Causality violations in Lovelock theories

NASA Astrophysics Data System (ADS)

Brustein, Ram; Sherf, Yotam

2018-04-01

Higher-derivative gravity theories, such as Lovelock theories, generalize Einstein's general relativity (GR). Modifications to GR are expected when curvatures are near Planckian and appear in string theory or supergravity. But can such theories describe gravity on length scales much larger than the Planck cutoff length scale? Here we find causality constraints on Lovelock theories that arise from the requirement that the equations of motion (EOM) of perturbations be hyperbolic. We find a general expression for the "effective metric" in field space when Lovelock theories are perturbed around some symmetric background solution. In particular, we calculate explicitly the effective metric for a general Lovelock theory perturbed around cosmological Friedman-Robertson-Walker backgrounds and for some specific cases when perturbed around Schwarzschild-like solutions. For the EOM to be hyperbolic, the effective metric needs to be Lorentzian. We find that, unlike for GR, the effective metric is generically not Lorentzian when the Lovelock modifications are significant. So, we conclude that Lovelock theories can only be considered as perturbative extensions of GR and not as truly modified theories of gravity. We compare our results to those in the literature and find that they agree with and reproduce the results of previous studies.

Stars and (furry) black holes in Lorentz breaking massive gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Comelli, D.; Nesti, F.; Pilo, L.

We study the exact spherically symmetric solutions in a class of Lorentz-breaking massive gravity theories, using the effective-theory approach where the graviton mass is generated by the interaction with a suitable set of Stueckelberg fields. We find explicitly the exact black-hole solutions which generalizes the familiar Schwarzschild one, which shows a nonanalytic hair in the form of a powerlike term r{sup {gamma}}. For realistic self-gravitating bodies, we find interesting features, linked to the effective violation of the Gauss law: (i) the total gravitational mass appearing in the standard 1/r term gets a multiplicative renormalization proportional to the area of themore » body itself; (ii) the magnitude of the powerlike hairy correction is also linked to size of the body. The novel features can be ascribed to the presence of the Goldstones fluid turned on by matter inside the body; its equation of state approaching that of dark energy near the center. The Goldstones fluid also changes the matter equilibrium pressure, leading to an upper limit for the graviton mass, m < or approx. 10{sup -28/29} eV, derived from the largest stable gravitational bound states in the Universe.« less

Estimation of mass outflow rates from viscous relativistic accretion discs around black holes

NASA Astrophysics Data System (ADS)

Chattopadhyay, Indranil; Kumar, Rajiv

2016-07-01

We investigated flow in Schwarzschild metric, around a non-rotating black hole and obtained self-consistent accretion-ejection solution in full general relativity. We covered the whole of parameter space in the advective regime to obtain shocked, as well as, shock-free accretion solution. We computed the jet streamline using von Zeipel surfaces and projected the jet equations of motion on to the streamline and solved them simultaneously with the accretion disc equations of motion. We found that steady shock cannot exist beyond α ≳ 0.06 in the general relativistic prescription, but is lower if mass-loss is considered too. We showed that for fixed outer boundary, the shock moves closer to the horizon with increasing viscosity parameter. The mass outflow rate increases as the shock moves closer to the black hole, but eventually decreases, maximizing at some intermediate value of shock location. The jet terminal speed increases with stronger shocks; quantitatively speaking, the terminal speed of jets vj∞ > 0.1 if rsh < 20rg. The maximum of the outflow rate obtained in the general relativistic regime is less than 6 per cent of the mass accretion rate.

On the generalized wormhole in the Eddington-inspired Born-Infeld gravity

NASA Astrophysics Data System (ADS)

Tamang, Amarjit; Potapov, Alexander A.; Lukmanova, Regina; Izmailov, Ramil; Nandi, Kamal K.

2015-12-01

In this paper, we wish to investigate certain observable effects in the recently obtained wormhole solution of the Eddington-inspired Born-Infeld (EiBI) theory, which generalizes the zero-mass Ellis-Bronnikov wormhole of general relativity. The solutions of EiBI theory contain an extra parameter κ having the inverse dimension of the cosmological constant Λ, and which is expected to modify various general relativistic observables such as the masses of wormhole mouths, tidal forces and light deflection. A remarkable result is that a non-zero κ could prevent the tidal forces in the geodesic orthonormal frame from becoming arbitrarily large near a small throat radius ({r}0˜ 0) contrary to what happens near a small Schwarzschild horizon radius (M˜ 0). The role of κ in the flare-out and energy conditions is also analyzed, which reveals that the energy conditions are violated. We show that the exotic matter in the EiBI wormhole cannot be interpreted as a phantom (ω =\\frac{{p}{{r}}}{ρ }\\lt -1) or ghost field ϕ of general relativity due to the fact that both ρ and p r are negative for all κ.

Self-similar Hot Accretion Flow onto a Neutron Star

NASA Astrophysics Data System (ADS)

Medvedev, Mikhail V.; Narayan, Ramesh

2001-06-01

We consider hot, two-temperature, viscous accretion onto a rotating, unmagnetized neutron star. We assume Coulomb coupling between the protons and electrons, as well as free-free cooling from the electrons. We show that the accretion flow has an extended settling region that can be described by means of two analytical self-similar solutions: a two-temperature solution that is valid in an inner zone, r<~102.5, where r is the radius in Schwarzschild units; and a one-temperature solution that is valid in an outer zone, r>~102.5. In both zones the density varies as ρ~r-2 and the angular velocity as Ω~r-3/2. We solve the flow equations numerically and confirm that the analytical solutions are accurate. Except for the radial velocity, all gas properties in the self-similar settling zone, such as density, angular velocity, temperature, luminosity, and angular momentum flux, are independent of the mass accretion rate; these quantities do depend sensitively on the spin of the neutron star. The angular momentum flux is outward under most conditions; therefore, the central star is nearly always spun down. The luminosity of the settling zone arises from the rotational energy that is released as the star is braked by viscosity, and the contribution from gravity is small; hence, the radiative efficiency, η=Lacc/Mc2, is arbitrarily large at low M. For reasonable values of the gas adiabatic index γ, the Bernoulli parameter is negative; therefore, in the absence of dynamically important magnetic fields, a strong outflow or wind is not expected. The flow is also convectively stable but may be thermally unstable. The described solution is not advection dominated; however, when the spin of the star is small enough, the flow transforms smoothly to an advection-dominated branch of solution.

A complete characterization of relativistic uniform acceleration

NASA Astrophysics Data System (ADS)

Scarr, Tzvi; Friedman, Yaakov

2017-05-01

We use the Frenet frame to define and completely characterize “uniform acceleration” in flat spacetime. We extend the definition to arbitrary curved spacetime and provide an example in Schwarzschild spacetime.

Hawking radiation and interacting fields

NASA Astrophysics Data System (ADS)

Frasca, Marco

2017-11-01

Hawking radiation is generally derived using a non-interacting field theory. Some time ago, Leahy and Unruh showed that, in two dimensions with a Schwarzschild geometry, a scalar field theory with a quartic interaction gets the coupling switched off near the horizon of the black hole. This would imply that interaction has no effect on Hawking radiation and free theory for particles can be used. Recently, a set of exact classical solutions for the quartic scalar field theory has been obtained. These solutions display a massive dispersion relation even if the starting theory is massless. When one considers the corresponding quantum field theory, this mass gap becomes a tower of massive excitations and, at the leading order, the theory is trivial. We apply these results to Hawking radiation for a Kerr geometry and prove that the Leahy-Unruh effect is at work. Approaching the horizon the scalar field theory has the mass gap going to zero. We devise a technique to study the interacting scalar theory very near the horizon increasing the coupling. As these solutions are represented by a Fourier series of plane waves, Hawking radiation can be immediately obtained with well-known techniques. These results open a question about the behavior of the Standard Model of particles very near the horizon of a black hole where the interactions turn out to be switched off and the electroweak symmetry could be restored.

Radiation drag in the field of a non-spherical source

NASA Astrophysics Data System (ADS)

Bini, D.; Geralico, A.; Passamonti, A.

2015-01-01

The motion of a test particle in the gravitational field of a non-spherical source endowed with both mass and mass quadrupole moment is investigated when a test radiation field is also present. The background is described by the Erez-Rosen solution, which is a static space-time belonging to the Weyl class of solutions to the vacuum Einstein's field equations, and reduces to the familiar Schwarzschild solution when the quadrupole parameter vanishes. The radiation flux has a fixed but arbitrary (non-zero) angular momentum. The interaction with the radiation field is assumed to be Thomson-like, i.e. the particles absorb and re-emit radiation, thus suffering for a friction-like drag force. Such an additional force is responsible for the Poynting-Robertson effect, which is well established in the framework of Newtonian gravity and has been recently extended to the general theory of relativity. The balance between gravitational attraction, centrifugal force and radiation drag leads to the occurrence of equilibrium circular orbits which are attractors for the surrounding matter for every fixed value of the interaction strength. The presence of the quadrupolar structure of the source introduces a further degree of freedom: there exists a whole family of equilibrium orbits parametrized by the quadrupole parameter, generalizing previous works. This scenario is expected to play a role in the context of accretion matter around compact objects.

Deflection of light by black holes and massless wormholes in massive gravity

NASA Astrophysics Data System (ADS)

Jusufi, Kimet; Sarkar, Nayan; Rahaman, Farook; Banerjee, Ayan; Hansraj, Sudan

2018-04-01

Weak gravitational lensing by black holes and wormholes in the context of massive gravity (Bebronne and Tinyakov, JHEP 0904:100, 2009) theory is studied. The particular solution examined is characterized by two integration constants, the mass M and an extra parameter S namely `scalar charge'. These black hole reduce to the standard Schwarzschild black hole solutions when the scalar charge is zero and the mass is positive. In addition, a parameter λ in the metric characterizes so-called `hair'. The geodesic equations are used to examine the behavior of the deflection angle in four relevant cases of the parameter λ . Then, by introducing a simple coordinate transformation r^λ =S+v^2 into the black hole metric, we were able to find a massless wormhole solution of Einstein-Rosen (ER) (Einstein and Rosen, Phys Rev 43:73, 1935) type with scalar charge S. The programme is then repeated in terms of the Gauss-Bonnet theorem in the weak field limit after a method is established to deal with the angle of deflection using different domains of integration depending on the parameter λ . In particular, we have found new analytical results corresponding to four special cases which generalize the well known deflection angles reported in the literature. Finally, we have established the time delay problem in the spacetime of black holes and wormholes, respectively.

Hawking radiation as tunneling in Schwarzschild anti-de Sitter black hole

NASA Astrophysics Data System (ADS)

Sefiedgar, A. S.; Ashrafinejad, A.

2017-08-01

The Hawking radiation from a (d+1) -dimensional Schwarzschild Anti-de Sitter (SAdS) black hole is investigated within rainbow gravity. Based on the method proposed by Kraus, Parikh and Wilczek, the Hawking radiation is considered as a tunneling process across the horizon. The emission rate of massless particles which are tunneling across the quantum-corrected horizon is calculated. Enforcing the energy conservation law leads to a dynamical geometry. Both the dynamical geometry and the quantum effects of space-time yield some corrections to the emission rate. The corrected radiation spectrum is not purely thermal. The emission rate is related to the changes of modified entropy in rainbow gravity and the corrected thermal spectrum may be consistent with an underlying unitary quantum theory. The correlations between emitted particles are also investigated in order to address the recovery of information.

Operating performance of the gamma-ray Cherenkov telescope: An end-to-end Schwarzschild-Couder telescope prototype for the Cherenkov Telescope Array

NASA Astrophysics Data System (ADS)

Dournaux, J. L.; De Franco, A.; Laporte, P.; White, R.; Greenshaw, T.; Sol, H.; Abchiche, A.; Allan, D.; Amans, J. P.; Armstrong, T. P.; Balzer, A.; Berge, D.; Boisson, C.; Bousquet, J. J.; Brown, A. M.; Bryan, M.; Buchholtz, G.; Chadwick, P. M.; Costantini, H.; Cotter, G.; Daniel, M.; De Frondat, F.; Dumas, D.; Ernenwein, J. P.; Fasola, G.; Funk, S.; Gaudemard, J.; Graham, J. A.; Gironnet, J.; Hervet, O.; Hidaka, N.; Hinton, J. A.; Huet, J. M.; Jégouzo, I.; Jogler, T.; Kawashima, T.; Kraus, M.; Lapington, J. S.; Lefaucheur, J.; Markoff, S.; Melse, T.; Morhrmann, L.; Molnyeux, P.; Nolan, S. J.; Okumura, A.; Parsons, R. D.; Ross, D.; Rowell, G.; Sato, Y.; Sayède, F.; Schmoll, J.; Schoorlemmer, H.; Servillat, M.; Stamatescu, V.; Stephan, M.; Stuik, R.; Sykes, J.; Tajima, H.; Thornhill, J.; Tibaldo, L.; Trichard, C.; Vink, J.; Watson, J.; Yamane, N.; Zech, A.; Zink, A.; CTA Consortium

2017-02-01

The Cherenkov Telescope Array (CTA) consortium aims to build the next-generation ground-based very-high-energy gamma-ray observatory. The array will feature different sizes of telescopes allowing it to cover a wide gamma-ray energy band from about 20 GeV to above 100 TeV. The highest energies, above 5 TeV, will be covered by a large number of Small-Sized Telescopes (SSTs) with a field-of-view of around 9°. The Gamma-ray Cherenkov Telescope (GCT), based on Schwarzschild-Couder dual-mirror optics, is one of the three proposed SST designs. The GCT is described in this contribution and the first images of Cherenkov showers obtained using the telescope and its camera are presented. These were obtained in November 2015 in Meudon,

Universal properties of the near-horizon optical geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gibbons, G. W.; Warnick, C. M.

2009-03-15

Making use of the fact that the optical geometry near a static nondegenerate Killing horizon is asymptotically hyperbolic, we investigate some universal features of black-hole horizons. Applying the Gauss-Bonnet theorem allows us to establish some general properties of gravitational lensing, valid for all black holes. Hyperbolic geometry allows us to find rates for the loss of scalar, vector, and fermionic ''hair'' as objects fall quasistatically towards the horizon, extending previous results for Schwarzschild to all static Killing horizons. In the process we find the Lienard-Wiechert potential for hyperbolic space and calculate the force between electrons mediated by neutrinos, extending themore » flat space result of Feinberg and Sucher. We further demonstrate how these techniques allow us to derive the exact Copson-Linet potential due to a point charge in a Schwarzschild background in a simple fashion.« less

The incompressible Rindler fluid versus the Schwarzschild-AdS fluid

NASA Astrophysics Data System (ADS)

Matsuo, Yoshinori; Natsuume, Makoto; Ohta, Masahiro; Okamura, Takashi

2013-02-01

We study the proposal by Bredberg et al. [J. High Energy Phys. 1103, 141 (2011)], where the fluid is defined by the Brown-York tensor on a timelike surface at r = rc in black hole backgrounds. We consider both Rindler space and the Schwarzschild-AdS (SAdS) black hole. The former describes an incompressible fluid, whereas the latter describes the vanishing bulk viscosity at arbitrary rc. Although the near-horizon limit of the SAdS black hole is Rindler space, these two results do not contradict each other. We also find an interesting "coincidence" with the black hole membrane paradigm that gives a negative bulk viscosity. In order to show these results, we rewrite the hydrodynamic stress tensor via metric perturbations using the conservation equation. The resulting expressions are suitable to compare with the Brown-York tensor.

Thermodynamics phase transition and Hawking radiation of the Schwarzschild black hole with quintessence-like matter and a deficit solid angle

NASA Astrophysics Data System (ADS)

Rodrigue, Kamiko Kouemeni Jean; Saleh, Mahamat; Thomas, Bouetou Bouetou; Kofane, Timoleon Crepin

2018-05-01

In this paper, we investigate the thermodynamics and Hawking radiation of Schwarzschild black hole with quintessence-like matter and deficit solid angle. From the metric of the black hole, we derive the expressions of temperature and specific heat using the laws of black hole thermodynamics. Using the null geodesics method and Parikh-Wilczeck tunneling method, we derive the expressions of Boltzmann factor and the change of Bekenstein-Hawking entropy for the black hole. The behaviors of the temperature, specific heat, Boltzmann factor and the change of Bekenstein entropy versus the deficit solid angle (ɛ 2) and the density of static spherically symmetric quintessence-like matter (ρ 0) were explicitly plotted. The results show that, when the deficit solid angle (ɛ 2) and the density of static spherically symmetric quintessence-like matter at r=1 (ρ 0) vanish (ρ 0=ɛ =0), these four thermodynamics quantities are reduced to those obtained for the simple case of Schwarzschild black hole. For low entropies, the presence of quintessence-like matter induces a first order phase transition of the black hole and for the higher values of the entropies, we observe the second order phase transition. When increasing ρ 0, the transition points are shifted to lower entropies. The same thing is observed when increasing ɛ 2. In the absence of quintessence-like matter (ρ 0=0), these transition phenomena disappear. Moreover the rate of radiation decreases when increasing ρ 0 or (ɛ ^2).

Vacuum Fluctuation Force on a Rigid Casimir Cavity in de Sitter and Schwarzschild-De Sitter Space-Time

NASA Astrophysics Data System (ADS)

Chen, Xiang

2012-11-01

We investigate the net force on a rigid Casimir cavity generated by vacuum fluctuations of electromagnetic field in three cases: de Sitter space-time, de Sitter space-time with weak gravitational field and Schwarzschild-de Sitter space-time. In de Sitter space-time the resulting net force follows the square inverse law but unfortunately it is too weak to be measurable due to the large universe radius. By introducing a weak gravitational field into the de Sitter space-time, we find that the net force can now be split into two parts, one is the gravitational force due to the induced effective mass between the two plates and the other one is generated by the metric structure of de Sitter space-time. In order to investigate the vacuum fluctuation force on the rigid cavity under strong gravitational field, we perform a similar analysis in Schwarzschild-de Sitter space-time and results are obtained in three different limits. The most interesting one is when the cavity gets closer to the horizon of a blackhole, square inverse law is recovered and the repulsive force due to negative energy/mass of the cavity now has an observable strength. More importantly the force changes from being repulsive to attractive when the cavity crosses the event horizon, so that the energy/mass of the cavity switches the sign, which suggests the unusual time direction inside the event horizon.

Light bending, static dark energy, and related uniqueness of Schwarzschild-de Sitter spacetime

NASA Astrophysics Data System (ADS)

Ali, Md Sabir; Bhattacharya, Sourav

2018-01-01

Since the Schwarzschild-de Sitter spacetime is static inside the cosmological event horizon, if the dark energy state parameter is sufficiently close to -1 , apparently one could still expect an effectively static geometry, in the attraction dominated region inside the maximum turnaround radius, RTA ,max, of a cosmic structure. We take the first order metric derived recently assuming a static and ideal dark energy fluid with equation of state P (r )=α ρ (r ) as a source in Bhattacharya and Tomaras [Eur. Phys. J. C 77, 526 (2017), 10.1140/epjc/s10052-017-5102-4], which reproduced the expression for RTA ,max found earlier in the cosmological McVittie spacetime. Here we show that the equality originates from the equivalence of geodesic motion in these two backgrounds, in the nonrelativistic regime. We extend this metric up to the third order and compute the bending of light using the Rindler-Ishak method. For α ≠-1 , a dark energy dependent term appears in the bending equation, unlike the case of the cosmological constant, α =-1 . Because of this new term in particular, existing data for the light bending at galactic scales yields (1 +α )≲O (10-14), thereby practically ruling out any such static and inhomogeneous dark energy fluid we started with. Implication of this result pertaining to the uniqueness of the Schwarzschild-de Sitter spacetime in such an inhomogeneous dark energy background is discussed.

Can we identify massless braneworld black holes by observations?

NASA Astrophysics Data System (ADS)

Kuniyasu, Masashi; Nanri, Keitaro; Sakai, Nobuyuki; Ohgami, Takayuki; Fukushige, Ryosuke; Komura, Subaru

2018-05-01

For an extension of the previous work on gravitational lensing by massless braneworld black holes, we investigate their microlensing phenomena and shadows and discuss how to distinguish them from standard Schwarzschild black holes and Ellis wormholes. Microlensing is known as the phenomenon in which luminosity amplification appears when a bright object passes behind a black hole or another massive object. We find that, for the braneworld black hole as well as for the Ellis wormhole, there appears luminosity reduction just before and after the amplification. This means that observation of such a reduction would indicate the lens object is either a braneworld black hole or a wormhole, though it is difficult to distinguish one from the other by microlensing solely. Therefore, we next analyze the optical images, or shadows of the braneworld black hole surrounded by optically thin dust, and compare them to those of the Ellis wormhole. Because the spacetime around the braneworld black hole possesses unstable circular orbits of photons, a bright ring appears in the image, just as in Schwarzschild spacetime or in the wormhole spacetime. This indicates that the appearance of a bright ring does not solely confirm a braneworld black hole, a Schwarzschild, nor an Ellis wormhole. However, we find that only for the wormhole is the intensity inside the ring larger than that the outsider intensity. Therefore, with future high-resolution observations of microlensing and shadows together, we could identify the braneworld black holes if they exist.

Off-equatorial circular orbits in magnetic fields of compact objects

NASA Astrophysics Data System (ADS)

Stuchlík, Zdeněk; Kovář, Jiří; Karas, Vladimír

2009-04-01

We present results of investigation of the off-equatorial circular orbits existence in the vicinity of neutron stars, Schwarzschild black holes with plasma ring, and near Kerr-Newman black holes and naked singularities.

Compact stars in the braneworld: A new branch of stellar configurations with arbitrarily large mass

NASA Astrophysics Data System (ADS)

Lugones, Germán; Arbañil, José D. V.

2017-03-01

We study the properties of compact stars in the Randall-Sundrum type-II braneworld (BW) model. To this end, we solve the braneworld generalization of the stellar structure equations for a static fluid distribution with spherical symmetry considering that the spacetime outside the star is described by a Schwarzschild metric. First, the stellar structure equations are integrated employing the so-called causal limit equation of state (EOS), which is constructed using a well-established EOS at densities below a fiducial density, and the causal EOS P =ρ above it. It is a standard procedure in general relativistic stellar structure calculations to use such EOSs for obtaining a limit in the mass radius diagram, known as the causal limit, above which no stellar configurations are possible if the EOS fulfills the condition that the sound velocity is smaller than the speed of light. We find that the equilibrium solutions in the braneworld model can violate the general relativistic causal limit, and for sufficiently large mass they approach asymptotically to the Schwarzschild limit M =2 R . Then, we investigate the properties of hadronic and strange quark stars using two typical EOSs: a nonlinear relativistic mean-field model for hadronic matter and the Massachusetts Institute of Technology (MIT) bag model for quark matter. For masses below ˜1.5 M⊙- 2 M⊙ , the mass versus radius curves show the typical behavior found within the frame of general relativity. However, we also find a new branch of stellar configurations that can violate the general relativistic causal limit and that, in principle, may have an arbitrarily large mass. The stars belonging to this new branch are supported against collapse by the nonlocal effects of the bulk on the brane. We also show that these stars are always stable under small radial perturbations. These results support the idea that traces of extra dimensions might be found in astrophysics, specifically through the analysis of masses and radii of compact objects.

Multiple Stars in the Field

DTIC Science & Technology

2008-01-01

Southern Observatory Karl - Schwarzschild -Str. 2 85748 Garching Germany :--. ,") 1 ’< ’ I () ___ I Andrei Tokovinin Inter-American Observatory...Chile Monika Petr-Gotzens European Southern Observatory Karl -Schwarschild-Str. 2 85748 Garching Germany Series Editor Bruno Leibundgut European

Detweiler's redshift invariant for spinning particles along circular orbits on a Schwarzschild background

NASA Astrophysics Data System (ADS)

Bini, Donato; Damour, Thibault; Geralico, Andrea; Kavanagh, Chris

2018-05-01

We study the metric perturbations induced by a classical spinning particle moving along a circular orbit on a Schwarzschild background, limiting the analysis to effects which are first order in spin. The particle is assumed to move on the equatorial plane and has its spin aligned with the z axis. The metric perturbations are obtained by using two different approaches, i.e., by working in two different gauges: the Regge-Wheeler gauge (using the Regge-Wheeler-Zerilli formalism) and a radiation gauge (using the Teukolsky formalism). We then compute the linear-in-spin contribution to the first-order self-force contribution to Detweiler's redshift invariant up to the 8.5 post-Newtonian order. We check that our result is the same in both gauges, as appropriate for a gauge-invariant quantity, and agrees with the currently known 3.5 post-Newtonian results.

Tidal disruptions by supermassive black holes - Hydrodynamic evolution of stars on a Schwarzschild background

NASA Technical Reports Server (NTRS)

Laguna, Pablo; Miller, Warner A.; Zurek, Wojciech H.; Davies, Melvyn B.

1993-01-01

We present a three-dimensional numerical study of tidal disruption of a main-sequence star by a supermassive black hole. The simulations include general relativistic effects which are important in this regime. We analyze stars in a marginally bound orbit around the black hole with pericentric separation of a few Schwarzschild radii. We show that during a close passage, as a result of relativistic effects analogous to the perihelion shift, the trajectories of the debris of the star fan out into a crescent-like shape centered on the black hole. We also discuss the increase of the central density of the star as it approaches pericentric distance, the fraction of the debris accreted by the hole, its accretion rate, the distribution of debris orbits bound to the hole, and the velocity of unbound ejected material. We compare these results with the disruption of the star by a Newtonian point mass.

Charge loss (or the lack thereof) for AdS black holes

NASA Astrophysics Data System (ADS)

Ong, Yen Chin; Chen, Pisin

2014-06-01

The evolution of evaporating charged black holes is complicated to model in general, but is nevertheless important since the hints to the Information Loss Paradox and its recent firewall incarnation may lie in understanding more generic geometries than that of Schwarzschild spacetime. Fortunately, for sufficiently large asymptotically flat Reissner-Nordström black holes, the evaporation process can be modeled via a system of coupled linear ordinary differential equations, with charge loss rate governed by Schwinger pair-production process. The same model can be generalized to study the evaporation of AdS Reissner-Nordström black holes with flat horizon. It was recently found that such black holes always evolve towards extremality since charge loss is inefficient. This property is completely opposite to the asymptotically flat case in which the black hole eventually loses its charges and tends towards Schwarzschild limit. We clarify the underlying reason for this different behavior.

The Advanced Gamma-ray Imaging System (AGIS): Schwarzschild-Couder (SC) Telescope Mechanical and Optical System Design

NASA Astrophysics Data System (ADS)

Byrum, Karen L.; Vassiliev, V.; AGIS Collaboration

2010-03-01

AGIS is a concept for the next-generation ground-based gamma-ray observatory. It will be an array of 36 imaging atmospheric Cherenkov telescopes (IACTs) sensitive in the energy range from 50 GeV to 200 TeV. The required improvements in sensitivity, angular resolution, and reliability of operation relative to the present generation instruments imposes demanding technological and cost requirements on the design of AGIS telescopes. In this submission, we outline the status of the development of the optical and mechanical systems for a novel Schwarzschild-Couder two-mirror aplanatic telescope. This design can provide a field of view and angular resolution significantly better to those offered by the traditional Davies-Cotton optics utilized in present-day IACTs. Other benefits of the novel design include isochronous focusing and compatibility with cost-effective, high quantum efficiency image sensors such as multi-anode PMTs, silicon PMTs (SiPMs), or image intensifiers.

Tripartite nonlocality for an open Dirac system in the background of Schwarzschild space-time

NASA Astrophysics Data System (ADS)

Ding, Zhi-Yong; Shi, Jia-Dong; Wu, Tao; He, Juan

2017-12-01

In this paper, the behavior of the tripartite nonlocality for a Dirac system in the background of Schwarzschild space-time is studied. It is shown that the nonlocality of the ultimate physical accessible state always decreases as the Hawking effect increases monotonically, which is independent of the number of particles located near the event horizon. Besides, the more particles there are located near the event horizon, the more difficult the violation of the Svetlichny inequality becomes. Furthermore, we investigate the property of these particles suffering from a non-Markovian environment, and derive that the nonlocality decreases quickly with the increasing decoherence time accompanied by damping revivals. To preserve tripartite nonlocality in the non-Markovian environment, we propose a scheme by means of prior weak measurement and post measurement reversal. It is worth noticing that the effect is better for larger measurement strengths, while it induces smaller success probability.

Convective instabilities in SN 1987A

NASA Technical Reports Server (NTRS)

Benz, Willy; Thielemann, Friedrich-Karl

1990-01-01

Following Bandiera (1984), it is shown that the relevant criterion to determine the stability of a blast wave, propagating through the layers of a massive star in a supernova explosion, is the Schwarzschild (or Ledoux) criterion rather than the Rayleigh-Taylor criterion. Both criteria coincide only in the incompressible limit. Results of a linear stability analysis are presented for a one-dimensional (spherical) explosion in a realistic model for the progenitor of SN 1987A. When applying the Schwarzschild criterion, unstable regions get extended considerably. Convection is found to develop behind the shock, with a characteristic growth rate corresponding to a time scale much smaller than the shock traversal time. This ensures that efficient mixing will take place. Since the entire ejected mass is found to be convectively unstable, Ni can be transported outward, even into the hydrogen envelope, while hydrogen can be mixed deep into the helium core.

Lagrangian equations of motion of particles and photons in a Schwarzschild field

NASA Astrophysics Data System (ADS)

Ritus, V. I.

2015-11-01

The equations of motion of a particle in the gravitational field of a black hole are considered in a formulation that uses generalized coordinates, velocities, and accelerations and is convenient for finding the integrals of motion. The equations are rewritten in terms of the physical velocities and accelerations measured in the Schwarzschild frame by a stationary observer using proper local length and time standards. The attractive force due to the field and the centripetal acceleration of a particle is proportional to the particle kinetic energy m/\\sqrt{1 - v^2}, consistently with the fact that the particle kinetic energy and the photon energy \\hbarω in the field increase by the same factor compared with their values without a field. The attraction exerted on particles and photons by a gravitational field source is proportional to their kinetic energies. The particle trajectory in the ultrarelativistic limit v \\to 1 coincides with the photon trajectory.

Pseudo-Newtonian Equations for Evolution of Particles and Fluids in Stationary Space-times

DOE Office of Scientific and Technical Information (OSTI.GOV)

Witzany, Vojtěch; Lämmerzahl, Claus, E-mail: vojtech.witzany@zarm.uni-bremen.de, E-mail: claus.laemmerzahl@zarm.uni-bremen.de

Pseudo-Newtonian potentials are a tool often used in theoretical astrophysics to capture some key features of a black hole space-time in a Newtonian framework. As a result, one can use Newtonian numerical codes, and Newtonian formalism, in general, in an effective description of important astrophysical processes such as accretion onto black holes. In this paper, we develop a general pseudo-Newtonian formalism, which pertains to the motion of particles, light, and fluids in stationary space-times. In return, we are able to assess the applicability of the pseudo-Newtonian scheme. The simplest and most elegant formulas are obtained in space-times without gravitomagnetic effects,more » such as the Schwarzschild rather than the Kerr space-time; the quantitative errors are smallest for motion with low binding energy. Included is a ready-to-use set of fluid equations in Schwarzschild space-time in Cartesian and radial coordinates.« less

Detection of Intrinsic Source Structure at ∼3 Schwarzschild Radii with Millimeter-VLBI Observations of SAGITTARIUS A*

NASA Astrophysics Data System (ADS)

Lu, Ru-Sen; Krichbaum, Thomas P.; Roy, Alan L.; Fish, Vincent L.; Doeleman, Sheperd S.; Johnson, Michael D.; Akiyama, Kazunori; Psaltis, Dimitrios; Alef, Walter; Asada, Keiichi; Beaudoin, Christopher; Bertarini, Alessandra; Blackburn, Lindy; Blundell, Ray; Bower, Geoffrey C.; Brinkerink, Christiaan; Broderick, Avery E.; Cappallo, Roger; Crew, Geoffrey B.; Dexter, Jason; Dexter, Matt; Falcke, Heino; Freund, Robert; Friberg, Per; Greer, Christopher H.; Gurwell, Mark A.; Ho, Paul T. P.; Honma, Mareki; Inoue, Makoto; Kim, Junhan; Lamb, James; Lindqvist, Michael; Macmahon, David; Marrone, Daniel P.; Martí-Vidal, Ivan; Menten, Karl M.; Moran, James M.; Nagar, Neil M.; Plambeck, Richard L.; Primiani, Rurik A.; Rogers, Alan E. E.; Ros, Eduardo; Rottmann, Helge; SooHoo, Jason; Spilker, Justin; Stone, Jordan; Strittmatter, Peter; Tilanus, Remo P. J.; Titus, Michael; Vertatschitsch, Laura; Wagner, Jan; Weintroub, Jonathan; Wright, Melvyn; Young, Ken H.; Zensus, J. Anton; Ziurys, Lucy M.

2018-05-01

We report results from very long baseline interferometric (VLBI) observations of the supermassive black hole in the Galactic center, Sgr A*, at 1.3 mm (230 GHz). The observations were performed in 2013 March using six VLBI stations in Hawaii, California, Arizona, and Chile. Compared to earlier observations, the addition of the APEX telescope in Chile almost doubles the longest baseline length in the array, provides additional uv coverage in the N–S direction, and leads to a spatial resolution of ∼30 μas (∼3 Schwarzschild radii) for Sgr A*. The source is detected even at the longest baselines with visibility amplitudes of ∼4%–13% of the total flux density. We argue that such flux densities cannot result from interstellar refractive scattering alone, but indicate the presence of compact intrinsic source structure on scales of ∼3 Schwarzschild radii. The measured nonzero closure phases rule out point-symmetric emission. We discuss our results in the context of simple geometric models that capture the basic characteristics and brightness distributions of disk- and jet-dominated models and show that both can reproduce the observed data. Common to these models are the brightness asymmetry, the orientation, and characteristic sizes, which are comparable to the expected size of the black hole shadow. Future 1.3 mm VLBI observations with an expanded array and better sensitivity will allow more detailed imaging of the horizon-scale structure and bear the potential for a deep insight into the physical processes at the black hole boundary.

The effects of massive graviton on the equilibrium between the black hole and radiation gas in an isolated box

NASA Astrophysics Data System (ADS)

Hu, Ya-Peng; Pan, Feng; Wu, Xin-Meng

2017-09-01

It is well known that the black hole can have temperature and radiate the particles with black body spectrum, i.e. Hawking radiation. Therefore, if the black hole is surrounded by an isolated box, there is a thermal equilibrium between the black hole and radiation gas. A simple case considering the thermal equilibrium between the Schwarzschild black hole and radiation gas in an isolated box has been well investigated previously in detail, i.e. taking the conservation of energy and principle of maximal entropy for the isolated system into account. In this paper, following the above spirit, the effects of massive graviton on the thermal equilibrium will be investigated. For the gravity with massive graviton, we will use the de Rham-Gabadadze-Tolley (dRGT) massive gravity which has been proven to be ghost free. Because the graviton mass depends on two parameters in the dRGT massive gravity, here we just investigate two simple cases related to the two parameters, respectively. Our results show that in the first case the massive graviton can suppress or increase the condensation of black hole in the radiation gas although the T-E diagram is similar as the Schwarzschild black hole case. For the second case, a new T-E diagram has been obtained. Moreover, an interesting and important prediction is that the condensation of black hole just increases from the zero radius of horizon in this case, which is very different from the Schwarzschild black hole case.

Quantum dynamics in phase space: Moyal trajectories 2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Braunss, G.

Continuing a previous paper [G. Braunss, J. Phys. A: Math. Theor. 43, 025302 (2010)] where we had calculated Planck-Constant-Over-Two-Pi {sup 2}-approximations of quantum phase space viz. Moyal trajectories of examples with one and two degrees of freedom, we present in this paper the calculation of Planck-Constant-Over-Two-Pi {sup 2}-approximations for four examples: a two-dimensional Toda chain, the radially symmetric Schwarzschild field, and two examples with three degrees of freedom, the latter being the nonrelativistic spherically Coulomb potential and the relativistic cylinder symmetrical Coulomb potential with a magnetic field H. We show in particular that an Planck-Constant-Over-Two-Pi {sup 2}-approximation of the nonrelativisticmore » Coulomb field has no singularity at the origin (r= 0) whereas the classical trajectories are singular at r= 0. In the third example, we show in particular that for an arbitrary function {gamma}(H, z) the expression {beta}{identical_to}p{sub z}+{gamma}(H, z) is classically ( Planck-Constant-Over-Two-Pi = 0) a constant of motion, whereas for Planck-Constant-Over-Two-Pi {ne} 0 this holds only if {gamma}(H, z) is an arbitrary polynomial of second order in z. This statement is shown to extend correspondingly to a cylinder symmetrical Schwarzschild field with a magnetic field. We exhibit in detail a number of properties of the radially symmetric Schwarzschild field. We exhibit finally the problems of the nonintegrable Henon-Heiles Hamiltonian and give a short review of the regular Hilbert space representation of Moyal operators.« less

Black Hole Firewalls and Lorentzian Relativity

NASA Astrophysics Data System (ADS)

Winterberg, Friedwardt

2013-04-01

In a paper published (Z. f. Naturforsch. 56a, 889, 2001) I had shown that the pre-Einstein theory of relativity by Lorentz and Poincare, extended to the general theory of relativity and quantum mechanics, predicts the disintegration of matter by passing through the event horizon. The zero point vacuum energy is there cut-off at the Planck energy, but Lorentz-invariant all the way up to this energy. The cut-off creates a distinguished reference system in which this energy is at rest. For non-relativistic velocities relative to this reference system, the special and general relativity remain a good approximations, with matter held together in a stable equilibrium by electrostatic forces (or forces acting like them) as a solution of an elliptic partial differential equation derived from Maxwell's equation. But in approaching and crossing the velocity of light in the distinguished reference system, which is equivalent in approaching and crossing of the event horizon, the elliptic differential equation goes over into a hyperbolic differential equation (as in fluid dynamics from subsonic to supersonic flow), and there is no such equilibrium. According to Schwarzschild's interior solution, the event horizon of a collapsing mass appears first as a point in its center, thereafter moving radially outwards, thereby converting all the mass into energy, explaining the observed gamma ray bursters.

Quasistationary solutions of scalar fields around accreting black holes

NASA Astrophysics Data System (ADS)

Sanchis-Gual, Nicolas; Degollado, Juan Carlos; Izquierdo, Paula; Font, José A.; Montero, Pedro J.

2016-08-01

Massive scalar fields can form long-lived configurations around black holes. These configurations, dubbed quasibound states, have been studied both in the linear and nonlinear regimes. In this paper, we show that quasibound states can form in a dynamical scenario in which the mass of the black hole grows significantly due to the capture of infalling matter. We solve the Klein-Gordon equation numerically in spherical symmetry, mimicking the evolution of the spacetime through a sequence of analytic Schwarzschild black hole solutions of increasing mass. It is found that the frequency of oscillation of the quasibound states decreases as the mass of the black hole increases. In addition, accretion leads to an increase of the exponential decay of the scalar field energy. We compare the black hole mass growth rates used in our study with estimates from observational surveys and extrapolate our results to values of the scalar field masses consistent with models that propose scalar fields as dark matter in the universe. We show that, even for unrealistically large mass accretion rates, quasibound states around accreting black holes can survive for cosmological time scales. Our results provide further support to the intriguing possibility of the existence of dark matter halos based on (ultralight) scalar fields surrounding supermassive black holes in galactic centers.

Newton gauge cosmological perturbations for static spherically symmetric modifications of the de Sitter metric

NASA Astrophysics Data System (ADS)

Santa Vélez, Camilo; Enea Romano, Antonio

2018-05-01

Static coordinates can be convenient to solve the vacuum Einstein's equations in presence of spherical symmetry, but for cosmological applications comoving coordinates are more suitable to describe an expanding Universe, especially in the framework of cosmological perturbation theory (CPT). Using CPT we develop a method to transform static spherically symmetric (SSS) modifications of the de Sitter solution from static coordinates to the Newton gauge. We test the method with the Schwarzschild de Sitter (SDS) metric and then derive general expressions for the Bardeen's potentials for a class of SSS metrics obtained by adding to the de Sitter metric a term linear in the mass and proportional to a general function of the radius. Using the gauge invariance of the Bardeen's potentials we then obtain a gauge invariant definition of the turn around radius. We apply the method to an SSS solution of the Brans-Dicke theory, confirming the results obtained independently by solving the perturbation equations in the Newton gauge. The Bardeen's potentials are then derived for new SSS metrics involving logarithmic, power law and exponential modifications of the de Sitter metric. We also apply the method to SSS metrics which give flat rotation curves, computing the radial energy density profile in comoving coordinates in presence of a cosmological constant.

On the usefulness of relativistic space-times for the description of the Earth's gravitational field

NASA Astrophysics Data System (ADS)

Soffel, Michael; Frutos, Francisco

2016-12-01

The usefulness of relativistic space-times for the description of the Earth's gravitational field is investigated. A variety of exact vacuum solutions of Einstein's field equations (Schwarzschild, Erez and Rosen, Gutsunayev and Manko, Hernández-Pastora and Martín, Kerr, Quevedo, and Mashhoon) are investigated in that respect. It is argued that because of their multipole structure and influences from external bodies, all these exact solutions are not really useful for the central problem. Then, approximate space-times resulting from an MPM or post-Newtonian approximation are considered. Only in the DSX formalism that is of the first post-Newtonian order, all aspects of the problem can be tackled: a relativistic description (a) of the Earth's gravity field in a well-defined geocentric reference system (GCRS), (b) of the motion of solar system bodies in a barycentric reference system (BCRS), and (c) of inertial and tidal terms in the geocentric metric describing the external gravitational field. A relativistic SLR theory is also discussed with respect to our central problem. Orders of magnitude of many effects related to the Earth's gravitational field and SLR are given. It is argued that a formalism with accuracies better than of the first post-Newtonian order is not yet available.

Expressions for optical scalars and deflection angle at second order in terms of curvature scalars

NASA Astrophysics Data System (ADS)

Crisnejo, Gabriel; Gallo, Emanuel

2018-04-01

We present formal expressions for the optical scalars in terms of the curvature scalars in the weak gravitational lensing regime at second order in perturbations of a flat background without mentioning the extension of the lens or their shape. Also, by considering the thin lens approximation for static and axially symmetric configurations we obtain an expression for the second-order deflection angle which generalizes our previous result presented by Gallo and Moreschi [Phys. Rev. D 83, 083007 (2011)., 10.1103/PhysRevD.83.083007]. As applications of these formulas we compute the optical scalars for some known family of metrics, and we recover expressions for the deflection angle. In contrast to other works in the subject, our formalism allows a straightforward identification of how the different components of the curvature tensor contribute to the optical scalars and deflection angle. We also discuss in what sense the Schwarzschild solution can be thought as a true thin lens at second order.

Gravitational waves during inflation from a 5D large-scale repulsive gravity model

NASA Astrophysics Data System (ADS)

Reyes, Luz M.; Moreno, Claudia; Madriz Aguilar, José Edgar; Bellini, Mauricio

2012-10-01

We investigate, in the transverse traceless (TT) gauge, the generation of the relic background of gravitational waves, generated during the early inflationary stage, on the framework of a large-scale repulsive gravity model. We calculate the spectrum of the tensor metric fluctuations of an effective 4D Schwarzschild-de Sitter metric on cosmological scales. This metric is obtained after implementing a planar coordinate transformation on a 5D Ricci-flat metric solution, in the context of a non-compact Kaluza-Klein theory of gravity. We found that the spectrum is nearly scale invariant under certain conditions. One interesting aspect of this model is that it is possible to derive the dynamical field equations for the tensor metric fluctuations, valid not just at cosmological scales, but also at astrophysical scales, from the same theoretical model. The astrophysical and cosmological scales are determined by the gravity-antigravity radius, which is a natural length scale of the model, that indicates when gravity becomes repulsive in nature.

Circular geodesics of naked singularities in the Kehagias-Sfetsos metric of Hořava's gravity

NASA Astrophysics Data System (ADS)

Vieira, Ronaldo S. S.; Schee, Jan; Kluźniak, Włodek; Stuchlík, Zdeněk; Abramowicz, Marek

2014-07-01

We discuss photon and test-particle orbits in the Kehagias-Sfetsos (KS) metric of Hořava's gravity. For any value of the Hořava parameter ω, there are values of the gravitational mass M for which the metric describes a naked singularity, and this is always accompanied by a vacuum "antigravity sphere" on whose surface a test particle can remain at rest (in a zero angular momentum geodesic), and inside which no circular geodesics exist. The observational appearance of an accreting KS naked singularity in a binary system would be that of a quasistatic spherical fluid shell surrounded by an accretion disk, whose properties depend on the value of M, but are always very different from accretion disks familiar from the Kerr-metric solutions. The properties of the corresponding circular orbits are qualitatively similar to those of the Reissner-Nordström naked singularities. When event horizons are present, the orbits outside the Kehagias-Sfetsos black hole are qualitatively similar to those of the Schwarzschild metric.

Dispersion of gravitational waves in cold spherical interstellar medium

NASA Astrophysics Data System (ADS)

Barta, Dániel; Vasúth, Mátyás

We investigate the propagation of locally plane, small-amplitude, monochromatic gravitational waves (GWs) through cold compressible interstellar gas in order to provide a more accurate picture of expected waveforms for direct detection. The quasi-isothermal gas is concentrated in a spherical symmetric cloud held together by self-gravitation. Gravitational waves can be treated as linearized perturbations on the background inner Schwarzschild spacetime. The perturbed quantities lead to the field equations governing the gas dynamics and describe the interaction of gravitational waves with matter. We have shown that the transport equation of these amplitudes provides numerical solutions for the frequency-alteration. The decrease in frequency is driven by the energy dissipating process of GW-matter interactions. The decrease is significantly smaller than the magnitude of the original frequency and too small to be detectable by present second-generation and planned third-generation detectors. It exhibits a power-law relationship between original and decreased frequencies. The frequency deviation was examined particularly for the transient signal GW150914.

Tidal Love Numbers of Neutron Stars

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hinderer, Tanja

For a variety of fully relativistic polytropic neutron star models we calculate the star's tidal Love number k{sub 2}. Most realistic equations of state for neutron stars can be approximated as a polytrope with an effective index n {approx} 0.5-1.0. The equilibrium stellar model is obtained by numerical integration of the Tolman-Oppenheimer-Volkhov equations. We calculate the linear l = 2 static perturbations to the Schwarzschild spacetime following the method of Thorne and Campolattaro. Combining the perturbed Einstein equations into a single second-order differential equation for the perturbation to the metric coefficient g{sub tt} and matching the exterior solution to themore » asymptotic expansion of the metric in the star's local asymptotic rest frame gives the Love number. Our results agree well with the Newtonian results in the weak field limit. The fully relativistic values differ from the Newtonian values by up to {approx}24%. The Love number is potentially measurable in gravitational wave signals from inspiralling binary neutron stars.« less

Ultrarelativistic boost of a black hole in the magnetic universe of Levi-Civita-Bertotti-Robinson

NASA Astrophysics Data System (ADS)

Ortaggio, Marcello; Astorino, Marco

2018-05-01

We consider an exact Einstein-Maxwell solution constructed by Alekseev and Garcia, which describes a Schwarzschild black hole immersed in the magnetic universe of Levi-Civita, Bertotti, and Robinson (LCBR). After reviewing the basic properties of this spacetime, we study the ultrarelativistic limit in which the black hole is boosted to the speed of light, while sending its mass to 0. This results in a nonexpanding impulsive wave traveling in the LCBR universe. The wave front is a 2-sphere carrying two null point particles at its poles—a remnant of the structure of the original static spacetime. It is also shown that the obtained line element belongs to the Kundt class of spacetimes, and the relation with the known family of exact gravitational waves of finite duration propagating in the LCBR background is clarified. In the limit of a vanishing electromagnetic field, one point particle is pushed away to infinity and the single-particle Aichelburg-Sexl p p -wave propagating in Minkowski space is recovered.

Buchdahl compactness limit for a pure Lovelock static fluid star

NASA Astrophysics Data System (ADS)

Dadhich, Naresh; Chakraborty, Sumanta

2017-03-01

We obtain the Buchdahl compactness limit for a pure Lovelock static fluid star and verify that the limit following from the uniform-density Schwarzschild's interior solution, which is universal irrespective of the gravitational theory (Einstein or Lovelock), is true in general. In terms of surface potential Φ (r ) , it means at the surface of the star r =r0, Φ (r0)<2 N (d -N -1 )/(d -1 )2, where d and N indicate spacetime dimensions and Lovelock order, respectively. For a given N , Φ (r0) is maximum for d =2 N +2 , while it is always 4 /9 , Buchdahl's limit, for d =3 N +1 . It is also remarkable that for N =1 Einstein gravity, or for pure Lovelock in d =3 N +1 , Buchdahl's limit is equivalent to the criterion that gravitational field energy exterior to the star must be less than half its gravitational mass, having no reference to the interior at all.

Relativistic low angular momentum accretion: long time evolution of hydrodynamical inviscid flows

NASA Astrophysics Data System (ADS)

Mach, Patryk; Piróg, Michał; Font, José A.

2018-05-01

We investigate relativistic low angular momentum accretion of inviscid perfect fluid onto a Schwarzschild black hole. The simulations are performed with a general-relativistic, high-resolution (second-order), shock-capturing, hydrodynamical numerical code. We use horizon-penetrating Eddington–Finkelstein coordinates to remove inaccuracies in regions of strong gravity near the black hole horizon and show the expected convergence of the code with the Michel solution and stationary Fishbone–Moncrief toroids. We recover, in the framework of relativistic hydrodynamics, the qualitative behavior known from previous Newtonian studies that used a Bondi background flow in a pseudo-relativistic gravitational potential with a latitude-dependent angular momentum at the outer boundary. Our models exhibit characteristic ‘turbulent’ behavior and the attained accretion rates are lower than those of the Bondi–Michel radial flow. For sufficiently low values of the asymptotic sound speed, geometrically thick tori form in the equatorial plane surrounding the black hole horizon while accretion takes place mainly through the poles.

Analytical Solutions of the Gravitational Field Equations in de Sitter and Anti-de Sitter Spacetimes

NASA Astrophysics Data System (ADS)

Da Rocha, R.; Capelas Oliveira, E.

2009-01-01

The generalized Laplace partial differential equation, describing gravitational fields, is investigated in de Sitter spacetime from several metric approaches—such as the Riemann, Beltrami, Börner-Dürr, and Prasad metrics—and analytical solutions of the derived Riccati radial differential equations are explicitly obtained. All angular differential equations trivially have solutions given by the spherical harmonics and all radial differential equations can be written as Riccati ordinary differential equations, which analytical solutions involve hypergeometric and Bessel functions. In particular, the radial differential equations predict the behavior of the gravitational field in de Sitter and anti-de Sitter spacetimes, and can shed new light on the investigations of quasinormal modes of perturbations of electromagnetic and gravitational fields in black hole neighborhood. The discussion concerning the geometry of de Sitter and anti-de Sitter spacetimes is not complete without mentioning how the wave equation behaves on such a background. It will prove convenient to begin with a discussion of the Laplace equation on hyperbolic space, partly since this is of interest in itself and also because the wave equation can be investigated by means of an analytic continuation from the hyperbolic space. We also solve the Laplace equation associated to the Prasad metric. After introducing the so called internal and external spaces—corresponding to the symmetry groups SO(3,2) and SO(4,1) respectively—we show that both radial differential equations can be led to Riccati ordinary differential equations, which solutions are given in terms of associated Legendre functions. For the Prasad metric with the radius of the universe independent of the parametrization, the internal and external metrics are shown to be of AdS-Schwarzschild-like type, and also the radial field equations arising are shown to be equivalent to Riccati equations whose solutions can be written in terms of generalized Laguerre polynomials and hypergeometric confluent functions.

Quasinormal Modes of a Noncommutative-Geometry-Inspired Schwarzschild Black Hole

NASA Astrophysics Data System (ADS)

Liang, Jun

2018-01-01

Not Available Supported by the Natural Science Foundation of Education Department of Shannxi Province under Grant No 15JK1077, and the Doctorial Scientific Research Starting Fund of Shannxi University of Science and Technology under Grant No BJ12-02.

More on accreting black hole spacetime in equatorial plane

NASA Astrophysics Data System (ADS)

Salahshoor, K.; Nozari, K.; Khesali, A. R.

2017-02-01

Spacetime around an accreting black hole is an interesting issue to study. The metric of an isolated black hole (rotating or non-rotating) spacetime has been well-known for decades. Although metrics of some spacetimes containing accreting black holes are known in some situations, the issue has some faces that are not well-known yet and need further investigation. In this paper, we construct a new form of metric which the effect of accretion disk on black hole spacetime is taken into account in the equatorial plane. We study motion and trajectories of massive particles and also photons falling from infinity towards black hole in equatorial plane around the black hole. We use an exponential form for the density profile of the accretion disk in equatorial plane as ρ =ρ0e^{-α r}. We show that with this density profile, the disk is radially stable if α ≤ 3 × 10^{-3} (in units of length inverse). In order to study some important quantities related to the accretion disks such as locations of marginally stable circular orbits (r_{ms} or r_{ISCO}), marginally bounded circular orbits (r_{mb}), and also photon orbits in equatorial plane, we use the effective potential approach. We show that in this spacetime metric the innermost stable circular orbit in equatorial plane is given by r_{ISCO}=4.03 μ (where μ =MG/c 2) which is different, but comparable, with the Schwarzschild spacetime result, r^{(Sch)}_{ISCO}=6 μ . We show that the maximum radiation efficiency of the accretion disk, η , in equatorial plane is 8.6 percent which is greater than the corresponding value for Schwarzschild spacetime. Finally, we show that in this setup photons can have stable circular orbits in equatorial plane unlike the Schwarzschild spacetime.

Effect of the Kerr Metric on Photosperic Radius Expansion in X Ray Burst

NASA Astrophysics Data System (ADS)

Kalita, S.; Barman, A.

2017-12-01

The main objective of this paper is to study general relativistic effects on the photospheric radius expansion during an X-ray burst. We examine how the Kerr metric causes a shift in the effective temperature and radiation flux with respect to the Schwarzschild values during mass accretion onto a neutron star or a black hole resulting in the X-ray burst. The spin of the compact object is used up to the maximal Kerr limit χ = 0.99 with different latitudes of accretion emission. The amplitude of temperature shift relative to the Schwarzschild case is found to be δ T/ T ≈ - (10-3 - 10-4) for the range χ = 0.1 - 0.99 at latitudes θ = 0o , 30o, 45o and 88o. The ratio of emission flux in the Kerr metric to that in the Schwarzschild metric, F(K)/F(S), is found to be less than unity. It goes up to a maximum of 0.9 for the lowest nonzero value of the spin parameter (i.e., 0.1). For the maximal Kerr limit, χ = 0.99 , it saturates near 0.8. This effect is more prominent towards the pole. This reduction in temperature and flux is found to be consistent with the absence of photospheric radius expansion in the X Ray burst LMXB 4U 1608-52, observed by NuSTAR. Although this is not uniquely ascribed to the metric, it is believed that the spacetime metric effect in the burst phenomena can be used as a probe for testing general relativity. Also, the shift in temperature or the radiation flux might have an observable signature in the element synthesis processes in such environments.

Imaging the supermassive black hole shadow and jet base of M87 with the event horizon telescope

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lu, Ru-Sen; Fish, Vincent L.; Doeleman, Sheperd S.

2014-06-20

The Event Horizon Telescope (EHT) is a project to assemble a Very Long Baseline Interferometry (VLBI) network of millimeter wavelength dishes that can resolve strong field general relativistic signatures near a supermassive black hole. As planned, the EHT will include enough dishes to enable imaging of the predicted black hole 'shadow', a feature caused by severe light bending at the black hole boundary. The center of M87, a giant elliptical galaxy, presents one of the most interesting EHT targets as it exhibits a relativistic jet, offering the additional possibility of studying jet genesis on Schwarzschild radius scales. Fully relativistic modelsmore » of the M87 jet that fit all existing observational constraints now allow horizon-scale images to be generated. We perform realistic VLBI simulations of M87 model images to examine the detectability of the black shadow with the EHT, focusing on a sequence of model images with a changing jet mass load radius. When the jet is launched close to the black hole, the shadow is clearly visible both at 230 and 345 GHz. The EHT array with a resolution of 20-30 μas resolution (∼2-4 Schwarzschild radii) is able to image this feature independent of any theoretical models and we show that imaging methods used to process data from optical interferometers are applicable and effective for EHT data sets. We demonstrate that the EHT is also capable of tracing real-time structural changes on a few Schwarzschild radii scales, such as those implicated by very high-energy flaring activity of M87. While inclusion of ALMA in the EHT is critical for shadow imaging, the array is generally robust against loss of a station.« less

Hawking radiation inside a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Hamilton, Andrew J. S.

2018-05-01

The boundary of any observer's spacetime is the boundary that divides what the observer can see from what they cannot see. The boundary of an observer's spacetime in the presence of a black hole is not the true (future event) horizon of the black hole, but rather the illusory horizon, the dimming, redshifting surface of the star that collapsed to the black hole long ago. The illusory horizon is the source of Hawking radiation seen by observers both outside and inside the true horizon. The perceived acceleration (gravity) on the illusory horizon sets the characteristic frequency scale of Hawking radiation, even if that acceleration varies dynamically, as it must do from the perspective of an infalling observer. The acceleration seen by a non-rotating free-faller both on the illusory horizon below and in the sky above is calculated for a Schwarzschild black hole. Remarkably, as an infaller approaches the singularity, the acceleration becomes isotropic, and diverging as a power law. The isotropic, power-law character of the Hawking radiation, coupled with conservation of energy-momentum, the trace anomaly, and the familiar behavior of Hawking radiation far from the black hole, leads to a complete description of the quantum energy-momentum inside a Schwarzschild black hole. The quantum energy-momentum near the singularity diverges as r^{-6}, and consists of relativistic Hawking radiation and negative energy vacuum in the ratio 3 : - 2. The classical back reaction of the quantum energy-momentum on the geometry, calculated using the Einstein equations, serves merely to exacerbate the singularity. All the results are consistent with traditional calculations of the quantum energy-momentum in 1 + 1 spacetime dimensions.

The Weak-Line T Tauri Star V410 Tau

DTIC Science & Technology

2003-01-01

700052 Tashkent, Uzbekistan 7 USRA/USNO Flagstaff Station, PO Box 1149, Flagstaff, AZ 86002-1149, USA 8 Thüringer Landessternwarte, Karl ... Schwarzschild -Observatorium, Sternwarte 5, 07778 Tautenburg, Germany 9 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA 10

THE EFFECT OF GRAVITATION ON THE POLARIZATION STATE OF A LIGHT RAY

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Tanay; Sen, A. K.

In the present work, detailed calculations have been carried out on the rotation of the polarization vector of an electromagnetic wave due to the presence of a gravitational field of a rotating body. This has been done using the general expression of Maxwell’s equation in curved spacetime. Considering the far-field approximation (i.e., the impact parameter is greater than the Schwarzschild radius and rotation parameter), the amount of rotation of the polarization vector as a function of impact parameter has been obtained for a rotating body (considering Kerr geometry). The present work shows that the rotation of the polarization vector cannotmore » be observed in the case of Schwarzschild geometry. This work also calculates the rotational effect when considering prograde and retrograde orbits for the light ray. Although the present work demonstrates the effect of rotation of the polarization vector, it confirms that there would be no net polarization of an electromagnetic wave due to the curved spacetime geometry in a Kerr field.« less

No-Hair Theorem for Black Holes in Astrophysical Environments

NASA Astrophysics Data System (ADS)

Gürlebeck, Norman

2015-04-01

According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if it is surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. Nonetheless, the subsequent formulation of the no-hair theorem holds: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity and, thus, all sources is that of a Schwarzschild black hole. It still has no hair. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure some aspects of the distortion, vanish as was already shown in approximations to general relativity. But here we prove this property for astrophysical relevant black holes in full general relativity.

Quantum Gravity Effects on Hawking Radiation of Schwarzschild-de Sitter Black Holes

NASA Astrophysics Data System (ADS)

Singh, T. Ibungochouba; Meitei, I. Ablu; Singh, K. Yugindro

2017-08-01

The correction of Hawking temperature of Schwarzschild-de Sitter (SdS) black hole is investigated using the generalized Klein-Gordon equation and the generalized Dirac equation by taking the quantum gravity effects into account. We derive the corrected Hawking temperatures for scalar particles and fermions crossing the event horizon. The quantum gravity effects prevent the rise of temperature in the SdS black hole. Besides correction of Hawking temperature, the Hawking radiation of SdS black hole is also investigated using massive particles tunneling method. By considering self gravitation effect of the emitted particles and the space time background to be dynamical, it is also shown that the tunneling rate is related to the change of Bekenstein-Hawking entropy and small correction term (1 + 2 β m 2). If the energy and the angular momentum are taken to be conserved, the derived emission spectrum deviates from the pure thermal spectrum. This result gives a correction to the Hawking radiation and is also in agreement with the result of Parikh and Wilczek.

Schwarzschild radius from Monte Carlo calculation of the Wilson loop in supersymmetric matrix quantum mechanics.

PubMed

Hanada, Masanori; Miwa, Akitsugu; Nishimura, Jun; Takeuchi, Shingo

2009-05-08

In the string-gauge duality it is important to understand how the space-time geometry is encoded in gauge theory observables. We address this issue in the case of the D0-brane system at finite temperature T. Based on the duality, the temporal Wilson loop W in gauge theory is expected to contain the information of the Schwarzschild radius RSch of the dual black hole geometry as log(W)=RSch/(2pialpha'T). This translates to the power-law behavior log(W)=1.89(T/lambda 1/3)-3/5, where lambda is the 't Hooft coupling constant. We calculate the Wilson loop on the gauge theory side in the strongly coupled regime by performing Monte Carlo simulations of supersymmetric matrix quantum mechanics with 16 supercharges. The results reproduce the expected power-law behavior up to a constant shift, which is explainable as alpha' corrections on the gravity side. Our conclusion also demonstrates manifestly the fuzzball picture of black holes.

No-hair theorem for black holes in astrophysical environments.

PubMed

Gürlebeck, Norman

2015-04-17

According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often violated, e.g., if the black hole is part of a binary system or if it is surrounded by an accretion disk. In these cases, the black hole is distorted due to tidal forces. Nonetheless, the subsequent formulation of the no-hair theorem holds: The contribution of the distorted black hole to the multipole moments that describe the gravitational field close to infinity and, thus, all sources is that of a Schwarzschild black hole. It still has no hair. This implies that there is no multipole moment induced in the black hole and that its second Love numbers, which measure some aspects of the distortion, vanish as was already shown in approximations to general relativity. But here we prove this property for astrophysical relevant black holes in full general relativity.

An Experience to be Remembered

NASA Astrophysics Data System (ADS)

Torres-Peimbert, S.

1999-05-01

In August 1960 the 106th Meeting of the American Astronomical Society took place in Mexico City (it was the first time such a meeting took place in Mexico). There were 80 technical papers presented. A highlight of the meeting was the Russell Memorial lecture, given by Martin Schwarzschild, of Princeton University Observatory; Schwarzschild spoke on convection in stars. A public lecture was given by Donald H. Menzel, director of Harvard Observatory. Among the social activities were the banquet at Chapultepec Castle and a visit to Observatorio Astrofísico de Tonantzintla. I was an undergraduate in Physics associated with the Observatorio Astronomico Nacional. My job was to assist with the projection of lantern slides (heavy 3 1/4" by 4" glass mounted films). It was an extraordinary experience to meet, in the flesh, authors of textbooks I was reading and to witness the scientific presentations and heated arguments that took place around them. This meeting indeed marked my life, because it was then that I decided to become a professional astronomer.

High-order tail in Schwarzschild spacetime

NASA Astrophysics Data System (ADS)

Casals, Marc; Ottewill, Adrian

2015-12-01

We present an analysis of the behavior at late times of linear field perturbations of a Schwarzschild black hole spacetime. In particular, we give explicit analytic expressions for the field perturbations (for a specific ℓ-multipole) of general spin up to the first four orders at late times. These expressions are valid at arbitrary radius and include, apart from the well-known power-law tail decay at leading order (˜t-2 ℓ-3), a new logarithmic behavior at third leading order (˜t-2 ℓ-5ln t ). We obtain these late-time results by developing an analytical formalism initially formulated by Mano, Suzuki and Takasugi (MST) [Prog. Theor. Phys. 95, 1079 (1996); 96, 549 (1996)] formalism and by expanding the various MST Fourier-mode quantities for small frequency. While we give explicit expansions up to the first four leading orders (for small frequency for the Fourier modes, for late time for the field perturbation), we give a prescription for obtaining expressions to arbitrary order within a "perturbative regime."

Possible Alternatives to the Supermassive Black Hole at the Galactic Center

NASA Astrophysics Data System (ADS)

Zakharov, A. F.

2015-12-01

Now there are two basic observational techniques to investigate a gravitational potential at the Galactic Center, namely, (a) monitoring the orbits of bright stars near the Galactic Center to reconstruct a gravitational potential; (b) measuring the size and shape of shadows around black hole giving an alternative possibility to evaluate black hole parameters in mm-band with VLBI-technique. At the moment, one can use a small relativistic correction approach for stellar orbit analysis (however, in the future the approximation will not be precise enough due to enormous progress of observational facilities) while for smallest structure analysis in VLBI observations one really needs a strong gravitational field approximation. We discuss results of observations, their conventional interpretations, tensions between observations and models and possible hints for a new physics from the observational data and tensions between observations and interpretations. We discuss an opportunity to use a Schwarzschild metric for data interpretation or we have to use more exotic models such as Reissner-Nordstrom or Schwarzschild-de-Sitter metrics for better fits.

Equilibrium configurations of perfect fluid orbiting Schwarzschild-de Sitter black holes

NASA Astrophysics Data System (ADS)

Stuchlík, Z.; Slaný, P.; Hledík, S.

2000-11-01

The hydrodynamical structure of perfect fluid orbiting Schwarzschild-de Sitter black holes is investigated for configurations with uniform distribution of angular momentum density. It is shown that in the black-hole backgrounds admitting the existence of stable circular geodesics, closed equipotential surfaces with a cusp, allowing the existence of toroidal accretion disks, can exist. Two surfaces with a cusp exist for the angular momentum density smaller than the one corresponding to marginally bound circular geodesics; the equipotential surface corresponding to the marginally bound circular orbit has just two cusps. The outer cusp is located nearby the static radius where the gravitational attraction is compensated by the cosmological repulsion. Therefore, due to the presence of a repulsive cosmological constant, the outflow from thick accretion disks can be driven by the same mechanism as the accretion onto the black hole. Moreover, properties of open equipotential surfaces in vicinity of the axis of rotation suggest a strong collimation effects of the repulsive cosmological constant acting on jets produced by the accretion disks.

Dirac Hamiltonian and Reissner-Nordström metric: Coulomb interaction in curved space-time

NASA Astrophysics Data System (ADS)

Noble, J. H.; Jentschura, U. D.

2016-03-01

We investigate the spin-1 /2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordström space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordström geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational and electrogravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electrogravitational correction terms to the potential proportional to αnG , where α is the fine-structure constant and G is the gravitational coupling constant. The particle-antiparticle symmetry found for the Dirac-Schwarzschild geometry (and for other geometries which do not include electromagnetic interactions) is shown to be explicitly broken due to the electrostatic coupling. The resulting spectrum of radially symmetric, electrostatically bound systems (with gravitational corrections) is evaluated for example cases.

Gravastars in f (R ,T ) gravity

NASA Astrophysics Data System (ADS)

Das, Amit; Ghosh, Shounak; Guha, B. K.; Das, Swapan; Rahaman, Farook; Ray, Saibal

2017-06-01

We propose a unique stellar model under the f (R ,T ) gravity by using the conjecture of Mazur-Mottola [P. Mazur and E. Mottola, Report No. LA-UR-01-5067, P. Mazur and E. Mottola, Proc. Natl. Acad. Sci. USA 101, 9545 (2004), 10.1073/pnas.0402717101] which is known as gravastar and a viable alternative to the black hole as available in literature. This gravastar is described by the three different regions, viz., (I) Interior core region, (II) Intermediate thin shell, and (III) Exterior spherical region. The pressure within the interior region is equal to the constant negative matter density which provides a repulsive force over the thin spherical shell. This thin shell is assumed to be formed by a fluid of ultrarelativistic plasma and the pressure, which is directly proportional to the matter-energy density according to Zel'dovich's conjecture of stiff fluid [Y. B. Zel'dovich, Mon. Not. R. Astron. Soc. 160, 1 (1972), 10.1093/mnras/160.1.1P], does counterbalance the repulsive force exerted by the interior core region. The exterior spherical region is completely vacuum and assumed to be de Sitter spacetime which can be described by the Schwarzschild solution. Under this specification we find out a set of exact and singularity-free solution of the gravastar which presents several other physically valid features within the framework of alternative gravity.

Quasinormal Modes of a Noncommutative-Geometry-Inspired Schwarzschild Black Hole: Gravitational, Electromagnetic and Massless Dirac Perturbations

NASA Astrophysics Data System (ADS)

Liang, >Jun

2018-05-01

Not Available Supported by the Natural Science Foundation of Education Department of Shannxi Province under Grant No 15JK1077, and the Doctorial Scientific Research Starting Fund of Shannxi University of Science and Technology under Grant No BJ12-02.

Nakedly singular non-vacuum gravitating equilibrium states

NASA Astrophysics Data System (ADS)

Woszczyna, Andrzej; Kutschera, Marek; Kubis, Sebastian; Czaja, Wojciech; Plaszczyk, Piotr; Golda, Zdzisław A.

2016-01-01

Non-vacuum static spherically symmetric spacetimes with central point-like repulsive gravity sources are investigated. Both the symmetries of spacetime and the degree of irregularity of curvature invariants, are the same as for the Schwarzschild case. The equilibrium configurations are modelled using the neutron star polytrope equation of state.

Two black hole initial data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leski, Szymon

2005-06-15

The Misner initial data are a standard example of time-symmetric initial data with two apparent horizons. Compact formulae describing such data are presented in the cases of equal or nonequal masses (i.e. isometric or nonisometric horizons). The interaction energy in the 'Schwarzschild + test-particle' limit of the Misner data is analyzed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ko, Sung Moon; Park, Jeong-Hyuck; Suh, Minwoo, E-mail: sinsmk2003@sogang.ac.kr, E-mail: park@sogang.ac.kr, E-mail: minsuh@usc.edu

Double Field Theory suggests to view the whole massless sector of closed strings as the gravitational unity. The fundamental symmetries therein, including the O( D , D ) covariance, can determine unambiguously how the Standard Model as well as a relativistic point particle should couple to the closed string massless sector. The theory also refines the notion of singularity. We consider the most general, spherically symmetric, asymptotically flat, static vacuum solution to D =4 Double Field Theory, which contains three free parameters and consequently generalizes the Schwarzschild geometry. Analyzing the circular geodesic of a point particle in string frame, wemore » obtain the orbital velocity as a function of R /( M {sub ∞} G ) which is the dimensionless radial variable normalized by mass. The rotation curve generically features a maximum and thus non-Keplerian over a finite range, while becoming asymptotically Keplerian at infinity, R /( M {sub ∞} G )→ ∞. The adoption of the string frame rather than Einstein frame is the consequence of the fundamental symmetry principle. Our result opens up a new scheme to solve the dark matter/energy problems by modifying General Relativity at 'short' range of R /( M {sub ∞} G ).« less

Eikonalization of conformal blocks

DOE PAGES

Fitzpatrick, A. Liam; Kaplan, Jared; Walters, Matthew T.; ...

2015-09-03

Classical field configurations such as the Coulomb potential and Schwarzschild solution are built from the t-channel exchange of many light degrees of freedom. We study the CFT analog of this phenomenon, which we term the 'eikonalization' of conformal blocks. We show that when an operator T appears in the OPE Ο(x)Ο(0), then the large spin Fock space states [TT···T] ℓ also appear in this OPE with a computable coefficient. The sum over the exchange of these Fock space states in an correlator build the classical 'T field' in the dual AdS description. In some limits the sum of all Fockmore » space exchanges can be represented as the exponential of a single T exchange in the 4-pt correlator of O. Our results should be useful for systematizing 1/ℓ perturbation theory in general CFTs and simplifying the computation of large spin OPE coefficients. As examples we obtain the leading log ℓ dependence of Fock space conformal block coefficients, and we directly compute the OPE coefficients of the simplest ‘triple-trace’ operators.« less

Radial accretion flows on static spherically symmetric black holes

NASA Astrophysics Data System (ADS)

Chaverra, Eliana; Sarbach, Olivier

2015-08-01

We analyze the steady radial accretion of matter into a nonrotating black hole. Neglecting the self-gravity of the accreting matter, we consider a rather general class of static, spherically symmetric and asymptotically flat background spacetimes with a regular horizon. In addition to the Schwarzschild metric, this class contains certain deformation of it, which could arise in alternative gravity theories or from solutions of the classical Einstein equations in the presence of external matter fields. Modeling the ambient matter surrounding the black hole by a relativistic perfect fluid, we reformulate the accretion problem as a dynamical system, and under rather general assumptions on the fluid equation of state, we determine the local and global qualitative behavior of its phase flow. Based on our analysis and generalizing previous work by Michel, we prove that for any given positive particle density number at infinity, there exists a unique radial, steady-state accretion flow which is regular at the horizon. We determine the physical parameters of the flow, including its accretion and compression rates, and discuss their dependency on the background metric.

Collapsing shells and black holes: a quantum analysis

NASA Astrophysics Data System (ADS)

Leal, P.; Bernardini, A. E.; Bertolami, O.

2018-06-01

The quantization of a spherically symmetric null shells is performed and extended to the framework of phase-space noncommutative (NC) quantum mechanics. This shell is considered to be inside a black hole event horizon. The encountered properties are investigated making use of the Israel junction conditions on the shell, considering that it is the boundary between two spherically symmetric spacetimes. Using this method, and considering two different Kantowski–Sachs spacetimes as a representation for the Schwarzschild spacetime, the relevant quantities on the shell are computed, such as its stress-energy tensor and the action for the whole spacetime. From the obtained action, the Wheeler–deWitt equation is deduced in order to provide the quantum framework for the system. Solutions for the wave function of the system are found on both the commutative and NC scenarios. It is shown that, on the commutative version, the wave function has a purely oscillatory behavior in the interior of the shell. In the NC setting, it is shown that the wave function vanishes at the singularity, as well as, at the event horizon of the black hole.

Gauge field back reaction on a black hole

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hochberg, D.; Kephart, T.W.

1993-02-15

The order-[h bar] fluctuations of gauge fields in the vicinity of a black hole can create a repulsive antigravity region extending out beyond the renormalized Schwarzschild horizon. If the strength of this repulsive force increases as higher orders in the back reaction are included, the formation of a wormholelike object could occur.

Direct Detection of the Close Companion of Polaris With the Hubble Space Telescope

DTIC Science & Technology

2008-09-01

Italy 4 European Southern Observatory, Karl - Schwarzschild -Str. 2, 85748 Garching bei München, Germany; bono@mporzio.astro.it 5 Harvard University, 60...the late Karl Kamper to the study of Polaris were crucial to this work. REFERENCES Anderson, J., & King, I. R. 2004, Instrument Science Report ACS 2004

A Hamiltonian approach for the Thermodynamics of AdS black holes

NASA Astrophysics Data System (ADS)

Baldiotti, M. C.; Fresneda, R.; Molina, C.

2017-07-01

In this work we study the Thermodynamics of D-dimensional Schwarzschild-anti de Sitter (SAdS) black holes. The minimal Thermodynamics of the SAdS spacetime is briefly discussed, highlighting some of its strong points and shortcomings. The minimal SAdS Thermodynamics is extended within a Hamiltonian approach, by means of the introduction of an additional degree of freedom. We demonstrate that the cosmological constant can be introduced in the thermodynamic description of the SAdS black hole with a canonical transformation of the Schwarzschild problem, closely related to the introduction of an anti-de Sitter thermodynamic volume. The treatment presented is consistent, in the sense that it is compatible with the introduction of new thermodynamic potentials, and respects the laws of black hole Thermodynamics. By demanding homogeneity of the thermodynamic variables, we are able to construct a new equation of state that completely characterizes the Thermodynamics of SAdS black holes. The treatment naturally generates phenomenological constants that can be associated with different boundary conditions in underlying microscopic theories. A whole new set of phenomena can be expected from the proposed generalization of SAdS Thermodynamics.

MEASURING DARK MATTER PROFILES NON-PARAMETRICALLY IN DWARF SPHEROIDALS: AN APPLICATION TO DRACO

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jardel, John R.; Gebhardt, Karl; Fabricius, Maximilian H.

2013-02-15

We introduce a novel implementation of orbit-based (or Schwarzschild) modeling that allows dark matter density profiles to be calculated non-parametrically in nearby galaxies. Our models require no assumptions to be made about velocity anisotropy or the dark matter profile. The technique can be applied to any dispersion-supported stellar system, and we demonstrate its use by studying the Local Group dwarf spheroidal galaxy (dSph) Draco. We use existing kinematic data at larger radii and also present 12 new radial velocities within the central 13 pc obtained with the VIRUS-W integral field spectrograph on the 2.7 m telescope at McDonald Observatory. Ourmore » non-parametric Schwarzschild models find strong evidence that the dark matter profile in Draco is cuspy for 20 {<=} r {<=} 700 pc. The profile for r {>=} 20 pc is well fit by a power law with slope {alpha} = -1.0 {+-} 0.2, consistent with predictions from cold dark matter simulations. Our models confirm that, despite its low baryon content relative to other dSphs, Draco lives in a massive halo.« less

Vacuum Stress in Schwarzschild Spacetime

NASA Astrophysics Data System (ADS)

Howard, Kenneth Webster

Vacuum stress in the conformally invariant scalar field in the region exterior to the horizon of a Schwarzschild black hole is examined. In the Hartle-Hawking vacuum state <(phi)('2)> and are calculated. Covariant point-splitting renormalization is used, as is a mode sum expression for the Hartle-Hawking propagator. It is found that <(phi)('2)> separates naturally into two parts, a part that has a simple analytic form coinciding with the approximate expression of Whiting and Page, and a small remainder. The results of our numerical evaluation of the remainder agree with, but are more accurate than, those previously given by Fawcett. We find that also separates into two terms. The first coincides with the approximate expression obtained by Page with a Gaussian approximation to the proper time Green function. The second term, composed of sums over mode functions, is evaluated numerically. It is found that the total expression is in good qualitative agreement with Page's approximation. Our results disagree with previous numerical results given by Fawcett. The error in Fawcett's calculation is explained.

Is there an ordinary supermassive black hole at the Galactic Center?

NASA Astrophysics Data System (ADS)

Zakharov, A. F.

Now there are two basic observational techniques to investigate a gravitational potential at the Galactic Center, namely, a) monitoring the orbits of bright stars near the Galactic Center to reconstruct a gravitational potential; b) measuring a size and a shape of shadows around black hole giving an alternative possibility to evaluate black hole parameters in mm-band with VLBI-technique. At the moment one can use a small relativistic correction approach for stellar orbit analysis (however, in the future the approximation will not be not precise enough due to enormous progress of observational facilities) while now for smallest structure analysis in VLBI observations one really needs a strong gravitational field approximation. We discuss results of observations, their conventional interpretations, tensions between observations and models and possible hints for a new physics from the observational data and tensions between observations and interpretations. We will discuss an opportunity to use a Schwarzschild metric for data interpretation or we have to use more exotic models such as Reissner - Nordström or Schwarzschild - de-Sitter metrics for better fits.

An ordinary supermassive black hole at the Galactic Center: pro and contra

NASA Astrophysics Data System (ADS)

Zakharov, Alexander

2016-07-01

Now there are two basic observational techniques to investigate a gravitational potential at the Galactic Center, namely, a) monitoring the orbits of bright stars near the Galactic Center to reconstruct a gravitational potential; b) measuring a size and a shape of shadows around black hole giving an alternative possibility to evaluate black hole parameters in mm-band with VLBI-technique. At the moment one can use a small relativistic correction approach for stellar orbit analysis (however, in the future the approximation will not be not precise enough due to enormous progress of observational facilities) while now for smallest structure analysis in VLBI observations one really needs a strong gravitational field approximation. We discuss results of observations, their conventional interpretations, tensions between observations and models and possible hints for a new physics from the observational data and tensions between observations and interpretations. We will discuss an opportunity to use a Schwarzschild metric for data interpretation or we have to use more exotic models such as Yukawa potential, Reissner -- Nordstrom or Schwarzschild -- de-Sitter metrics for better fits.

Radiative acceleration in Schwarzschild space-times

NASA Astrophysics Data System (ADS)

Keane, A. J.; Barrett, R. K.; Simmons, J. F. L.

2001-03-01

We examine the radial motion of a material particle in the intense radiation field of a static spherically symmetric compact object with spherical emitting surface outside the Schwarzschild radius. This paper generalizes previous work which dealt with radial motion in the Thomson limit, where the radiation force is simply proportional to the radiative flux. In the general case the average time component of the 4-momentum transferred to the particle is not negligible compared with its rest mass. Consequently, we find that the frequency dependence of the radiation force owing to Compton scattering for highly energetic photons gives rise to an increase in the effective mass of the test particle. In this work we outline the effects of this frequency dependence and compare these with the results in the Thomson limit. We present the frequency dependent saturation velocity curves for a range of stellar luminosities and radiation frequencies and present the resulting phase-space diagrams corresponding to the radial test particle trajectories. In particular, the stable equilibrium points which exist in the Thomson limit are found to be absent in the general case.

Spectroscopy of the Schwarzschild black hole at arbitrary frequencies.

PubMed

Casals, Marc; Ottewill, Adrian

2012-09-14

Linear field perturbations of a black hole are described by the Green function of the wave equation that they obey. After Fourier decomposing the Green function, its two natural contributions are given by poles (quasinormal modes) and a largely unexplored branch cut in the complex frequency plane. We present new analytic methods for calculating the branch cut on a Schwarzschild black hole for arbitrary values of the frequency. The branch cut yields a power-law tail decay for late times in the response of a black hole to an initial perturbation. We determine explicitly the first three orders in the power-law and show that the branch cut also yields a new logarithmic behavior T(-2ℓ-5)lnT for late times. Before the tail sets in, the quasinormal modes dominate the black hole response. For electromagnetic perturbations, the quasinormal mode frequencies approach the branch cut at large overtone index n. We determine these frequencies up to n(-5/2) and, formally, to arbitrary order. Highly damped quasinormal modes are of particular interest in that they have been linked to quantum properties of black holes.

Bound states of spin-half particles in a static gravitational field close to the black hole field

NASA Astrophysics Data System (ADS)

Spencer-Smith, A. F.; Gossel, G. H.; Berengut, J. C.; Flambaum, V. V.

2013-03-01

We consider the bound-state energy levels of a spin-1/2 fermion in the gravitational field of a near-black hole object. In the limit that the metric of the body becomes singular, all binding energies tend to the rest-mass energy (i.e. total energy approaches zero). We present calculations of the ground state energy for three specific interior metrics (Florides, Soffel and Schwarzschild) for which the spectrum collapses and becomes quasi-continuous in the singular metric limit. The lack of zero or negative energy states prior to this limit being reached prevents particle pair production occurring. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides and Soffel metrics the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the centre. The behaviour of the energy level spectrum is discussed in the context of the semi-classical approximation and using general properties of the metric.

A highly magnetized twin-jet base pinpoints a supermassive black hole

NASA Astrophysics Data System (ADS)

Baczko, A.-K.; Schulz, R.; Kadler, M.; Ros, E.; Perucho, M.; Krichbaum, T. P.; Böck, M.; Bremer, M.; Grossberger, C.; Lindqvist, M.; Lobanov, A. P.; Mannheim, K.; Martí-Vidal, I.; Müller, C.; Wilms, J.; Zensus, J. A.

2016-09-01

Supermassive black holes (SMBH) are essential for the production of jets in radio-loud active galactic nuclei (AGN). Theoretical models based on (Blandford & Znajek 1977, MNRAS, 179, 433) extract the rotational energy from a Kerr black hole, which could be the case for NGC 1052, to launch these jets. This requires magnetic fields on the order of 103G to 104G. We imaged the vicinity of the SMBH of the AGN NGC 1052 with the Global Millimetre VLBI Array and found a bright and compact central feature that is smaller than 1.9 light days (100 Schwarzschild radii) in radius. Interpreting this as a blend of the unresolved jet bases, we derive the magnetic field at 1 Schwarzschild radius to lie between 200 G and ~ 8.3 × 104 G consistent with Blandford & Znajek models. The VLBI images shown in Figs. 3 and 4 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/593/A47

BOOK REVIEW Exact Space-Times in Einstein's General Relativity Exact Space-Times in Einstein's General Relativity

NASA Astrophysics Data System (ADS)

Lake, Kayll

2010-12-01

The title immediately brings to mind a standard reference of almost the same title [1]. The authors are quick to point out the relationship between these two works: they are complementary. The purpose of this work is to explain what is known about a selection of exact solutions. As the authors state, it is often much easier to find a new solution of Einstein's equations than it is to understand it. Even at first glance it is very clear that great effort went into the production of this reference. The book is replete with beautifully detailed diagrams that reflect deep geometric intuition. In many parts of the text there are detailed calculations that are not readily available elsewhere. The book begins with a review of basic tools that allows the authors to set the notation. Then follows a discussion of Minkowski space with an emphasis on the conformal structure and applications such as simple cosmic strings. The next two chapters give an in-depth review of de Sitter space and then anti-de Sitter space. Both chapters contain a remarkable collection of useful diagrams. The standard model in cosmology these days is the ICDM model and whereas the chapter on the Friedmann-Lemaître-Robertson-Walker space-times contains much useful information, I found the discussion of the currently popular a representation rather too brief. After a brief but interesting excursion into electrovacuum, the authors consider the Schwarzschild space-time. This chapter does mention the Swiss cheese model but the discussion is too brief and certainly dated. Space-times related to Schwarzschild are covered in some detail and include not only the addition of charge and the cosmological constant but also the addition of radiation (the Vaidya solution). Just prior to a discussion of the Kerr space-time, static axially symmetric space-times are reviewed. Here one can find a very interesting discussion of the Curzon-Chazy space-time. The chapter on rotating black holes is rather brief and, for example, does not contain reference to the insights found by Pretorius and Israel [2]. This is perhaps justifiable in view of the many specialized texts devoted to the Kerr space-time (e.g. [3]). The large clear diagrams that one becomes accustomed to in this book show off the Taub-NUT (and related) space-times in the next chapter. After perhaps a somewhat standard discussion of stationary axially symmetric space-times, there is a very informative discussion of accelerating black holes. For example, the global structure of the C-metric is considered in detail. This is followed by a brief discussion of solutions for uniformly accelerating particles. The discussion of the Plebański-Demiański solutions contains two very useful flow charts that help to systematize two rather complex families of solutions. After a somewhat brief discussion of plane and pp-waves, the authors give an extensive discussion of the Kunt solutions. I note here that after this text was in production the importance of the Kunt space-times as regards the characterization of space-times by scalar curvature invariants was made clear [4]. The discussion of the Robinson-Trautman solutions that follows is extensive, containing, for example, details of the singularity structure and of the global structure. The final formal chapter in this text covers colliding plane waves. This contains, for example, discussions of the Khan-Penrose, Ferrari-Ibañez and Chandrasekhar-Xanthopoulos solutions. The text ends with a `final miscellany'. This covers a number of interesting topics, but I found the discussion of the Lemaître-Tolman solutions rather weak (compare e.g. [5]). The book has two quite useful appendices covering 2-spaces and 3-spaces of constant curvature. To conclude, I will quote from the dust jacket: `The book is an invaluable resource for both graduate students and academic researchers working in gravitational physics'. I highly recommend it. References [1] Stephani H, Kramer D, MacCallum M, Hoenselaers C and Herlt E 2003 Exact Solutions of Einstein's Field Equations (Second Edition) (Cambridge: Cambridge University Press) [2] Pretorius F and Israel W 1998 Class. Quantum Grav.15 2289 [3] Wiltshire D, Visser M and Scott S (ed) 2008 The Kerr Spacetime: Rotating Black Holes in General Relativity (Cambridge: Cambridge University Press) [4] Coley A, Hervik S and Pelavas N 2009 Class. Quantum Grav. 26 025013 [5] Plebański J and Krasiński A 2006 An Introduction to General Relativity and Cosmology (Cambridge: Cambridge University Press)

Entropy emission properties of near-extremal Reissner-Nordström black holes

NASA Astrophysics Data System (ADS)

Hod, Shahar

2016-05-01

Bekenstein and Mayo have revealed an interesting property of evaporating (3 +1 )-dimensional Schwarzschild black holes: their entropy emission rates S˙Sch are related to their energy emission rates P by the simple relation S˙Sch=CSch×(P /ℏ)1/2, where CSch is a numerically computed dimensionless coefficient. Remembering that (1 +1 )-dimensional perfect black-body emitters are characterized by the same functional relation, S˙1 +1=C1 +1×(P /ℏ)1/2 [with C1 +1=(π /3 )1/2], Bekenstein and Mayo have concluded that, in their entropy emission properties, (3 +1 )-dimensional Schwarzschild black holes behave effectively as (1 +1 )-dimensional entropy emitters. Later studies have shown that this intriguing property is actually a generic feature of all radiating (D +1 )-dimensional Schwarzschild black holes. One naturally wonders whether all black holes behave as simple (1 +1 )-dimensional entropy emitters? In order to address this interesting question, we shall study in this paper the entropy emission properties of Reissner-Nordström black holes. We shall show, in particular, that the physical properties which characterize the neutral sector of the Hawking emission spectra of these black holes can be studied analytically in the near-extremal TBH→0 regime (here TBH is the Bekenstein-Hawking temperature of the black hole). We find that the Hawking radiation spectra of massless neutral scalar fields and coupled electromagnetic-gravitational fields are characterized by the nontrivial entropy-energy relations S˙RNScalar=-CRNScalar×(A P3/ℏ3)1/4ln (A P /ℏ) and S˙RN Elec -Grav=-CRNElec -Grav×(A4P9/ℏ9)1 /10ln (A P /ℏ) in the near-extremal TBH→0 limit (here {CRNScalar,CRNElec -Grav} are analytically calculated dimensionless coefficients and A is the surface area of the Reissner-Nordström black hole). Our analytical results therefore indicate that not all black holes behave as simple (1 +1 )-dimensional entropy emitters.

Geometry of a naked singularity created by standing waves near a Schwarzschild horizon, and its application to the binary black hole problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mandel, Ilya

The most promising way to compute the gravitational waves emitted by binary black holes (BBHs) in their last dozen orbits, where post-Newtonian techniques fail, is a quasistationary approximation introduced by Detweiler and being pursued by Price and others. In this approximation the outgoing gravitational waves at infinity and downgoing gravitational waves at the holes' horizons are replaced by standing waves so as to guarantee that the spacetime has a helical Killing vector field. Because the horizon generators will not, in general, be tidally locked to the holes' orbital motion, the standing waves will destroy the horizons, converting the black holesmore » into naked singularities that resemble black holes down to near the horizon radius. This paper uses a spherically symmetric, scalar-field model problem to explore in detail the following BBH issues: (i) The destruction of a horizon by the standing waves. (ii) The accuracy with which the resulting naked singularity resembles a black hole. (iii) The conversion of the standing-wave spacetime (with a destroyed horizon) into a spacetime with downgoing waves by the addition of a 'radiation-reaction field'. (iv) The accuracy with which the resulting downgoing waves agree with the downgoing waves of a true black-hole spacetime (with horizon). The model problem used to study these issues consists of a Schwarzschild black hole endowed with spherical standing waves of a scalar field, whose wave frequency and near-horizon energy density are chosen to match those of the standing gravitational waves of the BBH quasistationary approximation. It is found that the spacetime metric of the singular, standing-wave spacetime, and its radiation-reaction-field-constructed downgoing waves are quite close to those for a Schwarzschild black hole with downgoing waves--sufficiently close to make the BBH quasistationary approximation look promising for non-tidally-locked black holes.« less

Self-force on a scalar charge in Kerr spacetime: Circular equatorial orbits

DOE Office of Scientific and Technical Information (OSTI.GOV)

Warburton, Niels; Barack, Leor

2010-04-15

We present a calculation of the scalar-field self-force (SSF) acting on a scalar-charge particle in a strong-field orbit around a Kerr black hole. Our calculation specializes to circular and equatorial geodesic orbits. The analysis is an implementation of the standard mode-sum regularization scheme: We first calculate the multipole modes of the scalar-field perturbation using numerical integration in the frequency domain, and then apply a certain regularization procedure to each of the modes. The dissipative piece of the SSF is found to be consistent with the flux of energy and angular-momentum carried by the scalar waves through the event horizon andmore » out to infinity. The conservative (radial) component of the SSF is calculated here for the first time. When the motion is retrograde this component is found to be repulsive (outward pointing, as in the Schwarzschild case) for any spin parameter a and (Boyer-Lindquist) orbital radius r{sub 0}. However, for prograde orbits we find that the radial SSF becomes attractive (inward pointing) for r{sub 0}>r{sub c}(a), where r{sub c} is a critical a-dependent radius at which the radial SSF vanishes. The dominant conservative effect of the SSF in Schwarzschild spacetime is known to be of third post-Newtonian (3PN) order (with a logarithmic running). Our numerical results suggest that the leading-order PN correction due to the black hole's spin arises from spin-orbit coupling at 3PN order, which dominates the overall SSF effect at large r{sub 0}. In PN language, the change of sign of the radial SSF is attributed to an interplay between the spin-orbit term ({proportional_to}-ar{sub 0}{sup -4.5}) and the Schwarzschild term ({proportional_to}r{sub 0}{sup -5}logr{sub 0}).« less

BEYOND MIXING-LENGTH THEORY: A STEP TOWARD 321D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arnett, W. David; Meakin, Casey; Viallet, Maxime

2015-08-10

We examine the physical basis for algorithms to replace mixing-length theory (MLT) in stellar evolutionary computations. Our 321D procedure is based on numerical solutions of the Navier–Stokes equations. These implicit large eddy simulations (ILES) are three-dimensional (3D), time-dependent, and turbulent, including the Kolmogorov cascade. We use the Reynolds-averaged Navier–Stokes (RANS) formulation to make concise the 3D simulation data, and use the 3D simulations to give closure for the RANS equations. We further analyze this data set with a simple analytical model, which is non-local and time-dependent, and which contains both MLT and the Lorenz convective roll as particular subsets ofmore » solutions. A characteristic length (the damping length) again emerges in the simulations; it is determined by an observed balance between (1) the large-scale driving, and (2) small-scale damping. The nature of mixing and convective boundaries is analyzed, including dynamic, thermal and compositional effects, and compared to a simple model. We find that (1) braking regions (boundary layers in which mixing occurs) automatically appear beyond the edges of convection as defined by the Schwarzschild criterion, (2) dynamic (non-local) terms imply a non-zero turbulent kinetic energy flux (unlike MLT), (3) the effects of composition gradients on flow can be comparable to thermal effects, and (4) convective boundaries in neutrino-cooled stages differ in nature from those in photon-cooled stages (different Péclet numbers). The algorithms are based upon ILES solutions to the Navier–Stokes equations, so that, unlike MLT, they do not require any calibration to astronomical systems in order to predict stellar properties. Implications for solar abundances, helioseismology, asteroseismology, nucleosynthesis yields, supernova progenitors and core collapse are indicated.« less

Beyond Mixing-length Theory: A Step Toward 321D

NASA Astrophysics Data System (ADS)

Arnett, W. David; Meakin, Casey; Viallet, Maxime; Campbell, Simon W.; Lattanzio, John C.; Mocák, Miroslav

2015-08-01

We examine the physical basis for algorithms to replace mixing-length theory (MLT) in stellar evolutionary computations. Our 321D procedure is based on numerical solutions of the Navier-Stokes equations. These implicit large eddy simulations (ILES) are three-dimensional (3D), time-dependent, and turbulent, including the Kolmogorov cascade. We use the Reynolds-averaged Navier-Stokes (RANS) formulation to make concise the 3D simulation data, and use the 3D simulations to give closure for the RANS equations. We further analyze this data set with a simple analytical model, which is non-local and time-dependent, and which contains both MLT and the Lorenz convective roll as particular subsets of solutions. A characteristic length (the damping length) again emerges in the simulations; it is determined by an observed balance between (1) the large-scale driving, and (2) small-scale damping. The nature of mixing and convective boundaries is analyzed, including dynamic, thermal and compositional effects, and compared to a simple model. We find that (1) braking regions (boundary layers in which mixing occurs) automatically appear beyond the edges of convection as defined by the Schwarzschild criterion, (2) dynamic (non-local) terms imply a non-zero turbulent kinetic energy flux (unlike MLT), (3) the effects of composition gradients on flow can be comparable to thermal effects, and (4) convective boundaries in neutrino-cooled stages differ in nature from those in photon-cooled stages (different Péclet numbers). The algorithms are based upon ILES solutions to the Navier-Stokes equations, so that, unlike MLT, they do not require any calibration to astronomical systems in order to predict stellar properties. Implications for solar abundances, helioseismology, asteroseismology, nucleosynthesis yields, supernova progenitors and core collapse are indicated.

General relativistic hydrodynamics with Adaptive-Mesh Refinement (AMR) and modeling of accretion disks

NASA Astrophysics Data System (ADS)

Donmez, Orhan

We present a general procedure to solve the General Relativistic Hydrodynamical (GRH) equations with Adaptive-Mesh Refinement (AMR) and model of an accretion disk around a black hole. To do this, the GRH equations are written in a conservative form to exploit their hyperbolic character. The numerical solutions of the general relativistic hydrodynamic equations is done by High Resolution Shock Capturing schemes (HRSC), specifically designed to solve non-linear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. We use Marquina fluxes with MUSCL left and right states to solve GRH equations. First, we carry out different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations to verify the second order convergence of the code in 1D, 2 D and 3D. Second, we solve the GRH equations and use the general relativistic test problems to compare the numerical solutions with analytic ones. In order to this, we couple the flux part of general relativistic hydrodynamic equation with a source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time. The test problems examined include shock tubes, geodesic flows, and circular motion of particle around the black hole. Finally, we apply this code to the accretion disk problems around the black hole using the Schwarzschild metric at the background of the computational domain. We find spiral shocks on the accretion disk. They are observationally expected results. We also examine the star-disk interaction near a massive black hole. We find that when stars are grounded down or a hole is punched on the accretion disk, they create shock waves which destroy the accretion disk.

A Useful Expression for Relativistic Energy Conservation of a Point Mass in an Isotropic Static Gravitational Field

ERIC Educational Resources Information Center

Augousti, A. T.; Radosz, A.; Ostasiewicz, K.

2011-01-01

By using the symmetry and time-independence properties of Schwarzschild spacetime it is demonstrated that an energy conservation law may be expressed in terms of local velocity. From this form three important results may be derived very concisely. This highlights analogies and differences between relativistic and classical approaches to mechanics…

On the black hole lens and its foci

NASA Technical Reports Server (NTRS)

Eshleman, Von R.; Gurrola, Eric M.; Lindal, Gunnar F.

1989-01-01

Methods developed for radio occultation studies of planetary atmospheres are used to predict the electromagnetic focusing properties of a refracting lens representation of a Schwarzschild black hole. The infinity of foci are of three distinct types: a principal forward axial focus which is by far the strongest; higher-order forward axial foci; and backward conical foci with axial nulls.

Dynamics of test particles in thin-shell wormhole spacetimes

NASA Astrophysics Data System (ADS)

Diemer, Valeria; Smolarek, Elena

2013-09-01

Geodesic motion in traversable Schwarzschild and Kerr thin-shell wormholes constructed by the cut-and-paste method introduced by Visser (1989 Nucl. Phys. B 328 203; 1995 Wormholes: from Einstein to Hawking (Woodbury, MN: American Institute of Physics)) is studied. The orbits are calculated exactly in terms of elliptic functions and visualized with the help of embedding diagrams.

Dynamical Mass of the O-Type Supergiant in Zeta Orionis A

DTIC Science & Technology

2013-01-01

A. Hummel1, Th. Rivinius2, M.-F. Nieva3,4, O. Stahl5, G. van Belle6, and R. T. Zavala7 1 European Southern Observatory, Karl - Schwarzschild -Str. 2...85748 Garching, Germany e-mail: chummel@eso.org 2 European Southern Observatory, Casilla 19001, Santiago 19, Chile 3 Dr. Karl Remeis–Sternwarte & ECAP

Astrophysical Institute, Potsdam

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

Built upon a tradition of almost 300 years, the Astrophysical Institute Potsdam (AIP) is in an historical sense the successor of one of the oldest astronomical observatories in Germany. It is the first institute in the world which incorporated the term `astrophysical' in its name, and is connected with distinguished scientists such as Karl Schwarzschild and Albert Einstein. The AIP constitutes on...

University Observatory, Ludwig-Maximilians-Universität

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

The University Observatory of Ludwig-Maximilians-Universität was founded in 1816. Astronomers who worked or graduated at the Munich Observatory include: Fraunhofer, Soldner, Lamont, Seeliger and Karl Schwarzschild. At present four professors and ten staff astronomers work here. Funding comes from the Bavarian Government, the German Science Foundation, and other German and European research progra...

Hertzsprung, Ejnar (1873-1967)

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

Danish astronomer, studied chemical engineering and worked as a chemist in St Petersburg before returning to Denmark to take up astronomy, worked in Göttingen and Potsdam with KARL SCHWARZSCHILD, and then at the Leiden Observatory (Netherlands) where he became director. Hertzsprung determined the proper motions of stars, and about a million positions of binary stars, as well as the brightnesses o...

n-dimensional isotropic Finch-Skea stars

NASA Astrophysics Data System (ADS)

Chilambwe, Brian; Hansraj, Sudan

2015-02-01

We study the impact of dimension on the physical properties of the Finch-Skea astrophysical model. It is shown that a positive definite, monotonically decreasing pressure and density are evident. A decrease in stellar radius emerges as the order of the dimension increases. This is accompanied by a corresponding increase in energy density. The model continues to display the necessary qualitative features inherent in the 4-dimensional Finch-Skea star and the conformity to the Walecka theory is preserved under dimensional increase. The causality condition is always satisfied for all dimensions considered resulting in the proposed models demonstrating a subluminal sound speed throughout the interior of the distribution. Moreover, the pressure and density decrease monotonically outwards from the centre and a pressure-free hypersurface exists demarcating the boundary of the perfect-fluid sphere. Since the study of the physical conditions is performed graphically, it is necessary to specify certain constants in the model. Reasonable values for such constants are arrived at on examining the behaviour of the model at the centre and demanding the satisfaction of all elementary conditions for physical plausibility. Finally two constants of integration are settled on matching of our solutions with the appropriate Schwarzschild-Tangherlini exterior metrics. Furthermore, the solution admits a barotropic equation of state despite the higher dimension. The compactification parameter as well as the density variation parameter are also computed. The models satisfy the weak, strong and dominant energy conditions in the interior of the stellar configuration.

General relativity exactly described in terms of Newton's laws within curved geometries

NASA Astrophysics Data System (ADS)

Savickas, D.

2014-07-01

Many years ago Milne and McCrea showed in their well-known paper that the Hubble expansion occurring in general relativity could be exactly described by the use of Newtonian mechanics. It will be shown that a similar method can be extended to, and used within, curved geometries when Newton's second law is expressed within a four-dimensional curved spacetime. The second law will be shown to yield an equation that is exactly identical to the geodesic equation of motion of general relativity. This in itself yields no new information concerning relativity since the equation is mathematically identical to the relativistic equation. However, when the time in the second law is defined to have a constant direction as effectively occurs in Newtonian mechanics, and no longer acts as a fourth dimension as exists in relativity theory, it separates into a vector equation in a curved three-dimensional space and an additional second scalar equation that describes conservation of energy. It is shown that the curved Newtonian equations of motion define the metric coefficients which occur in the Schwarzschild solution and that they also define its equations of motion. Also, because the curved Newtonian equations developed here use masses as gravitational sources, as occurs in Newtonian mechanics, they make it possible to derive the solution for other kinds of mass distributions and are used here to find the metric equation for a thin mass-rod and the equation of motion for a mass particle orbiting it in its relativistic gravitational field.

Spherically-symmetric solutions in general relativity using a tetrad-based approach

NASA Astrophysics Data System (ADS)

Kim, Do Young; Lasenby, Anthony N.; Hobson, Michael P.

2018-03-01

We present a tetrad-based method for solving the Einstein field equations for spherically-symmetric systems and compare it with the widely-used Lemaître-Tolman-Bondi (LTB) model. In particular, we focus on the issues of gauge ambiguity and the use of comoving versus `physical' coordinate systems. We also clarify the correspondences between the two approaches, and illustrate their differences by applying them to the classic examples of the Schwarzschild and Friedmann-Lemaître-Robertson-Walker spacetimes. We demonstrate that the tetrad-based method does not suffer from the gauge freedoms inherent to the LTB model, naturally accommodates non-uniform pressure and has a more transparent physical interpretation. We further apply our tetrad-based method to a generalised form of `Swiss cheese' model, which consists of an interior spherical region surrounded by a spherical shell of vacuum that is embedded in an exterior background universe. In general, we allow the fluid in the interior and exterior regions to support pressure, and do not demand that the interior region be compensated. We pay particular attention to the form of the solution in the intervening vacuum region and illustrate the validity of Birkhoff's theorem at both the metric and tetrad level. We then reconsider critically the original theoretical arguments underlying the so-called Rh = ct cosmological model, which has recently received considerable attention. These considerations in turn illustrate the interesting behaviour of a number of `horizons' in general cosmological models.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davis, Anne-Christine; Jha, Rahul; Gregory, Ruth, E-mail: acd@damtp.cam.ac.uk, E-mail: r.a.w.gregory@durham.ac.uk, E-mail: r.jha@damtp.cam.ac.uk

We present a novel way to investigate scalar field profiles around black holes with an accretion disc for a range of models where the Compton wavelength of the scalar is large compared to other length scales. By analysing the problem in ''Weyl' coordinates, we are able to calculate the scalar profiles for accretion discs in the static Schwarzschild, as well as rotating Kerr, black holes. We comment on observational effects.

Fate of inhomogeneity in Schwarzschild-deSitter space-time

NASA Astrophysics Data System (ADS)

Nambu, Yasusada

1994-03-01

We investigate the global structure of the space-time with a spherically symmetric inhomogeneity using a metric junction, and classify all possible types. We found that a motion with a negative gravitational mass is possible although the energy condition of the matter is not violated. Using the result, formation of black hole and worm hole during the inflationary era is discussed.

Schwarzschild, Karl (1873-1916)

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

Mathematical physicist, born in Frankfurt am Main, Germany, at first worked on celestial mechanics, including POINCARÉ's theory of rotating bodies, the tidal deformation of moons and LAPLACE's origin of the solar system. He became professor at Göttingen and Potsdam. He wrote on relativity and quantum theory. He early on proposed that space was non-Euclidean, giving a lower limit for the radius of...

J, H, K Spectro-Interferometry of the Mira Variable S Orionis

DTIC Science & Technology

2008-01-01

the Mira variable S Orionis M. Wittkowski1, D. A. Boboltz2, T. Driebe3, J.-B. Le Bouquin4 F. Millour3 K. Ohnaka3, and M. Scholz5,6 1 ESO, Karl ... Schwarzschild -Str. 2, 85748 Garching bei München, Germany e-mail: mwittkow@eso.org 2 US Naval Observatory, 3450 Massachusetts Avenue, NW, Washington, DC

Generic effective source for scalar self-force calculations

NASA Astrophysics Data System (ADS)

Wardell, Barry; Vega, Ian; Thornburg, Jonathan; Diener, Peter

2012-05-01

A leading approach to the modeling of extreme mass ratio inspirals involves the treatment of the smaller mass as a point particle and the computation of a regularized self-force acting on that particle. In turn, this computation requires knowledge of the regularized retarded field generated by the particle. A direct calculation of this regularized field may be achieved by replacing the point particle with an effective source and solving directly a wave equation for the regularized field. This has the advantage that all quantities are finite and require no further regularization. In this work, we present a method for computing an effective source which is finite and continuous everywhere, and which is valid for a scalar point particle in arbitrary geodesic motion in an arbitrary background spacetime. We explain in detail various technical and practical considerations that underlie its use in several numerical self-force calculations. We consider as examples the cases of a particle in a circular orbit about Schwarzschild and Kerr black holes, and also the case of a particle following a generic timelike geodesic about a highly spinning Kerr black hole. We provide numerical C code for computing an effective source for various orbital configurations about Schwarzschild and Kerr black holes.

Quasi-periodic accretion and gravitational waves from oscillating `toroidal neutron stars' around a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Zanotti, Olindo; Rezzolla, Luciano; Font, José A.

2003-05-01

We present general relativistic hydrodynamics simulations of constant specific angular momentum tori orbiting a Schwarzschild black hole. These tori are expected to form as a result of stellar gravitational collapse, binary neutron star merger or disruption, can reach very high rest-mass densities and behave effectively as neutron stars but with a toroidal topology (i.e. `toroidal neutron stars'). Here our attention is focused on the dynamical response of these objects to axisymmetric perturbations. We show that upon the introduction of perturbations, these systems either become unstable to the runaway instability or exhibit a regular oscillatory behaviour, resulting in a quasi-periodic variation of the accretion rate as well as of the mass quadrupole. The latter, in particular, is responsible for the emission of intense gravitational radiation for which the signal-to-noise ratio at the detector is comparable to or larger than the typical one expected in stellar-core collapse, making these new sources of gravitational waves potentially detectable. We discuss a systematic investigation of the parameter space in both the linear and non-linear regimes, providing estimates of how the gravitational radiation emitted depends on the mass of the torus and on the strength of the perturbation.

Distorting general relativity: gravity's rainbow and f(R) theories at work

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garattini, Remo, E-mail: Remo.Garattini@unibg.it

2013-06-01

We compute the Zero Point Energy in a spherically symmetric background combining the high energy distortion of Gravity's Rainbow with the modification induced by a f(R) theory. Here f(R) is a generic analytic function of the Ricci curvature scalar R in 4D and in 3D. The explicit calculation is performed for a Schwarzschild metric. Due to the spherically symmetric property of the Schwarzschild metric we can compare the effects of the modification induced by a f(R) theory in 4D and in 3D. We find that the final effect of the combined theory is to have finite quantities that shift themore » Zero Point Energy. In this context we setup a Sturm-Liouville problem with the cosmological constant considered as the associated eigenvalue. The eigenvalue equation is a reformulation of the Wheeler-DeWitt equation which is analyzed by means of a variational approach based on gaussian trial functionals. With the help of a canonical decomposition, we find that the relevant contribution to one loop is given by the graviton quantum fluctuations around the given background. A final discussion on the connection of our result with the observed cosmological constant is also reported.« less

Comment on ‘Gravitational lensing of massive particles in Schwarzschild gravity’ (2016 Class. Quantum Grav. 33 175014)

NASA Astrophysics Data System (ADS)

Zakharov, Alexander F.

2018-01-01

Recently, Liu et al published a paper (2016 Class. Quantum Grav. 33 175014). In the abstract, the authors claimed as a key result of the paper that a particle sphere is found for the Schwarzschild black hole (BH), with its radius as a simple function of the particle velocity and proportional to the BH mass. Usually, if there are no references for the result it is assumed that the result was obtained originally in the paper; but this is not the case for the quoted paper. The concept of a particle sphere was introduced by Mielnik and Plebański (1962 Acta Phys. Pol. 21 239) and a simple derivation of the critical impact parameter was given in Zakharov A F (1988 Sov. Astron. 32 456 and Zakharov A F 1994 Class. Quantum Grav. 11 1027). We show that in slightly different notations, equation (17) for the critical impact parameter in Liu X et al (2016 Class. Quantum Grav. 33 175014) coincides with equation (12) in Zakharov (1994 Class. Quantum Grav. 11 1027) and with the corresponding equation (10.10) in Mielnik and Plebański (1962 Acta Phys. Pol. 21 239).

Confirming and improving post-Newtonian and effective-one-body results from self-force computations along eccentric orbits around a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Bini, Donato; Damour, Thibault; Geralico, Andrea

2016-03-01

We analytically compute, through the six-and-a-half post-Newtonian order, the second-order-in-eccentricity piece of the Detweiler-Barack-Sago gauge-invariant redshift function for a small mass in eccentric orbit around a Schwarzschild black hole. Using the first law of mechanics for eccentric orbits [A. Le Tiec, First law of mechanics for compact binaries on eccentric orbits, Phys. Rev. D 92, 084021 (2015).] we transcribe our result into a correspondingly accurate knowledge of the second radial potential of the effective-one-body formalism [A. Buonanno and T. Damour, Effective one-body approach to general relativistic two-body dynamics, Phys. Rev. D 59, 084006 (1999).]. We compare our newly acquired analytical information to several different numerical self-force data and find good agreement, within estimated error bars. We also obtain, for the first time, independent analytical checks of the recently derived, comparable-mass fourth-post-Newtonian order dynamics [T. Damour, P. Jaranowski, and G. Schaefer, Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems, Phys. Rev. D 89, 064058 (2014).].

Influence of matter geometry on shocked flows-I: Accretion in the Schwarzschild metric

NASA Astrophysics Data System (ADS)

Tarafdar, Pratik; Das, Tapas K.

2018-07-01

This work presents a comprehensive and extensive study to illustrate how the geometrical configurations of low angular momentum axially symmetric general relativistic matter flow in the Schwarzschild metric may influence the formation of energy-preserving shocks for adiabatic/polytropic accretion as well as of temperature-preserving dissipative shocks for the isothermal accretion onto non-rotating astrophysical black holes. The dynamical and thermodynamic states of post-shock polytropic and isothermal flow have been studied extensively for three possible matter geometries, and it has been thoroughly discussed about how such states depend on the flow structure, even when the self gravity and the back reaction on the metric are not taken into account. Main purpose of this paper is thus to mathematically demonstrate that for non-self gravitating accretion, various matter geometries, in addition to the corresponding space-time geometry, control the shock induced phenomena as observed within the black hole accretion discs. This work is expected to reveal how the shock generated phenomena (emergence of the outflows/flare in the associated light curves) observed at the close proximity of the horizon depend on the physical environment of the source harbouring a supermassive black hole.

Exponential fading to white of black holes in quantum gravity

NASA Astrophysics Data System (ADS)

Barceló, Carlos; Carballo-Rubio, Raúl; Garay, Luis J.

2017-05-01

Quantization of the gravitational field may allow the existence of a decay channel of black holes into white holes with an explicit time-reversal symmetry. The definition of a meaningful decay probability for this channel is studied in spherically symmetric situations. As a first nontrivial calculation, we present the functional integration over a set of geometries using a single-variable function to interpolate between black-hole and white-hole geometries in a bounded region of spacetime. This computation gives a finite result which depends only on the Schwarzschild mass and a parameter measuring the width of the interpolating region. The associated probability distribution displays an exponential decay law on the latter parameter, with a mean lifetime inversely proportional to the Schwarzschild mass. In physical terms this would imply that matter collapsing to a black hole from a finite radius bounces back elastically and instantaneously, with negligible time delay as measured by external observers. These results invite to reconsider the ultimate nature of astrophysical black holes, providing a possible mechanism for the formation of black stars instead of proper general relativistic black holes. The existence of both this decay channel and black stars can be tested in future observations of gravitational waves.

Weak deflection gravitational lensing for photons coupled to Weyl tensor in a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Cao, Wei-Guang; Xie, Yi

2018-03-01

Beyond the Einstein-Maxwell model, electromagnetic field might couple with gravitational field through the Weyl tensor. In order to provide one of the missing puzzles of the whole physical picture, we investigate weak deflection lensing for photons coupled to the Weyl tensor in a Schwarzschild black hole under a unified framework that is valid for its two possible polarizations. We obtain its coordinate-independent expressions for all observables of the geometric optics lensing up to the second order in the terms of ɛ which is the ratio of the angular gravitational radius to angular Einstein radius of the lens. These observables include bending angle, image position, magnification, centroid and time delay. The contributions of such a coupling on some astrophysical scenarios are also studied. We find that, in the cases of weak deflection lensing on a star orbiting the Galactic Center Sgr A*, Galactic microlensing on a star in the bulge and astrometric microlensing by a nearby object, these effects are beyond the current limits of technology. However, measuring the variation of the total flux of two weak deflection lensing images caused by the Sgr A* might be a promising way for testing such a coupling in the future.

Wolter-Schwarzschild optics for the extreme-ultraviolet - The Berkeley stellar spectrometer and the EUV Explorer

NASA Technical Reports Server (NTRS)

Malina, R. F.; Bowyer, S.; Finley, D.; Cash, W.

1979-01-01

The design, fabrication and performance of two Wolter-Schwarzschild grazing incidence optics are described. Both telescopes have been figured by single point diamond turning and have achieved better than 15-arcsec on-axis imaging. The telescope for the stellar spectrometer is an f/10 Type II system with an effective area of 225 sq cm at 250 A and 300 cm2 at 500 A. The primary has a maximum diameter of 38 cm and was fabricated in three elements. The copper-plated aluminum substrate was diamond turned; following nickel plating, the surface was polished and coated with evaporated gold. The performance during a sounding rocket flight is discussed. The prototype telescope for the Extreme Ultraviolet Explorer is an f/1.24 Type I system with an effective field of view of 5.0-deg diameter. The telescope has a maximum diameter of 40 cm and was fabricated as a single element. The aluminum substrate is to be diamond turned; the nickel plated surface will be polished and electroplated with gold. The design choice and defocusing optimization aimed at maximizing the field of view and number of image pixels is examined.

Heavy fields and gravity

NASA Astrophysics Data System (ADS)

Goon, Garrett

2017-01-01

We study the effects of heavy fields on 4D spacetimes with flat, de Sitter and anti-de Sitter asymptotics. At low energies, matter generates specific, calculable higher derivative corrections to the GR action which perturbatively alter the Schwarzschild-( A) dS family of solutions. The effects of massive scalars, Dirac spinors and gauge fields are each considered. The six-derivative operators they produce, such as ˜ R 3 terms, generate the leading corrections. The induced changes to horizon radii, Hawking temperatures and entropies are found. Modifications to the energy of large AdS black holes are derived by imposing the first law. An explicit demonstration of the replica trick is provided, as it is used to derive black hole and cosmological horizon entropies. Considering entropy bounds, it's found that scalars and fermions increase the entropy one can store inside a region bounded by a sphere of fixed size, but vectors lead to a decrease, oddly. We also demonstrate, however, that many of the corrections fall below the resolving power of the effective field theory and are therefore untrustworthy. Defining properties of black holes, such as the horizon area and Hawking temperature, prove to be remarkably robust against higher derivative gravitational corrections.

General relativistic considerations of the field shedding model of fast radio bursts

NASA Astrophysics Data System (ADS)

Punsly, Brian; Bini, Donato

2016-06-01

Popular models of fast radio bursts (FRBs) involve the gravitational collapse of neutron star progenitors to black holes. It has been proposed that the shedding of the strong neutron star magnetic field (B) during the collapse is the power source for the radio emission. Previously, these models have utilized the simplicity of the Schwarzschild metric which has the restriction that the magnetic flux is magnetic `hair' that must be shed before final collapse. But neutron stars have angular momentum and charge and a fully relativistic Kerr-Newman solution exists in which B has its source inside of the event horizon. In this Letter, we consider the magnetic flux to be shed as a consequence of the electric discharge of a metastable collapsed state of a Kerr-Newman black hole. It has also been argued that the shedding model will not operate due to pair creation. By considering the pulsar death line, we find that for a neutron star with B = 1011-1013 G and a long rotation period, >1s this is not a concern. We also discuss the observational evidence supporting the plausibility of magnetic flux shedding models of FRBs that are spawned from rapidly rotating progenitors.

Deformation-Induced Precession of a Robot Moving on Curved Space

NASA Astrophysics Data System (ADS)

Li, Shengkai; Aydin, Yasemin; Lofaro, Olivia; Rieser, Jennifer; Goldman, Daniel

Previous studies have demonstrated that passive particles rolling on a deformed surface can mimic aspects of general relativity [Ford et al, AJP, 2015]. However, these systems are dissipative. To explore steady-state dynamics, we study the movement of a self-propelled robot car on a large deformable elastic membrane: a spandex sheet stretched over a metal frame with a diameter of 2.5 m. Two wheels in the rear of the car are differentially-driven by a DC motor, and a caster in the front helps maintain directional stability; in the absence of curvature the car drives straight. A linear actuator attached below the membrane allows for controlled deformation at the center of the membrane. We find that closed elliptic orbits occur when the membrane is highly depressed ( 10 cm). However, when the center is only slightly indented, the elliptical orbits precess at a rate depending on the orbit shape and the depression. Remarkably, this dynamic is well described by the Schwarzschild metric solution, typically used to describe the effects of gravity on bodies orbiting a massive object. Experiments with multiple cars reveal complex interactions that are mediated through car-induced deformations of the membrane.

Spinning particles in general relativity: Momentum-velocity relation for the Mathisson-Pirani spin condition

NASA Astrophysics Data System (ADS)

Costa, L. Filipe O.; Lukes-Gerakopoulos, Georgios; Semerák, Oldřich

2018-04-01

The Mathisson-Papapetrou-Dixon (MPD) equations, providing the "pole-dipole" description of spinning test particles in general relativity, have to be supplemented by a condition specifying the worldline that will represent the history of the studied body. It has long been thought that the Mathisson-Pirani (MP) spin condition—unlike other major choices made in the literature—does not yield an explicit momentum-velocity relation. We derive here the desired (and very simple) relation and show that it is in fact equivalent to the MP condition. We clarify the apparent paradox between the existence of such a definite relation and the known fact that the MP condition is degenerate (does not specify a unique worldline), thus shedding light on some conflicting statements made in the literature. We then show how, for a given body, this spin condition yields infinitely many possible representative worldlines, and derive a detailed method how to switch between them in a curved spacetime. The MP condition is a convenient choice in situations when it is easy to recognize its "nonhelical" solution, as exemplified here by bodies in circular orbits and in radial fall in the Schwarzschild spacetime.

The origin of the energy-momentum conservation law

NASA Astrophysics Data System (ADS)

Chubykalo, Andrew E.; Espinoza, Augusto; Kosyakov, B. P.

2017-09-01

The interplay between the action-reaction principle and the energy-momentum conservation law is revealed by the examples of the Maxwell-Lorentz and Yang-Mills-Wong theories, and general relativity. These two statements are shown to be equivalent in the sense that both hold or fail together. Their mutual agreement is demonstrated most clearly in the self-interaction problem by taking account of the rearrangement of degrees of freedom appearing in the action of the Maxwell-Lorentz and Yang-Mills-Wong theories. The failure of energy-momentum conservation in general relativity is attributed to the fact that this theory allows solutions having nontrivial topologies. The total energy and momentum of a system with nontrivial topological content prove to be ambiguous, coordinatization-dependent quantities. For example, the energy of a Schwarzschild black hole may take any positive value greater than, or equal to, the mass of the body whose collapse is responsible for forming this black hole. We draw the analogy to the paradoxial Banach-Tarski theorem; the measure becomes a poorly defined concept if initial three-dimensional bounded sets are rearranged in topologically nontrivial ways through the action of free non-Abelian isometry groups.

2T Physics, Weyl Symmetry and the Geodesic Completion of Black Hole Backgrounds

NASA Astrophysics Data System (ADS)

Araya Quezada, Ignacio Jesus

In this thesis, we discuss two different contexts where the idea of gauge symmetry and duality is used to solve the dynamics of physical systems. The first of such contexts is 2T-physics in the worldline in d+2 dimensions, where the principle of Sp(2,R) gauge symmetry in phase space is used to relate different 1T systems in (d -- 1) + 1 dimensions, such as a free relativistic particle, and a relativistic particle in an arbitrary V(x2) potential. Because each 1T shadow system corresponds to a particular gauge of the underlying symmetry, there is a web of dualities relating them. The dualities between said systems amount to canonical transformations including time and energy, which allows the different systems to be described by different Hamiltonians, and consequently, to correspond to different dynamics in the (d -- 1)+1 phase space. The second context, corresponds to a Weyl invariant scalar-tensor theory of gravity, obtained as a direct prediction of 2T gravity, where the Weyl symmetry is used to obtain geodesically complete dynamics both in the context of cosmology and black hole (BH) backgrounds. The geodesic incompleteness of usual Einstein gravity, in the presence of singularities in spacetime, is related to the definition of the Einstein gauge, which fixes the sign and magnitude of the gravitational constant GN, and therefore misses the existence of antigravity patches, which are expected to arise generically just beyond gravitational singularities. The definition of the Einstein gauge can be generalized by incorporating a sign flip of the gravitational constant GN at the transitions between gravity and antigravity. This sign is a key aspect that allows us to define geodesically complete dynamics in cosmology and in BH backgrounds, particularly, in the case of the 4D Schwarzschild BH and the 2D stringy BH. The complete nature of particle geodesics in these BH backgrounds is exhibited explicitly at the classical level, and the extension of these results to the behavior of fields, interpreted as the first quantized particle wavefunctions in the backgrounds is discussed for the 2D stringy BH case. It is shown that the geodesic completion also carries through at the quantum level, by examining the effective potential of the corresponding Schwarzschild problem. Also, in the case of the 2D stringy BH, it is explicitly shown that the spacetime has a multi-sheeted structure, which resolves possible issues like the presence of closed timelike curves. This multi-sheeted structure is conjectured to exist also for the 4D Schwarzschild BH (and perhaps for all BH backgrounds). The main new results of this thesis are the extended network of dualities, in the form of canonical transformations including time and energy, between the 1T dynamical systems, presented in Chapter 2 and the construction of the geodesically complete 4D Schwarzschild and 2D stringy black hole backgrounds, presented in Chapter 3.

Addressing the missing matter problem in galaxies through a new fundamental gravitational radius

DOE Office of Scientific and Technical Information (OSTI.GOV)

Capozziello, S.; Jovanović, P.; Jovanović, V. Borka

We demonstrate that the existence of a Noether symmetry in f ( R ) theories of gravity gives rise to a further gravitational radius, besides the standard Schwarzschild one, determining the dynamics at galactic scales. By this feature, it is possible to explain the baryonic Tully-Fisher relation and the rotation curve of gas-rich galaxies without the dark matter hypothesis.

Novel fast catadioptric objective with wide field of view

NASA Astrophysics Data System (ADS)

Muñoz, Fernando; Infante Herrero, José M.; Benítez, Pablo; Miñano, Juan C.; Lin, Wang; Vilaplana, Juan; Biot, Guillermo; de la Fuente, Marta

2010-08-01

Using the Simultaneous Multiple Surface method in 2D (SMS2D), we present a fast catadioptric objective with a wide field of view (125°×96°) designed for a microbolometer detector with 640×480 pixels and 25 microns pixel pitch Keywords: Infrared lens design, thermal imaging, Schwarzschild configuration, SMS2D, wide field of view, driving cameras, panoramic systems

Construction of Penrose Diagrams for Dynamic Black Holes

NASA Technical Reports Server (NTRS)

Brown, Beth A.; Lindesay, James

2008-01-01

A set of Penrose diagrams is constructed in order to examine the large-scale causal structure of black holes with dynamic horizons. Coordinate dependencies of significant features, such as the event horizon and radial mass scale, are demonstrated on the diagrams. Unlike in static Schwarzschild geometries, the radial mass scale is clearly seen to differ from the horizon. Trajectories for photons near the horizon are briefly discussed.

A reflective optical transport system for ultraviolet Thomson scattering from electron plasma waves on OMEGA.

PubMed

Katz, J; Boni, R; Sorce, C; Follett, R; Shoup, M J; Froula, D H

2012-10-01

A reflective optical transport system has been designed for the OMEGA Thomson-scattering diagnostic. A Schwarzschild objective that uses two concentric spherical mirrors coupled to a Pfund objective provides diffraction-limited imaging across all reflected wavelengths. This enables the operator to perform Thomson-scattering measurements of ultraviolet (0.263 μm) light scattered from electron plasma waves.

History of optical theory of reflecting telescopes and implications for future projects

NASA Astrophysics Data System (ADS)

Wilson, Raymond N.

1997-03-01

This contribution, The History of Optical Theory of Reflecting Telescopes and Implications for Future Projects, is a shortened form of the Karl Schwarzschild lecture given in Bochum in September 1993. Some material has been added from an invited paper given in Padua in December 1992. For a full account, with figures and tables, the reader is referred to these two papers.

Amistad Symposium on Southern Civil Rights Litigation Records for the 1960s (New Orleans, Louisiana, December 8-9, 1978).

ERIC Educational Resources Information Center

Dillard Univ., New Orleans, LA. Armistad Research Center.

This report contains transcripts of speeches given at the Amistad Symposium by lawyers, judges, and others active in the civil rights movement since the 1960s. Speakers include Clifton Johnson, J. Skelly Wright, John P. Nelson, Edwin King, Fred L. Banks, Jr., Lawrence A. Aschenbrenner, Frank R. Parker, Henry Schwarzschild, and Richard B. Sobol.…

Conservative corrections to the innermost stable circular orbit (ISCO) of a Kerr black hole: A new gauge-invariant post-Newtonian ISCO condition, and the ISCO shift due to test-particle spin and the gravitational self-force

DOE Office of Scientific and Technical Information (OSTI.GOV)

Favata, Marc

2011-01-15

The innermost stable circular orbit (ISCO) delimits the transition from circular orbits to those that plunge into a black hole. In the test-mass limit, well-defined ISCO conditions exist for the Kerr and Schwarzschild spacetimes. In the finite-mass case, there are a large variety of ways to define an ISCO in a post-Newtonian (PN) context. Here I generalize the gauge-invariant ISCO condition of Blanchet and Iyer [Classical Quantum Gravity 20, 755 (2003)] to the case of spinning (nonprecessing) binaries. The Blanchet-Iyer ISCO condition has two desirable and unexpected properties: (1) it exactly reproduces the Schwarzschild ISCO in the test-mass limit, andmore » (2) it accurately approximates the recently calculated shift in the Schwarzschild ISCO frequency due to the conservative-piece of the gravitational self-force [L. Barack and N. Sago, Phys. Rev. Lett. 102, 191101 (2009)]. The generalization of this ISCO condition to spinning binaries has the property that it also exactly reproduces the Kerr ISCO in the test-mass limit (up to the order at which PN spin corrections are currently known). The shift in the ISCO due to the spin of the test-particle is also calculated. Remarkably, the gauge-invariant PN ISCO condition exactly reproduces the ISCO shift predicted by the Papapetrou equations for a fully relativistic spinning particle. It is surprising that an analysis of the stability of the standard PN equations of motion is able (without any form of 'resummation') to accurately describe strong-field effects of the Kerr spacetime. The ISCO frequency shift due to the conservative self-force in Kerr is also calculated from this new ISCO condition, as well as from the effective-one-body Hamiltonian of Barausse and Buonanno [Phys. Rev. D 81, 084024 (2010)]. These results serve as a useful point of comparison for future gravitational self-force calculations in the Kerr spacetime.« less

Vaidya spacetime in the diagonal coordinates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berezin, V. A., E-mail: berezin@inr.ac.ru; Dokuchaev, V. I., E-mail: dokuchaev@inr.ac.ru; Eroshenko, Yu. N., E-mail: eroshenko@inr.ac.ru

We have analyzed the transformation from initial coordinates (v, r) of the Vaidya metric with light coordinate v to the most physical diagonal coordinates (t, r). An exact solution has been obtained for the corresponding metric tensor in the case of a linear dependence of the mass function of the Vaidya metric on light coordinate v. In the diagonal coordinates, a narrow region (with a width proportional to the mass growth rate of a black hole) has been detected near the visibility horizon of the Vaidya accreting black hole, in which the metric differs qualitatively from the Schwarzschild metric andmore » cannot be represented as a small perturbation. It has been shown that, in this case, a single set of diagonal coordinates (t, r) is insufficient to cover the entire range of initial coordinates (v, r) outside the visibility horizon; at least three sets of diagonal coordinates are required, the domains of which are separated by singular surfaces on which the metric components have singularities (either g{sub 00} = 0 or g{sub 00} = ∞). The energy–momentum tensor diverges on these surfaces; however, the tidal forces turn out to be finite, which follows from an analysis of the deviation equations for geodesics. Therefore, these singular surfaces are exclusively coordinate singularities that can be referred to as false fire-walls because there are no physical singularities on them. We have also considered the transformation from the initial coordinates to other diagonal coordinates (η, y), in which the solution is obtained in explicit form, and there is no energy–momentum tensor divergence.« less

Motion4D-library extended

NASA Astrophysics Data System (ADS)

Müller, Thomas

2011-06-01

The new version of the Motion4D-library now also includes the integration of a Sachs basis and the Jacobi equation to determine gravitational lensing of pointlike sources for arbitrary spacetimes.New version program summaryProgram title: Motion4D-libraryCatalogue identifier: AEEX_v3_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEX_v3_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 219 441No. of bytes in distributed program, including test data, etc.: 6 968 223Distribution format: tar.gzProgramming language: C++Computer: All platforms with a C++ compilerOperating system: Linux, WindowsRAM: 61 MbytesClassification: 1.5External routines: Gnu Scientic Library (GSL) (http://www.gnu.org/software/gsl/)Catalogue identifier of previous version: AEEX_v2_0Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 703Does the new version supersede the previous version?: YesNature of problem: Solve geodesic equation, parallel and Fermi-Walker transport in four-dimensional Lorentzian spacetimes. Determine gravitational lensing by integration of Jacobi equation and parallel transport of Sachs basis.Solution method: Integration of ordinary differential equations.Reasons for new version: The main novelty of the current version is the extension to integrate the Jacobi equation and the parallel transport of the Sachs basis along null geodesics. In combination, the change of the cross section of a light bundle and thus the gravitational lensing effect of a spacetime can be determined. Furthermore, we have implemented several new metrics.Summary of revisions: The main novelty of the current version is the integration of the Jacobi equation and the parallel transport of the Sachs basis along null geodesics. The corresponding set of equations readd2xμdλ2=-Γρσμdxρdλdxσdλ, ds1,2μdλ=-Γρσμdxρdλs1,2σ, d2Y1,2μdλ2=-2ΓρσμdxρdλdY1,2σdλ-Γρσ,νμdxρdλdxσdλYν, where (1) is the geodesic equation, (2) represents the parallel transport of the two Sachs basis vectors s, and (3) is the Jacobi equation for the two Jacobi fields Y.The initial directions of the Sachs basis vectors s=(0,s)=s1,2μ∂ are defined perpendicular to the initial direction υ→ of the light ray, see also Fig. 1,s=(-, s=(-. Display OmittedA congruence of null geodesics with central null geodesic γ which starts at the observer O with an infinitesimal circular cross section is defined by the above mentioned two Jacobi fields with initial conditions Y1,2μ|=0 and (dY1,2μ/dλ)|=s1,2μ. The cross section of this congruence along γ is described by the Jacobian J(λ)=gYiμsjν|. However, to determine the gravitational lensing of a pointlike source S that is connected to the observer via γ, we need the reverse Jacobian JS. Fortunately, the reverse Jacobian is just the negative transpose of the original Jacobian JO,J:=JS=-(J)T. The Jacobian J transforms the circular shape of the congruence into an ellipse whose shape parameters (M: major/minor axis, ψ: angle of major axis, ɛ: ellipticity) readM=2αsinζcosζ-βsin2ζ+J112+J212, ψ=arctan2(Jcosζ+Jsinζ,Jcosζ+Jsinζ), ɛ=‖M-M‖‖M+M‖ withζ=12arctan2αβ,ζ=ζ+π2, and the parameters α=JJ+JJ, β=J112-J122+J212-J222. The magnification factor is given byμ=λ2MM. These shape parameters can be easily visualized in the new version of the GeodesicViewer, see Ref. [1]. A detailed discussion of gravitational lensing can be found, for example, in Schneider et al. [2].In the following, a list of newly implemented metrics is given:BertottiKasner: see Rindler [3].BesselGravWaveCart: gravitational Bessel wave from Kramer [4].DeSitterUniv, DeSitterUnivConf: de Sitter universe in Cartesian and conformal coordinates.Ernst: Black hole in a magnetic universe by Ernst [5].ExtremeReissnerNordstromDihole: see Chandrasekhar [6].HalilsoyWave: see Ref. [7].JaNeWi: Janis-Newman-Winicour metric, see Ref. [8].MinkowskiConformal: Minkowski metric in conformally rescaled coordinates.PTD_AI, PTD_AII, PTD_AIII, PTD_BI, PTD_BII, PTD_BIII, PTD_C Petrov-Type D - Levi-Civita spacetimes, see Ref. [7].PainleveGullstrand: Schwarzschild metric in Painlevé-Gullstrand coordinates, see Ref. [9].PlaneGravWave: Plane gravitational wave, see Ref. [10].SchwarzschildIsotropic: Schwarzschild metric in isotropic coordinates, see Ref. [11].SchwarzschildTortoise: Schwarzschild metric in tortoise coordinates, see Ref. [11].Sultana-Dyer: A black hole in the Einstein-de Sitter universe by Sultana and Dyer [12].TaubNUT: see Ref. [13]. The Christoffel symbols and the natural local tetrads of these new metrics are given in the Catalogue of Spacetimes, Ref. [14].To study the behavior of geodesics, it is often useful to determine an effective potential like in classical mechanics. For several metrics, we followed the Euler-Lagrangian approach as described by Rindler [10] and implemented an effective potential for a specific situation. As an example, consider the Lagrangian L=-αt˙+α-1r˙+r2φ˙ for timelike geodesics in the ϑ=π/2 hypersurface in the Schwarzschild spacetime with α=1-2m/r. The Euler-Lagrangian equations lead to the energy balance equation r˙+V(r)=k2 with the effective potential V(r)=(r-2m)(r2+h2)/r3 and the constants of motion k=αt˙ and h=r2φ˙. The constants of motion for a timelike geodesic that starts at (r=10m,φ=0) with initial direction ξ=π/4 with respect to the black hole direction and with initial velocity β=0.7 read k≈1.252 and h≈6.931. Then, from the energy balance equation we immediately obtain the radius of closest approach r≈5.927.Beside a standard Runge-Kutta fourth-order integrator and the integrators of the Gnu Scientific Library (GSL), we also implemented a standard Bulirsch-Stoer integrator.Running time: The test runs provided with the distribution require only a few seconds to run.References:T. Müller, New version announcement to the GeodesicViewer, http://cpc.cs.qub.ac.uk/summaries/AEFP_v2_0.html.P. Schneider, J. Ehlers, E. E. Falco, Gravitational Lenses, Springer, 1992.W. Rindler, Phys. Lett. A 245 (1998) 363.D. Kramer, Ann. Phys. 9 (2000) 331.F.J. Ernst, J. Math. Phys. 17 (1976) 54.S. Chandrasekhar, Proc. R. Soc. Lond. A 421 (1989) 227.H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, E. Herlt, Exact Solutions of the Einstein Field Equations, Cambridge University Press, 2009.A.I. Janis, E.T. Newman, J. Winicour, Phys. Rev. Lett. 20 (1968) 878.K. Martel, E. Poisson, Am. J. Phys. 69 (2001) 476.W. Rindler, Relativity - Special, General, and Cosmology, Oxford University Press, Oxford, 2007.C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation, W.H. Freeman, 1973.J. Sultana, C.C. Dyer, Gen. Relativ. Gravit. 37 (2005) 1349.D. Bini, C. Cherubini, Robert T. Jantzen, Class. Quantum Grav. 19 (2002) 5481.T. Muller, F. Grave, arXiv:0904.4184 [gr-qc].

Optical design and system characterization of an imaging microscope at 121.6 nm

NASA Astrophysics Data System (ADS)

Gao, Weichuan; Finan, Emily; Kim, Geon-Hee; Kim, Youngsik; Milster, Thomas D.

2018-03-01

We present the optical design and system characterization of an imaging microscope prototype at 121.6 nm. System engineering processes are demonstrated through the construction of a Schwarzschild microscope objective, including tolerance analysis, fabrication, alignment, and testing. Further improvements on the as-built system with a correction phase plate are proposed and analyzed. Finally, the microscope assembly and the imaging properties of the prototype are demonstrated.

Gravitational Radiation - a New Window Onto the Universe. (Karl Schwarzschild Lecture 1996)

NASA Astrophysics Data System (ADS)

Thorne, K. S.

A summary is given of the current status and plans for gravitational-wave searches at all plausible wavelengths, from the size of the observable universe to a few kilometers. The anticipated scientific payoff from these searches is described, including expectations for detailed studies of black holes and neutron stars, high-accuracy tests of general relativity, and hopes for the discovery of exotic new kinds of objects.

The X-ray view of EROs

NASA Astrophysics Data System (ADS)

Brusa, M.; Comastri, A.; Daddi, E.; Cimatti, A.; Vignali, C.

(1) Dip. Astronomia Bologna University, via Ranzani 1, I-40127 Bologna ITALY (2) INAF - Osservatorio Astronomico di Bologna, via Ranzani 1, I-40127 Bologna ITALY (3) ESO - European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748 Garching bei Muenchen Germany (4) INAF - Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-55025 Firenze, Italy (5) Dept. of Astronomy and Astrophysics, The Pennsylvania State University, 525 Davey Lab, University Park, PA 16802, USA

Design of a normal incidence multilayer imaging x-ray microscope.

PubMed

Shealy, D L; Gabardi, D R; Hoover, R B; Walker, A B; Lindblom, J F; Barbee, T W

1989-01-01

Normal incidence multilayer Cassegrain x-ray telescopes were flown on the Stanford/MSFC Rocket X-Ray Spectroheliograph. These instruments produced high spatial resolution images of the Sun and conclusively demonstrated that doubly reflecting multilayer x-ray optical systems are feasible. The images indicated that aplanatic imaging soft x-ray /EUV microscopes should be achievable using multilayer optics technology. We have designed a doubly reflecting normal incidence multilayer imaging x-ray microscope based on the Schwarzschild configuration. The Schwarzschild microscope utilizes two spherical mirrors with concentric radii of curvature which are chosen such that the third-order spherical aberration and coma are minimized. We discuss the design of the microscope and the results of the optical system ray trace analysis which indicates that diffraction-limited performance with 600 Å spatial resolution should be obtainable over a 1 mm field of view at a wavelength of 100 Å. Fabrication of several imaging soft x-ray microscopes based upon these designs, for use in conjunction with x-ray telescopes and laser fusion research, is now in progress. High resolution aplanatic imaging x-ray microscopes using normal incidence multilayer x-ray mirrors should have many important applications in advanced x-ray astronomical instrumentation, x-ray lithography, biological, biomedical, metallurgical, and laser fusion research.

Resonance interatomic energy in a Schwarzschild spacetime

NASA Astrophysics Data System (ADS)

Zhou, Wenting; Yu, Hongwei

2017-08-01

We study, in the Schwarzschild spacetime, the resonance interatomic energy (RIE) of two static identical atoms with an interatomic separation L along the radial direction and correlated by a symmetric/antisymmetric entangled state. The atoms are assumed to be coupled to massless scalar fields in the Boulware, Unruh, and Hartle-Hawking vacua, and approximate analytical results are obtained both at infinity and near the horizon. Our results show that at infinity, the RIE approaches that in a flat spacetime, while, near the horizon, they can deviate dramatically from each other. Besides, different from other atomic radiative properties such as the Lamb shift of a single atom or the interatomic energy between two uncorrelated atoms, which can be obviously affected by the thermal character of quantum fields, the RIE of two atoms in a symmetric/antisymmetric entangled state in the Boulware, Unruh, and Hartle-Hawking vacua are exactly the same as a result of the fact that the RIE of two such atoms depends only on the atomic self-reaction, i.e., it does not feel the vacuum fluctuations. This suggests that the RIE of two static atoms in a symmetric/antisymmetric entangled state outside a black hole is oblivious to the Hawking radiation, in contrast to those uncorrelated atoms.

Extended source effect on microlensing light curves by an Ellis wormhole

NASA Astrophysics Data System (ADS)

Tsukamoto, Naoki; Gong, Yungui

2018-04-01

We can survey an Ellis wormhole which is the simplest Morris-Thorne wormhole in our Galaxy with microlensing. The light curve of a point source microlensed by the Ellis wormhole shows approximately 4% demagnification while the total magnification of images lensed by a Schwarzschild lens is always larger than unity. We investigate an extended source effect on the light curves microlensed by the Ellis wormhole. We show that the depth of the gutter of the light curves of an extended source is smaller than the one of a point source since the magnified part of the extended source cancels the demagnified part out. We can, however, distinguish between the light curves of the extended source microlensed by the Ellis wormhole and the ones by the Schwarzschild lens in their shapes even if the size of the source is a few times larger than the size of an Einstein ring on a source plane. If the relative velocity of a star with the radius of 1 06 km at 8 kpc in the bulge of our Galaxy against an observer-lens system is smaller than 10 km /s on a source plane, we can detect microlensing of the star lensed by the Ellis wormhole with the throat radius of 1 km at 4 kpc.

The interaction of Dirac particles with a Hawking charged radiating black hole

NASA Astrophysics Data System (ADS)

Kubik, Erik

2007-08-01

The interaction of spin 1/2 fields with a charged, evaporating black hole (EBH) is investigated. Using the Vaidya metric to model the Hawking evaporating black hole, the wave equation for a massless spinor field is obtained. The resulting field equation is solved utilizing techniques developed by Brill and Wheeler. Unlike previous efforts, a charged, evaporating black hole has never been used as a background to investigate spin 1/2 quantum field propagation, e.g., Brill and Wheeler considered massless spin 1/2 interactions in a static, Schwarzschild background. Using the WKB approximation, the wave equation is solved for the case of an EBH with constant luminosity. Analysis of the effective potential at different stages of evaporation is made including the dependence on the parameters of the system such as the total angular momentum, energy of the incident field, and luminosity of the evaporating black hole. Utilizing techniques of Mukhopad-hey, the transmission and reflection coefficients for the massless spinors are computed and compared to Schwarzschild result for both the high energy and hard scattering cases. The effect of the time dependence of the space-time metric has an important effect on the behavior of quantum fields over the lifetime of the evaporating black hole and may provide a signature for the detection of such objects.

Thermodynamics and luminosities of rainbow black holes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mu, Benrong; Wang, Peng; Yang, Haitang, E-mail: mubenrong@uestc.edu.cn, E-mail: pengw@scu.edu.cn, E-mail: hyanga@scu.edu.cn

2015-11-01

Doubly special relativity (DSR) is an effective model for encoding quantum gravity in flat spacetime. As result of the nonlinearity of the Lorentz transformation, the energy-momentum dispersion relation is modified. One simple way to import DSR to curved spacetime is ''Gravity's rainbow'', where the spacetime background felt by a test particle would depend on its energy. Focusing on the ''Amelino-Camelia dispersion relation'' which is E{sup 2} = m{sup 2}+p{sup 2}[1−η(E/m{sub p}){sup n}] with n > 0, we investigate the thermodynamical properties of a Schwarzschild black hole and a static uncharged black string for all possible values of η and n in the framework ofmore » rainbow gravity. It shows that there are non-vanishing minimum masses for these two black holes in the cases with η < 0 and n ≥ 2. Considering effects of rainbow gravity on both the Hawking temperature and radius of the event horizon, we use the geometric optics approximation to compute luminosities of a 2D black hole, a Schwarzschild one and a static uncharged black string. It is found that the luminosities can be significantly suppressed or boosted depending on the values of η and n.« less

Mass-independent area (or entropy) and thermodynamic volume products in conformal gravity

NASA Astrophysics Data System (ADS)

Pradhan, Parthapratim

2017-06-01

In this work, we investigate the thermodynamic properties of conformal gravity in four dimensions. We compute the area (or entropy) functional relation for this black hole (BH). We consider both de Sitter (dS) and anti-de Sitter (AdS) cases. We derive the Cosmic-Censorship-Inequality which is an important relation in general relativity that relates the total mass of a spacetime to the area of all the BH horizons. Local thermodynamic stability is studied by computing the specific heat. The second-order phase transition occurs at a certain condition. Various types of second-order phase structure have been given for various values of a and the cosmological constant Λ in the Appendix. When a = 0, one obtains the result of Schwarzschild-dS and Schwarzschild-AdS cases. In the limit aM ≪ 1, one obtains the result of Grumiller spacetime, where a is nontrivial Rindler parameter or Rindler acceleration and M is the mass parameter. The thermodynamic volume functional relation is derived in the extended phase space, where the cosmological constant is treated as a thermodynamic pressure and its conjugate variable as a thermodynamic volume. The mass-independent area (or entropy) functional relation and thermodynamic volume functional relation that we have derived could turn out to be a universal quantity.

A new Schwarzschild optical system for two-dimensional EUV imaging of MRX plasmas

NASA Astrophysics Data System (ADS)

Bolgert, P.; Bitter, M.; Efthimion, P.; Hill, K. W.; Ji, H.; Myers, C. E.; Yamada, M.; Yoo, J.; Zweben, S.

2013-10-01

This poster describes the design and construction of a new Schwarzschild optical system for two-dimensional EUV imaging of plasmas. This optical system consists of two concentric spherical mirrors with radii R1 and R2, and is designed to operate with certain angles of incidence θ1 and θ2. The special feature of this system resides in the fact that all the rays passing through the system are tangential to a third concentric circle; it assures that the condition for Bragg reflection is simultaneously fulfilled at each point on the two reflecting surfaces if the spherical mirrors are replaced by spherical multi-layer structures. A prototype of this imaging system will be implemented in the Magnetic Reconnection Experiment (MRX) at PPPL to obtain two-dimensional EUV images of the plasma in the energy range from 18 to 62 eV; the relative intensity of the emitted radiation in this energy range was determined from survey measurements with a photodiode. It is thought that the radiation at these energies is due to Bremsstrahlung and line emission caused by suprathermal electrons. This research is supported by DoE Contract Number DE-AC02-09CH11466 and by the Center for Magnetic Self-Organization (CMSO).

Tidal coupling of a Schwarzschild black hole and circularly orbiting moon

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fang Hua; Lovelace, Geoffrey

2005-12-15

We describe the possibility of using the laser interferometer space antenna (LISA) 's gravitational-wave observations to study, with high precision, the response of a massive central body (e.g. a black hole or a soliton star) to the tidal gravitational pull of an orbiting, compact, small-mass object (a white dwarf, neutron star, or small-mass black hole). Motivated by this LISA application, we use first-order perturbation theory to study tidal coupling for a special, idealized case: a Schwarzschild black hole of mass M, tidally perturbed by a 'moon' with mass {mu}<>M with orbital angularmore » velocity {omega}. We investigate the details of how the tidal deformation of the hole gives rise to an induced quadrupole moment I{sub ij} in the hole's external gravitational field at large radii, including the vicinity of the moon. In the limit that the moon is static, we find, in Schwarzschild coordinates and Regge-Wheeler gauge, the surprising result that there is no induced quadrupole moment. We show that this conclusion is gauge dependent and that the static, induced quadrupole moment for a black hole is inherently ambiguous, and we contrast this with an earlier result of Suen, which gave, in a very different gauge, a nonzero static induced quadrupole moment with a sign opposite to what one would get for a fluid central body. For the orbiting moon and the central Schwarzschild hole, we find (in agreement with a recent result of Poisson) a time-varying induced quadrupole moment that is proportional to the time derivative of the moon's tidal field, I{sub ij}=(32/45)M{sup 6}E{sub ij} and that therefore is out of phase with the tidal field by a spatial angle {pi}/4 and by a temporal phase shift {pi}/2. This induced quadrupole moment produces a gravitational force on the moon that reduces its orbital energy and angular momentum at the same rate as the moon's tidal field sends energy and angular momentum into the hole's horizon. As a partial analog of a result derived long ago by Hartle for a spinning hole and a static distant companion, we show that the orbiting moon's tidal field induces a tidal bulge on the hole's horizon, and that the rate of change of the horizon shape (i.e. the horizon shear) leads the perturbing tidal field at the horizon by an angle 4M{omega}. We prefer to avoid introducing an ingoing null geodesic, as Hartle did in his definition of the phase shift, because the moon is in the central body's near zone (b<<1/{omega}) and thus should interact with the horizon instantaneously, not causally. We discuss the implications of these results for LISA's future observations of tidal coupling, including the inappropriateness of using the concepts of tidal polarizability and tidal lag or lead angle, for the massive central body, when discussing LISA's observations.« less

Light refraction in the Swiss-cheese model

NASA Astrophysics Data System (ADS)

Csapó, Adelinda; Bene, Gyula

2012-08-01

We investigate light propagation in the Swiss-cheese model. On both sides of Swiss-cheese sphere surfaces, observers resting in the flat Friedmann-Robertson-Walker (FRW) space and the Schwarzschild space respectively, see the same light ray enclosing different angles with the normal. We examine light refraction at each crossing of the boundary surfaces, showing that the angle of refraction is larger than the angle of incidence for both directions of the light.

Solar physics in Potsdam. (German Title: Sonnenphysik in Potsdam)

NASA Astrophysics Data System (ADS)

Staude, Jürgen

Solar research initiated the establishment of the Astrophysical Observatory Potsdam (AOP) in 1874. The present contribution outlines the development of solar physics in Potsdam from the early history of the AOP to this day. The main topics are the work of Karl Schwarzschild, the investigations related to the general theory of relativity, the foundation of the Einstein tower, Walter Grotrian's founding of modern coronal physics, and the investigations of sunspot magnetic fields.

Relativistic model for anisotropic strange stars

NASA Astrophysics Data System (ADS)

Deb, Debabrata; Chowdhury, Sourav Roy; Ray, Saibal; Rahaman, Farook; Guha, B. K.

2017-12-01

In this article, we attempt to find a singularity free solution of Einstein's field equations for compact stellar objects, precisely strange (quark) stars, considering Schwarzschild metric as the exterior spacetime. To this end, we consider that the stellar object is spherically symmetric, static and anisotropic in nature and follows the density profile given by Mak and Harko (2002) , which satisfies all the physical conditions. To investigate different properties of the ultra-dense strange stars we have employed the MIT bag model for the quark matter. Our investigation displays an interesting feature that the anisotropy of compact stars increases with the radial coordinate and attains its maximum value at the surface which seems an inherent property for the singularity free anisotropic compact stellar objects. In this connection we also perform several tests for physical features of the proposed model and show that these are reasonably acceptable within certain range. Further, we find that the model is consistent with the energy conditions and the compact stellar structure is stable with the validity of the TOV equation and Herrera cracking concept. For the masses below the maximum mass point in mass vs radius curve the typical behavior achieved within the framework of general relativity. We have calculated the maximum mass and radius of the strange stars for the three finite values of bag constant Bg.

Interior of black holes and information recovery

NASA Astrophysics Data System (ADS)

Kawai, Hikaru; Yokokura, Yuki

2016-02-01

We analyze time evolution of a spherically symmetric collapsing matter from a point of view that black holes evaporate by nature. We first consider a spherical thin shell that falls in the metric of an evaporating Schwarzschild black hole of which the radius a (t ) decreases in time. The important point is that the shell can never reach a (t ) but it approaches a (t )-a (t )d/a (t ) d t . This situation holds at any radius because the motion of a shell in a spherically symmetric system is not affected by the outside. In this way, we find that the collapsing matter evaporates without forming a horizon. Nevertheless, a Hawking-like radiation is created in the metric, and the object looks the same as a conventional black hole from the outside. We then discuss how the information of the matter is recovered. We also consider a black hole that is adiabatically grown in the heat bath and obtain the interior metric. We show that it is the self-consistent solution of Gμ ν=8 π G ⟨Tμ ν⟩ and that the four-dimensional Weyl anomaly induces the radiation and a strong angular pressure. Finally, we analyze the internal structures of the charged and the slowly rotating black holes.

Structure of the effective potential for a spherical wormhole

DOE Office of Scientific and Technical Information (OSTI.GOV)

Montelongo Garcia, N.; Zannias, T.

2008-09-15

The structure of the effective potential V describing causal geodesics near the throat of an arbitrary spherical wormhole is analyzed. Einstein's equations relative to a set of regular coordinates covering a vicinity of the throat imply that any spherical wormhole can be constructed from solutions of an effective initial value problem with the throat serving as an initial value surface. The initial data involve matter variables, the area A(0) of the throat, and the gradient {lambda}(0) of the redshift factor on the throat. Whenever {lambda}(0)=0, the effective potential V has a critical point on the throat. Conditions upon the datamore » are derived ensuring that the critical point is a local minimum (respectively maximum). For particular families of quasi-Schwarzschild wormholes, V exhibits a local minimum on the throat independently upon the energy E and angular momentum L{sup 2} of the test particles and thus such wormholes admit stable circular timelike and null geodesics on the throat. For families of Chaplygin wormholes, we show that such geodesics are unstable. Based on a suitable power series representation of the metric, properties of V away from the throat are obtained that are useful for the analysis of accretion disks and radiation processes near the throat of any spherical wormhole.« less

Hamiltonian General Relativity in Finite Space and Cosmological Potential Perturbations

NASA Astrophysics Data System (ADS)

Barbashov, B. M.; Pervushin, V. N.; Zakharov, A. F.; Zinchuk, V. A.

The Hamiltonian formulation of general relativity is considered in finite space-time and a specific reference frame given by the diffeo-invariant components of the Fock simplex in terms of the Dirac-ADM variables. The evolution parameter and energy invariant with respect to the time-coordinate transformations are constructed by the separation of the cosmological scale factor a(x0) and its identification with the spatial averaging of the metric determinant, so that the dimension of the kinemetric group of diffeomorphisms coincides with the dimension of a set of variables whose velocities are removed by the Gauss-type constraints in accordance with the second Nöther theorem. This coincidence allows us to solve the energy constraint, fulfil Dirac's Hamiltonian reduction, and to describe the potential perturbations in terms of the Lichnerowicz scale-invariant variables distinguished by the absence of the time derivatives of the spatial metric determinant. It was shown that the Hamiltonian version of the cosmological perturbation theory acquires attributes of the theory of superfluid liquid, and it leads to a generalization of the Schwarzschild solution. The astrophysical application of this approach to general relativity is considered under supposition that the Dirac-ADM Hamiltonian frame is identified with that of the Cosmic Microwave Background radiation distinguished by its dipole component in the frame of an Earth observer.

Circular geodesic of Bardeen and Ayon-Beato-Garcia regular black-hole and no-horizon spacetimes

NASA Astrophysics Data System (ADS)

Stuchlík, Zdeněk; Schee, Jan

2015-12-01

In this paper, we study circular geodesic motion of test particles and photons in the Bardeen and Ayon-Beato-Garcia (ABG) geometry describing spherically symmetric regular black-hole or no-horizon spacetimes. While the Bardeen geometry is not exact solution of Einstein's equations, the ABG spacetime is related to self-gravitating charged sources governed by Einstein's gravity and nonlinear electrodynamics. They both are characterized by the mass parameter m and the charge parameter g. We demonstrate that in similarity to the Reissner-Nordstrom (RN) naked singularity spacetimes an antigravity static sphere should exist in all the no-horizon Bardeen and ABG solutions that can be surrounded by a Keplerian accretion disc. However, contrary to the RN naked singularity spacetimes, the ABG no-horizon spacetimes with parameter g/m > 2 can contain also an additional inner Keplerian disc hidden under the static antigravity sphere. Properties of the geodesic structure are reflected by simple observationally relevant optical phenomena. We give silhouette of the regular black-hole and no-horizon spacetimes, and profiled spectral lines generated by Keplerian rings radiating at a fixed frequency and located in strong gravity region at or nearby the marginally stable circular geodesics. We demonstrate that the profiled spectral lines related to the regular black-holes are qualitatively similar to those of the Schwarzschild black-holes, giving only small quantitative differences. On the other hand, the regular no-horizon spacetimes give clear qualitative signatures of their presence while compared to the Schwarschild spacetimes. Moreover, it is possible to distinguish the Bardeen and ABG no-horizon spacetimes, if the inclination angle to the observer is known.

Frequency-domain algorithm for the Lorenz-gauge gravitational self-force

NASA Astrophysics Data System (ADS)

Akcay, Sarp; Warburton, Niels; Barack, Leor

2013-11-01

State-of-the-art computations of the gravitational self-force (GSF) on massive particles in black hole spacetimes involve numerical evolution of the metric perturbation equations in the time domain, which is computationally very costly. We present here a new strategy based on a frequency-domain treatment of the perturbation equations, which offers considerable computational saving. The essential ingredients of our method are (i) a Fourier-harmonic decomposition of the Lorenz-gauge metric perturbation equations and a numerical solution of the resulting coupled set of ordinary equations with suitable boundary conditions; (ii) a generalized version of the method of extended homogeneous solutions [L. Barack, A. Ori, and N. Sago, Phys. Rev. D 78, 084021 (2008)] used to circumvent the Gibbs phenomenon that would otherwise hamper the convergence of the Fourier mode sum at the particle’s location; (iii) standard mode-sum regularization, which finally yields the physical GSF as a sum over regularized modal contributions. We present a working code that implements this strategy to calculate the Lorenz-gauge GSF along eccentric geodesic orbits around a Schwarzschild black hole. The code is far more efficient than existing time-domain methods; the gain in computation speed (at a given precision) is about an order of magnitude at an eccentricity of 0.2, and up to 3 orders of magnitude for circular or nearly circular orbits. This increased efficiency was crucial in enabling the recently reported calculation of the long-term orbital evolution of an extreme mass ratio inspiral [N. Warburton, S. Akcay, L. Barack, J. R. Gair, and N. Sago, Phys. Rev. D 85, 061501(R) (2012)]. Here we provide full technical details of our method to complement the above report.

Fossil dust shells around luminous supergiants

NASA Technical Reports Server (NTRS)

Stothers, R.

1975-01-01

The observed frequency with which infrared excesses appear in F, G, and K supergiants of luminosity class Ia supports the idea that these excesses arise in a 'fossil' circumstellar dust shell that was formed during a prior M-super-giant phase of evolution. The required leftward evolution of the star on the H-R diagram would then imply that the Ledoux, rather than the Schwarzschild, criterion for convective mixing is the correct criterion to use in stellar evolution calculations.

Probing the Higgs vacuum with general relativity

NASA Technical Reports Server (NTRS)

Mannheim, Philip D.; Kazanas, Demosthenes

1991-01-01

It is shown that the structure of the Higgs vacuum can be revealed in gravitational experiments which probe the Schwarzschild geometry to only one order in MG/r beyond that needed for the classical tests of general relativity. The possibility that deviations from the conventional geometry are at least theoretically conceivable is explored. The deviations obtained provide a diagnostic test for searching for the existence of macroscopic scalar fields and open up the possiblity for further exploring the Higgs mechanism.

Holographic screening length in a hot plasma of two sphere

NASA Astrophysics Data System (ADS)

Atmaja, A. Nata; Kassim, H. Abu; Yusof, N.

2015-11-01

We study the screening length L_{max} of a moving quark-antiquark pair in a hot plasma, which lives in a two sphere, S^2, using the AdS/CFT correspondence in which the corresponding background metric is the four-dimensional Schwarzschild-AdS black hole. The geodesic of both ends of the string at the boundary, interpreted as the quark-antiquark pair, is given by a stationary motion in the equatorial plane by which the separation length L of both ends of the string is parallel to the angular velocity ω . The screening length and total energy H of the quark-antiquark pair are computed numerically and show that the plots are bounded from below by some functions related to the momentum transfer P_c of the drag force configuration. We compare the result by computing the screening length in the reference frame of the moving quark-antiquark pair, in which the background metrics are "Boost-AdS" and Kerr-AdS black holes. Comparing both black holes, we argue that the mass parameters M_{Sch} of the Schwarzschild-AdS black hole and M_{Kerr} of the Kerr-AdS black hole are related at high temperature by M_{Kerr}=M_{Sch}(1-a^2l^2)^{3/2}, where a is the angular momentum parameter and l is the AdS curvature.

Charged perfect fluid tori in strong central gravitational and dipolar magnetic fields

NASA Astrophysics Data System (ADS)

Kovář, Jiří; Slaný, Petr; Cremaschini, Claudio; Stuchlík, Zdeněk; Karas, Vladimír; Trova, Audrey

2016-06-01

We study electrically charged perfect fluid toroidal structures encircling a spherically symmetric gravitating object with Schwarzschild spacetime geometry and endowed with a dipole magnetic field. The work represents a direct continuation of our previous general-relativistic studies of electrically charged fluid in the approximation of zero conductivity, which formed tori around a Reissner-Nordström black hole or a Schwarzschild black hole equipped with a test electric charge and immersed in an asymptotically uniform magnetic field. After a general introduction of the zero-conductivity charged fluid model, we discuss a variety of possible topologies of the toroidal fluid configurations. Along with the charged equatorial tori forming interesting coupled configurations, we demonstrate the existence of the off-equatorial tori, for which the dipole type of magnetic field seems to be necessary. We focus on orbiting structures with constant specific angular momentum and on those in permanent rigid rotation. We stress that the general analytical treatment developed in our previous works is enriched here by the integrated form of the pressure equations. To put our work into an astrophysical context, we identify the central object with an idealization of a nonrotating magnetic neutron star. Constraining ranges of its parameters and also parameters of the circling fluid, we discuss a possible relevance of the studied toroidal structures, presenting along with their topology also pressure, density, temperature and charge profiles.

Modified hoop conjecture in expanding spacetimes and primordial black hole production in FRW universe

NASA Astrophysics Data System (ADS)

Saini, Anshul; Stojkovic, Dejan

2018-05-01

According to a variant of the hoop conjecture, if we localize two particles within the Schwarzschild radius corresponding to their center of mass energy, then a black hole will form. Despite a large body of work on the formation of primordial black holes, so far this conjecture has not been generalized to expanding spacetimes. We derive a formula which gives the distance within which two particles must be localized to give a black hole, and which crucially depends on the expansion rate of the background space. In the limit of a very slow expansion, we recover the flat spacetime case. In the opposite limit of the large expansion rate when the inverse Hubble radius is smaller than the Schwarzschild radius of a "would be" black hole, the new critical distance between two particles that can make a black hole becomes equal to the particle horizon, which is just a requirement that the particles are in a causal contact. This behavior also nicely illustrates why the Big Bang singularity is not a black hole. We then use our formula to calculate the number density, energy density and production rate of black holes produced in collisions of particles. We find that though black holes might be numerous at high temperatures, they never dominate over the background radiation below the Planck temperature.

Entropy in Spacetime and Topological Hair

NASA Astrophysics Data System (ADS)

Hyun, Young-Hwan; Kim, Yoonbai

2018-01-01

Global topological soliton of the hedgehog ansatz is added to de Sitter spacetime in arbitrary dimensions larger than three, and then thermodynamic law is checked at the cosmological horizon. All geometric and thermodynamic quantities are varied in the presence of a long-range interacting matter distribution with negative pressure, however the entropy-area relation is satisfied in the exact form. Its geometry involves deficit solid angle but maintains a single horizon which allows unique temperature normalization, different from the case of Schwarzschild-de Sitter spacetime.

Black hole squeezers

NASA Astrophysics Data System (ADS)

Su, Daiqin; Ho, C. T. Marco; Mann, Robert B.; Ralph, Timothy C.

2017-09-01

We show that the gravitational quasinormal modes (QNMs) of a Schwarzschild black hole play the role of a multimode squeezer that can generate particles. For a minimally coupled scalar field, the QNMs "squeeze" the initial state of the scalar field (even for the vacuum) and produce scalar particles. The maximal squeezing amplitude is inversely proportional to the cube of the imaginary part of the QNM frequency, implying that the particle generation efficiency is higher for lower decaying QNMs. Our results show that the gravitational perturbations can amplify Hawking radiation.

Quasi-local energy in presence of gravitational radiation

NASA Astrophysics Data System (ADS)

Chen, Po-Ning; Wang, Mu-Tao; Yau, Shing-Tung

2016-07-01

We discuss our recent work [P.-N. Chen, M.-T. Wang and S.-T. Yau, Quasi-local mass in the gravitational perturbations of black holes, to appear.] in which gravitational radiation was studied by evaluating the Wang-Yau quasi-local mass of surfaces of fixed size at the infinity of both axial and polar perturbations of the Schwarzschild spacetime, à la Chandrasekhar. [S. Chandrasekhar, The Mathematical Theory of Black Holes, Oxford Classic Texts in the Physical Sciences (Oxford University Press, New York, 1998).

Across-horizon scattering and information transfer

NASA Astrophysics Data System (ADS)

Emelyanov, V. A.; Klinkhamer, F. R.

2018-06-01

We address the question whether or not two electrically charged elementary particles can Coulomb scatter if one of these particles is inside the Schwarzschild black-hole horizon and the other outside. It can be shown that the quantum process is consistent with the local energy–momentum conservation law. This result implies that across-horizon scattering is a physical effect, relevant to astrophysical black holes. We propose a Gedankenexperiment which uses the quantum scattering process to transfer information from inside the black-hole horizon to outside.

Chaos in the gauge/gravity correspondence

NASA Astrophysics Data System (ADS)

Pando Zayas, Leopoldo A.; Terrero-Escalante, César A.

2010-09-01

We study the motion of a string in the background of the Schwarzschild black hole in AdS 5 by applying the standard arsenal of dynamical systems. Our description of the phase space includes: the power spectrum, the largest Lyapunov exponent, Poincare sections and basins of attractions. We find convincing evidence that the motion is chaotic. We discuss the implications of some of the quantities associated with chaotic systems for aspects of the gauge/gravity correspondence. In particular, we suggest some potential relevance for the information loss paradox.

Ray-trace analysis of glancing-incidence X-ray optical systems

NASA Technical Reports Server (NTRS)

Foreman, J. W., Jr.; Cardone, J. M.

1976-01-01

The results of a ray-trace analysis of several glancing-incidence X-ray optical systems are presented. The object of the study was threefold. First, the vignetting characteristics of the S-056 X-ray telescope were calculated using experimental data to determine mirror reflectivities. Second, a small Wolter Type I X-ray telescope intended for possible use in the Geostationary Operational Environmental Satellite program was designed and ray traced. Finally, a ray-trace program was developed for a Wolter-Schwarzschild X-ray telescope.

Gravitational radiation during plunge - a Green's function approach

NASA Astrophysics Data System (ADS)

Nampalliwar, Sourabh; Price, Richard; Khanna, Gaurav

2015-04-01

During the merger of binary compact objects, an important stage is the plunge. A short part of the Gravitational waveform, it marks the end of early inspiral and determines the quasinormal ringing (QNR) of the final product of the merger. In this talk, we describe the approach of using the Fourier domain Green's function in the particle perturbation approximation to understand the excitation of QNR. We show that the resulting understanding is successful in explaining QNR in toy models and in the Schwarzschild background.

Are black holes springlike?

NASA Astrophysics Data System (ADS)

Good, Michael R. R.; Ong, Yen Chin

2015-02-01

A (3 +1 )-dimensional asymptotically flat Kerr black hole angular speed Ω+ can be used to define an effective spring constant, k =m Ω+2. Its maximum value is the Schwarzschild surface gravity, k =κ , which rapidly weakens as the black hole spins down and the temperature increases. The Hawking temperature is expressed in terms of the spring constant: 2 π T =κ -k . Hooke's law, in the extremal limit, provides the force F =1 /4 , which is consistent with the conjecture of maximum force in general relativity.

Second order hydrodynamics for a special class of gravity duals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Springer, T.

2009-04-15

The sound mode hydrodynamic dispersion relation is computed up to order q{sup 3} for a class of gravitational duals which includes both Schwarzschild AdS and Dp-brane metrics. The implications for second order transport coefficients are examined within the context of Israel-Stewart theory. These sound mode results are compared with previously known results for the shear mode. This comparison allows one to determine the third order hydrodynamic contributions to the shear mode for the class of metrics considered here.

The East German Research Landscape in Transition Part A: Status and Transition

DTIC Science & Technology

1993-03-02

traditional Meteorologisches Observatorium Potsdam, and Prof. Siegfried Marx of the Karl - Schwarzschild -Observatorium Tautenburg. G804L32-00-01 07 APR...Telefax: +37 (091) 53409 or 51959 The Ministry is on Breiter Weg (the former Karl -Marx StraBe) north of Wilhelm Pieck Allee, near Alter Markt. Non...27 69 Karl StraBe 4 D/W-6900 Heidelberg Telephone: +49 (6221) 54-3265 Telefax: +49 (6221) 54-3355 Akademie der Wissenschaften und der Literatur Mainz

Design and Analysis of Experiments and More Realistic Techniques for Data Analysis.

DTIC Science & Technology

1986-03-01

Schwarzschild 1974-79 (Ph.D. 1979) P. Slasor 1984-85 (still a graduate student) David E. Tyler 1974-75 (Ph.D. 1979) Paul Velleman 1973-1974 (Ph.D...Statistics: Proceedings of the 14th Symposium on the Interface, eds. Karl W. Heiner, Richard S. Sacher and John W. Wilkinson, Springer-Verlag, New York...Proceedings of the 14th Symposium on the Interface, eds. Karl W. Heiner, Richard S. Sacher and John W. Wilkinson, Springer-Verlag, New York, 60-66. Tukey, John

Two-Dimensional One-Component Plasma on Flamm's Paraboloid

NASA Astrophysics Data System (ADS)

Fantoni, Riccardo; Téllez, Gabriel

2008-11-01

We study the classical non-relativistic two-dimensional one-component plasma at Coulomb coupling Γ=2 on the Riemannian surface known as Flamm's paraboloid which is obtained from the spatial part of the Schwarzschild metric. At this special value of the coupling constant, the statistical mechanics of the system are exactly solvable analytically. The Helmholtz free energy asymptotic expansion for the large system has been found. The density of the plasma, in the thermodynamic limit, has been carefully studied in various situations.

The mirrors for the Extreme Ultraviolet Explorer

NASA Technical Reports Server (NTRS)

Finley, David S.; Green, James C.; Bowyer, Stuart; Malina, Roger F.

1986-01-01

Flight mirrors for the Extreme Ultraviolet Explorer satellite are currently under fabrication. The grazing incidence metal mirrors are Wolter-Schwarzschild Type I and II and are figured by diamond turning. Imaging performance is excellent, with the figure after polishing for the best mirror being such that the full width-half maximum is 1.0 arc seconds and the half energy width is 8 arc seconds measured at visible wavelengths. Surface finish, as determined from scattering measurements in the extreme ultraviolet, is about 20 A rms.

Riemann curvature of a boosted spacetime geometry

NASA Astrophysics Data System (ADS)

Battista, Emmanuele; Esposito, Giampiero; Scudellaro, Paolo; Tramontano, Francesco

2016-10-01

The ultrarelativistic boosting procedure had been applied in the literature to map the metric of Schwarzschild-de Sitter spacetime into a metric describing de Sitter spacetime plus a shock-wave singularity located on a null hypersurface. This paper evaluates the Riemann curvature tensor of the boosted Schwarzschild-de Sitter metric by means of numerical calculations, which make it possible to reach the ultrarelativistic regime gradually by letting the boost velocity approach the speed of light. Thus, for the first time in the literature, the singular limit of curvature, through Dirac’s δ distribution and its derivatives, is numerically evaluated for this class of spacetimes. Moreover, the analysis of the Kretschmann invariant and the geodesic equation shows that the spacetime possesses a “scalar curvature singularity” within a 3-sphere and it is possible to define what we here call “boosted horizon”, a sort of elastic wall where all particles are surprisingly pushed away, as numerical analysis demonstrates. This seems to suggest that such “boosted geometries” are ruled by a sort of “antigravity effect” since all geodesics seem to refuse to enter the “boosted horizon” and are “reflected” by it, even though their initial conditions are aimed at driving the particles toward the “boosted horizon” itself. Eventually, the equivalence with the coordinate shift method is invoked in order to demonstrate that all δ2 terms appearing in the Riemann curvature tensor give vanishing contribution in distributional sense.

The quantum emission spectra of rapidly-rotating Kerr black holes: Discrete or continuous?

NASA Astrophysics Data System (ADS)

Hod, Shahar

2015-10-01

Bekenstein and Mukhanov (BM) have suggested that, in a quantum theory of gravity, black holes may have discrete emission spectra. Using the time-energy uncertainty principle they have also shown that, for a (non-rotating) Schwarzschild black hole, the natural broadening δω of the black-hole emission lines is expected to be small on the scale set by the characteristic frequency spacing Δω of the spectral lines: ζSch ≡ δω / Δω ≪ 1. BM have therefore concluded that the expected discrete emission lines of the quantized Schwarzschild black hole are unlikely to overlap. In this paper we calculate the characteristic dimensionless ratio ζ (a bar) ≡ δω / Δω for the predicted BM emission spectra of rapidly-rotating Kerr black holes (here a bar ≡ J /M2 is the dimensionless angular momentum of the black hole). It is shown that ζ (a bar) is an increasing function of the black-hole angular momentum. In particular, we find that the quantum emission lines of Kerr black holes in the regime a bar ≳ 0.9 are characterized by the dimensionless ratio ζ (a bar) ≳ 1 and are therefore effectively blended together. Our results thus suggest that, even if the underlying mass (energy) spectrum of these rapidly-rotating Kerr black holes is fundamentally discrete as suggested by Bekenstein and Mukhanov, the natural broadening phenomenon (associated with the time-energy uncertainty principle) is expected to smear the black-hole radiation spectrum into a continuum.

Building a linear equation-of-state for trapped gravitons from finite size effects and the Schwarzschild black hole case

NASA Astrophysics Data System (ADS)

Viaggiu, Stefano

In this paper, we continue the investigations present in [S. Viaggiu, Physica A 473 (2017) 412; 488 (2017) 72.] concerning the spectrum of trapped gravitons in a spherical box, and in particular, inside a Schwarzschild black hole (BH). We explore the possibility that, due to finite size effects, the frequency of the radiation made of trapped gravitons can be modified in such a way that a linear equation-of-state PV = γU for the pressure P and the internal energy U arises. Firstly, we study the case with U ˜ R, where only fluids with γ > ‑1 3 are possible. If corrections ˜ 1/R are added to U, for γ ∈ [0, 1 3], we found no limitation on the allowed value for the areal radius of the trapped sphere R. Moreover, for γ > 1 3, we have a minimum allowed value for R of the order of the Planck length LP. Conversely, a fluid with P < 0 can be obtained but with a maximum allowed value for R. With the added term looking like ˜ 1/R to the BH internal energy U, the well-known logarithmic corrections to the BH entropy naturally emerge for any linear equation-of-state. The results of this paper suggest that finite size effects could modify the structure of graviton’s radiation inside, showing a possible mechanism to transform radiation into dark energy.

The EDGE-CALIFA survey: validating stellar dynamical mass models with CO kinematics

NASA Astrophysics Data System (ADS)

Leung, Gigi Y. C.; Leaman, Ryan; van de Ven, Glenn; Lyubenova, Mariya; Zhu, Ling; Bolatto, Alberto D.; Falcón-Barroso, Jesus; Blitz, Leo; Dannerbauer, Helmut; Fisher, David B.; Levy, Rebecca C.; Sanchez, Sebastian F.; Utomo, Dyas; Vogel, Stuart; Wong, Tony; Ziegler, Bodo

2018-06-01

Deriving circular velocities of galaxies from stellar kinematics can provide an estimate of their total dynamical mass, provided a contribution from the velocity dispersion of the stars is taken into account. Molecular gas (e.g. CO), on the other hand, is a dynamically cold tracer and hence acts as an independent circular velocity estimate without needing such a correction. In this paper, we test the underlying assumptions of three commonly used dynamical models, deriving circular velocities from stellar kinematics of 54 galaxies (S0-Sd) that have observations of both stellar kinematics from the Calar Alto Legacy Integral Field Area (CALIFA) survey, and CO kinematics from the Extragalactic Database for Galaxy Evolution (EDGE) survey. We test the asymmetric drift correction (ADC) method, as well as Jeans, and Schwarzschild models. The three methods each reproduce the CO circular velocity at 1Re to within 10 per cent. All three methods show larger scatter (up to 20 per cent) in the inner regions (R < 0.4Re) that may be due to an increasingly spherical mass distribution (which is not captured by the thin disc assumption in ADC), or non-constant stellar M/L ratios (for both the JAM and Schwarzschild models). This homogeneous analysis of stellar and gaseous kinematics validates that all three models can recover Mdyn at 1Re to better than 20 per cent, but users should be mindful of scatter in the inner regions where some assumptions may break down.

Uncertainty relation in Schwarzschild spacetime

NASA Astrophysics Data System (ADS)

Feng, Jun; Zhang, Yao-Zhong; Gould, Mark D.; Fan, Heng

2015-04-01

We explore the entropic uncertainty relation in the curved background outside a Schwarzschild black hole, and find that Hawking radiation introduces a nontrivial modification on the uncertainty bound for particular observer, therefore it could be witnessed by proper uncertainty game experimentally. We first investigate an uncertainty game between a free falling observer and his static partner holding a quantum memory initially entangled with the quantum system to be measured. Due to the information loss from Hawking decoherence, we find an inevitable increase of the uncertainty on the outcome of measurements in the view of static observer, which is dependent on the mass of the black hole, the distance of observer from event horizon, and the mode frequency of quantum memory. To illustrate the generality of this paradigm, we relate the entropic uncertainty bound with other uncertainty probe, e.g., time-energy uncertainty. In an alternative game between two static players, we show that quantum information of qubit can be transferred to quantum memory through a bath of fluctuating quantum fields outside the black hole. For a particular choice of initial state, we show that the Hawking decoherence cannot counteract entanglement generation after the dynamical evolution of system, which triggers an effectively reduced uncertainty bound that violates the intrinsic limit -log2 ⁡ c. Numerically estimation for a proper choice of initial state shows that our result is comparable with possible real experiments. Finally, a discussion on the black hole firewall paradox in the context of entropic uncertainty relation is given.

Holographic entanglement entropies for Schwarzschild and Reisner-Nordström black holes in asymptotically Minkowski spacetimes

NASA Astrophysics Data System (ADS)

Sun, Yuan; Zhao, Liu

2017-04-01

Holographic entanglement entropies (HEE) associated with four-dimensional Schwarzschild and Reisner-Nordström (RN) black holes in asymptotically Minkowski spacetimes are investigated. Unlike the cases of asymptotically AdS spacetimes for which the boundaries are always taken at (timelike) conformal infinities, we take the boundaries at either large but finite radial coordinates (far boundary) or very close to the black hole event horizons (near horizon boundary). The reason for such choices is that such boundaries are similar to the conformal infinity of AdS spacetime in that they are all timelike, so that there may be some hope to define dual systems with ordinary time evolution on such boundaries. Our results indicate that, in the case of far boundaries, the leading-order contribution to HEEs comes from the background Minkowski spacetime; however, the next-to-leading-order contribution which arises from the presence of the black holes is always proportional to the black hole mass, which constitutes a version of the first law of HEE for asymptotically flat spacetimes, and the higher-order contributions are always negligibly small. In the case of near horizon boundaries, the leading-order contribution to HEE is always proportional to the area of the black hole event horizon, and the case of extremal RN black holes is distinguished from the cases of nonextremal black holes in that the minimal surface defining HEE is completely immersed inside the boundary up to the second order in the perturbative expansion.

Finding Coefficients of the Full Array of Motion-Independent N-Body Potentials of Metric Gravity from Gravity's Exterior and Interior Effacement Algebra

NASA Astrophysics Data System (ADS)

Nordtvedt, Kenneth

2018-01-01

In the author's previous publications, a recursive linear algebraic method was introduced for obtaining (without gravitational radiation) the full potential expansions for the gravitational metric field components and the Lagrangian for a general N-body system. Two apparent properties of gravity— Exterior Effacement and Interior Effacement—were defined and fully enforced to obtain the recursive algebra, especially for the motion-independent potential expansions of the general N-body situation. The linear algebraic equations of this method determine the potential coefficients at any order n of the expansions in terms of the lower-order coefficients. Then, enforcing Exterior and Interior Effacement on a selecedt few potential series of the full motion-independent potential expansions, the complete exterior metric field for a single, spherically-symmetric mass source was obtained, producing the Schwarzschild metric field of general relativity. In this fourth paper of this series, the complete spatial metric's motion-independent potentials for N bodies are obtained using enforcement of Interior Effacement and knowledge of the Schwarzschild potentials. From the full spatial metric, the complete set of temporal metric potentials and Lagrangian potentials in the motion-independent case can then be found by transfer equations among the coefficients κ( n, α) → λ( n, ɛ) → ξ( n, α) with κ( n, α), λ( n, ɛ), ξ( n, α) being the numerical coefficients in the spatial metric, the Lagrangian, and the temporal metric potential expansions, respectively.

Chaos in matrix models and black hole evaporation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berkowitz, Evan; Hanada, Masanori; Maltz, Jonathan

Is the evaporation of a black hole described by a unitary theory? In order to shed light on this question—especially aspects of this question such as a black hole’s negative specific heat—we consider the real-time dynamics of a solitonic object in matrix quantum mechanics, which can be interpreted as a black hole (black zero-brane) via holography. We point out that the chaotic nature of the system combined with the flat directions of its potential naturally leads to the emission of D0-branes from the black brane, which is suppressed in the large N limit. Simple arguments show that the black zero-brane,more » like the Schwarzschild black hole, has negative specific heat, in the sense that the temperature goes up when it evaporates by emitting D0-branes. While the largest Lyapunov exponent grows during the evaporation, the Kolmogorov-Sinai entropy decreases. These are consequences of the generic properties of matrix models and gauge theory. Based on these results, we give a possible geometric interpretation of the eigenvalue distribution of matrices in terms of gravity. Applying the same argument in the M-theory parameter region, we provide a scenario to derive the Hawking radiation of massless particles from the Schwarzschild black hole. In conclusion, we suggest that by adding a fraction of the quantum effects to the classical theory, we can obtain a matrix model whose classical time evolution mimics the entire life of the black brane, from its formation to the evaporation.« less

Chaos in matrix models and black hole evaporation

DOE PAGES

Berkowitz, Evan; Hanada, Masanori; Maltz, Jonathan

2016-12-19

Is the evaporation of a black hole described by a unitary theory? In order to shed light on this question—especially aspects of this question such as a black hole’s negative specific heat—we consider the real-time dynamics of a solitonic object in matrix quantum mechanics, which can be interpreted as a black hole (black zero-brane) via holography. We point out that the chaotic nature of the system combined with the flat directions of its potential naturally leads to the emission of D0-branes from the black brane, which is suppressed in the large N limit. Simple arguments show that the black zero-brane,more » like the Schwarzschild black hole, has negative specific heat, in the sense that the temperature goes up when it evaporates by emitting D0-branes. While the largest Lyapunov exponent grows during the evaporation, the Kolmogorov-Sinai entropy decreases. These are consequences of the generic properties of matrix models and gauge theory. Based on these results, we give a possible geometric interpretation of the eigenvalue distribution of matrices in terms of gravity. Applying the same argument in the M-theory parameter region, we provide a scenario to derive the Hawking radiation of massless particles from the Schwarzschild black hole. In conclusion, we suggest that by adding a fraction of the quantum effects to the classical theory, we can obtain a matrix model whose classical time evolution mimics the entire life of the black brane, from its formation to the evaporation.« less

Two approaches for the gravitational self-force in black hole spacetime: Comparison of numerical results

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sago, Norichika; Barack, Leor; Detweiler, Steven

2008-12-15

Recently, two independent calculations have been presented of finite-mass ('self-force') effects on the orbit of a point mass around a Schwarzschild black hole. While both computations are based on the standard mode-sum method, they differ in several technical aspects, which makes comparison between their results difficult--but also interesting. Barack and Sago [Phys. Rev. D 75, 064021 (2007)] invoke the notion of a self-accelerated motion in a background spacetime, and perform a direct calculation of the local self-force in the Lorenz gauge (using numerical evolution of the perturbation equations in the time domain); Detweiler [Phys. Rev. D 77, 124026 (2008)] describesmore » the motion in terms a geodesic orbit of a (smooth) perturbed spacetime, and calculates the metric perturbation in the Regge-Wheeler gauge (using frequency-domain numerical analysis). Here we establish a formal correspondence between the two analyses, and demonstrate the consistency of their numerical results. Specifically, we compare the value of the conservative O({mu}) shift in u{sup t} (where {mu} is the particle's mass and u{sup t} is the Schwarzschild t component of the particle's four-velocity), suitably mapped between the two orbital descriptions and adjusted for gauge. We find that the two analyses yield the same value for this shift within mere fractional differences of {approx}10{sup -5}-10{sup -7} (depending on the orbital radius)--comparable with the estimated numerical error.« less

Orbital decomposition of CALIFA spiral galaxies

NASA Astrophysics Data System (ADS)

Zhu, Ling; van den Bosch, Remco; van de Ven, Glenn; Lyubenova, Mariya; Falcón-Barroso, Jesús; Meidt, Sharon E.; Martig, Marie; Shen, Juntai; Li, Zhao-Yu; Yildirim, Akin; Walcher, C. Jakob; Sanchez, Sebastian F.

2018-01-01

Schwarzschild orbit-based dynamical models are widely used to uncover the internal dynamics of early-type galaxies and globular clusters. Here we present for the first time the Schwarzschild models of late-type galaxies: an SBb galaxy NGC 4210 and an S0 galaxy NGC 6278 from the Calar Alto Legacy Integral Field Area (CALIFA) survey. The mass profiles within 2Re are constrained well with 1σ statistical error of ∼ 10 per cent. The luminous and dark mass can be disentangled with uncertainties of ∼20 and ∼ 50 per cent, respectively. From Re to 2Re, the dark matter fraction increases from 14 ± 10 to 18 ± 10 per cent for NGC 4210 and from 15 ± 10 to 30 ± 20 per cent for NGC 6278. The velocity anisotropy profiles of both σr/σt and σz/σR are well constrained. The inferred internal orbital distributions reveal clear substructures. The orbits are naturally separated into three components: a cold component with near circular orbits; a hot component with near radial orbits and a warm component in between. The photometrically identified exponential discs are predominantly made up of cold orbits only beyond ∼1Re, while they are constructed mainly with the warm orbits inside. Our dynamical hot components are concentrated in the inner regions, similar to the photometrically identified bulges. The reliability of the results, especially the orbit distribution, is verified by applying the model to mock data.

Newton's absolute time and space in general relativity

NASA Astrophysics Data System (ADS)

Gautreau, Ronald

2000-04-01

I describe a reference system in a spherically symmetric gravitational field that is built around times recorded by radially moving geodesic clocks. The geodesic time coordinate t and the curvature spatial radial coordinate R result in spacetime descriptions of the motion of the geodesic clocks that are exactly identical with equations following from Newton's absolute time and space used with his inverse square law. I show how to use the resulting Newtonian/general-relativistic equations for geodesic clocks to generate exact relativistic metric forms in terms of the coordinates (R,t). Newtonian theory does not describe light. However, the motion of light can be determined from the (R,t) general-relativistic metric forms obtained from Newtonian theory by setting ds2(R,t)=0. In this sense, a theory of light can be related to absolute time and space of Newtonian gravitational theory. I illustrate the (R,t) methodology by first solving the equations that result from a Newtonian picture and then examining the exact metric forms for the general-relativistic problems of the Schwarzschild field, gravitational collapse and expansion of a zero-pressure perfect fluid, and zero-pressure big-bang cosmology. I also briefly describe other applications of the Newtonian/general-relativistic formulation to: embedding a Schwarzschild mass into cosmology; continuously following an expanding universe from radiation to matter domination; Dirac's Large Numbers hypothesis; the incompleteness of Kruskal-Szekeres spacetime; double valuedness in cosmology; and the de Sitter universe.

Reading BEA II in Irvine (And Elsewhere)

NASA Astrophysics Data System (ADS)

Trimble, Virginia L.

2017-01-01

It is just possible that the number of BEA authors and editors exceeds the number of its readers, but I doubt this, having done all three. Perhaps unusually, I have gone through each edition page by page: BEA I several years ago, looking for what everybody who was alive at the time did during World War I, and BEA II just recently, in the process of compiling potted history of the development of stellar astronomy and astrophysics in Germany. Neither task would have been possible without BEA, which I therefore celebrate, along with Tom Hockey's enormous foresight, energy, and persistence. If we were starting over, I (and probably he!) would ask authors and editors for at least two things -- closer adherence to a format that puts the most notable work (why this person is here!) first, followed by "life" and "works" - and, where the information is available, what the person did or had happen that must surely have influenced life, beliefs, philosophy, what haveyou, beyond the scientific achievements. We know what Einstein, Karl Schwarzschild, and Rudolph Minkowski were doing in 1916, while a number of other articles have holes about that time. And it is obvious why Martin Schwarzschild and Hans Bethe ceased to be German astronomers; not so obvious for others. And, while we are at it, what turned von Weizsäcker and Albert Wilson so firmly away from the science in which they had already left large footprints?

Black branes and black strings in the astrophysical and cosmological context

NASA Astrophysics Data System (ADS)

Akarsu, Özgür; Chopovsky, Alexey; Zhuk, Alexander

2018-03-01

We consider Kaluza-Klein models where internal spaces are compact flat or curved Einstein spaces. This background is perturbed by a compact gravitating body with the dust-like equation of state (EoS) in the external/our space and an arbitrary EoS parameter Ω in the internal space. Without imposing any restrictions on the form of the perturbed metric and the distribution of the perturbed energy densities, we perform the general analysis of the Einstein and conservation equations in the weak-field limit. All conclusions follow from this analysis. For example, we demonstrate that the perturbed model is static and perturbed metric preserves the block-diagonal form. In a particular case Ω = - 1 / 2, the found solution corresponds to the weak-field limit of the black strings/branes. The black strings/branes are compact gravitating objects which have the topology (four-dimensional Schwarzschild spacetime) × (d-dimensional internal space) with d ≥ 1. We present the arguments in favour of these objects. First, they satisfy the gravitational tests for the parameterized post-Newtonian parameter γ at the same level of accuracy as General Relativity. Second, they are preferable from the thermodynamical point of view. Third, averaging over the Universe, they do not destroy the stabilization of the internal space. These are the astrophysical and cosmological aspects of the black strings/branes.

GARLIC - A general purpose atmospheric radiative transfer line-by-line infrared-microwave code: Implementation and evaluation

NASA Astrophysics Data System (ADS)

Schreier, Franz; Gimeno García, Sebastián; Hedelt, Pascal; Hess, Michael; Mendrok, Jana; Vasquez, Mayte; Xu, Jian

2014-04-01

A suite of programs for high resolution infrared-microwave atmospheric radiative transfer modeling has been developed with emphasis on efficient and reliable numerical algorithms and a modular approach appropriate for simulation and/or retrieval in a variety of applications. The Generic Atmospheric Radiation Line-by-line Infrared Code - GARLIC - is suitable for arbitrary observation geometry, instrumental field-of-view, and line shape. The core of GARLIC's subroutines constitutes the basis of forward models used to implement inversion codes to retrieve atmospheric state parameters from limb and nadir sounding instruments. This paper briefly introduces the physical and mathematical basics of GARLIC and its descendants and continues with an in-depth presentation of various implementation aspects: An optimized Voigt function algorithm combined with a two-grid approach is used to accelerate the line-by-line modeling of molecular cross sections; various quadrature methods are implemented to evaluate the Schwarzschild and Beer integrals; and Jacobians, i.e. derivatives with respect to the unknowns of the atmospheric inverse problem, are implemented by means of automatic differentiation. For an assessment of GARLIC's performance, a comparison of the quadrature methods for solution of the path integral is provided. Verification and validation are demonstrated using intercomparisons with other line-by-line codes and comparisons of synthetic spectra with spectra observed on Earth and from Venus.

Stability of Horndeski vector-tensor interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiménez, Jose Beltrán; Durrer, Ruth; Heisenberg, Lavinia

2013-10-01

We study the Horndeski vector-tensor theory that leads to second order equations of motion and contains a non-minimally coupled abelian gauge vector field. This theory is remarkably simple and consists of only 2 terms for the vector field, namely: the standard Maxwell kinetic term and a coupling to the dual Riemann tensor. Furthermore, the vector sector respects the U(1) gauge symmetry and the theory contains only one free parameter, M{sup 2}, that controls the strength of the non-minimal coupling. We explore the theory in a de Sitter spacetime and study the presence of instabilities and show that it corresponds tomore » an attractor solution in the presence of the vector field. We also investigate the cosmological evolution and stability of perturbations in a general FLRW spacetime. We find that a sufficient condition for the absence of ghosts is M{sup 2} > 0. Moreover, we study further constraints coming from imposing the absence of Laplacian instabilities. Finally, we study the stability of the theory in static and spherically symmetric backgrounds (in particular, Schwarzschild and Reissner-Nordström-de Sitter). We find that the theory, quite generally, do have ghosts or Laplacian instabilities in regions of spacetime where the non-minimal interaction dominates over the Maxwell term. We also calculate the propagation speed in these spacetimes and show that superluminality is a quite generic phenomenon in this theory.« less

Quasinormal acoustic oscillations in the Michel flow

NASA Astrophysics Data System (ADS)

Chaverra, Eliana; Morales, Manuel D.; Sarbach, Olivier

2015-05-01

We study spherical and nonspherical linear acoustic perturbations of the Michel flow, which describes the steady radial accretion of a perfect fluid into a nonrotating black hole. The dynamics of such perturbations are governed by a scalar wave equation on an effective curved background geometry determined by the acoustic metric, which is constructed from the spacetime metric and the particle density and four-velocity of the fluid. For the problem under consideration in this paper the acoustic metric has the same qualitative features as an asymptotically flat, static and spherically symmetric black hole, and thus it represents a natural astrophysical analogue black hole. As for the case of a scalar field propagating on a Schwarzschild background, we show that acoustic perturbations of the Michel flow exhibit quasinormal oscillations. Based on a new numerical method for determining the solutions of the radial mode equation, we compute the associated frequencies and analyze their dependency on the mass of the black hole, the radius of the sonic horizon and the angular momentum number. Our results for the fundamental frequencies are compared to those obtained from an independent numerical Cauchy evolution, finding good agreement between the two approaches. When the radius of the sonic horizon is large compared to the event horizon radius, we find that the quasinormal frequencies scale approximately like the surface gravity associated with the sonic horizon.

Karl Schwarzschild Lecture: The Ups and Downs of the Hubble Constant (With 12 Figures)

NASA Astrophysics Data System (ADS)

Tammann, G. Andreas

2006-01-01

A brief history of the determination of the Hubble constant H_0 is given. Early attempts following Lemaitre (1927) gave much too high values due to errors of the magnitude scale, Malmquist bias and calibration problems. By 1962 most authors agreed that 75< H_0 <130. After 1975 a dichotomy arose with values near 100 and others around 55. The former came from apparent-magnitude-limited samples and were affected by Malmquist bias. New distance indicators were introduced; they were sometimes claimed to yield high values of H_0, but the most recent data lead to H_0 in the 60's, yet with remaining difficulties as to the zero-point of the respective distance indicators. SNe Ia with their large range and very small luminosity dispersion (avoiding Malmquist bias) offer a unique opportunity to determine the large-scale value of H_0. Their maximum luminosity can be well calibrated from 10 SNe Ia in local parent galaxies whose Cepheids have been observed with HST. An unforeseen difficulty - affecting all Cepheid distances - is that their P-L relation varies from galaxy to galaxy, presumably in function of metallicity. A proposed solution is summarized here. The conclusion is that H_0 = 63.2 +/- 1.3 (random) +/- 5.3 (systematic) on all scales. The expansion age becomes then (with Omega_m=0.3, Omega_Lambda=0.7) 15.1 Gyr.

Multiple shadows from distorted static black holes

NASA Astrophysics Data System (ADS)

Grover, Jai; Kunz, Jutta; Nedkova, Petya; Wittig, Alexander; Yazadjiev, Stoytcho

2018-04-01

We study the local shadow of the Schwarzschild black hole with a quadrupole distortion and the influence of the external gravitational field on the photon dynamics. The external matter sources modify the light ring structure and lead to the appearance of multiple shadow images. In the case of negative quadrupole moments we identify the most prominent mechanism causing multiple shadow formation. Furthermore, we obtain a condition under which this mechanism can be realized. This condition depends on the quadrupole moment, but also on the position of the observer and the celestial sphere.

Relativistic Positioning Systems and Gravitational Perturbations

NASA Astrophysics Data System (ADS)

Gomboc, Andreja; Kostić, Uroš; Horvat, Martin; Carloni, Sante; Delva, Pacôme

2013-11-01

In order to deliver a high accuracy relativistic positioning system, several gravitational perturbations need to be taken into account. We therefore consider a system of satellites, such as the Galileo system, in a space-time described by a background Schwarzschild metric and small gravitational perturbations due to the Earth’s rotation, multipoles and tides, and the gravity of the Moon, the Sun, and planets. We present the status of this work currently carried out in the ESA Slovenian PECS project Relativistic Global Navigation System, give the explicit expressions for the perturbed metric, and briefly outline further steps.

Design of an imaging microscope for soft X-ray applications

NASA Astrophysics Data System (ADS)

Hoover, Richard B.; Shealy, David L.; Gabardi, David R.; Walker, Arthur B. C., Jr.; Lindblom, Joakim F.

1988-01-01

An imaging soft X-ray microscope with a spatial resolution of 0.1 micron and normal incidence multilayer optics is discussed. The microscope has a Schwarzschild configuration, which consists of two concentric spherical mirrors with radii of curvature which minimize third-order spherical aberration, coma, and astigmatism. The performance of the Stanford/MSFC Cassegrain X-ray telescope and its relevance to the present microscope are addressed. A ray tracing analysis of the optical system indicates that diffraction-limited performance can be expected for an object height of 0.2 mm.

Black hole evaporation in conformal gravity

NASA Astrophysics Data System (ADS)

Bambi, Cosimo; Modesto, Leonardo; Porey, Shiladitya; Rachwał, Lesław

2017-09-01

We study the formation and the evaporation of a spherically symmetric black hole in conformal gravity. From the collapse of a spherically symmetric thin shell of radiation, we find a singularity-free non-rotating black hole. This black hole has the same Hawking temperature as a Schwarzschild black hole with the same mass, and it completely evaporates either in a finite or in an infinite time, depending on the ensemble. We consider the analysis both in the canonical and in the micro-canonical statistical ensembles. Last, we discuss the corresponding Penrose diagram of this physical process.

The Gamma-ray Cherenkov Telescope, an end-to end Schwarzschild-Couder telescope prototype proposed for the Cherenkov Telescope Array

NASA Astrophysics Data System (ADS)

Dournaux, J. L.; Abchiche, A.; Allan, D.; Amans, J. P.; Armstrong, T. P.; Balzer, A.; Berge, D.; Boisson, C.; Bousquet, J.-J.; Brown, A. M.; Bryan, M.; Buchholtz, G.; Chadwick, P. M.; Costantini, H.; Cotter, G.; Dangeon, L.; Daniel, M. K.; De Franco, A.; De Frondat, F.; Dumas, D.; Ernenwein, J. P.; Fasola, G.; Funk, S.; Gironnet, J.; Graham, J. A.; Greenshaw, T.; Hameau, B.; Hervet, O.; Hidaka, N.; Hinton, J. A.; Huet, J. M.; Jégouzo, I.; Jogler, T.; Kawashima, T.; Kraush, M.; Lapington, J. S.; Laporte, P.; Lefaucheur, J.; Markoff, S.; Melse, T.; Mohrmann, L.; Molyneux, P.; Nolan, S. J.; Okumura, A.; Osborne, J. P.; Parsons, R. D.; Rosen, S.; Ross, D.; Rowell, G.; Rulten, C. B.; Sato, Y.; Sayède, F.; Schmoll, J.; Schoorlemmer, H.; Servillat, M.; Sol, H.; Stamatescu, V.; Stephan, M.; Stuik, R.; Sykes, J.; Tajima, H.; Thornhill, J.; Tibaldo, L.; Trichard, C.; Vink, J.; Watson, J. J.; White, R.; Yamane, N.; Zech, A.; Zink, A.

2016-08-01

The GCT (Gamma-ray Cherenkov Telescope) is a dual-mirror prototype of Small-Sized-Telescopes proposed for the Cherenkov Telescope Array (CTA) and made by an Australian-Dutch-French-German-Indian-Japanese-UK-US consortium. The integration of this end-to-end telescope was achieved in 2015. On-site tests and measurements of the first Cherenkov images on the night sky began on November 2015. This contribution describes the telescope and plans for the pre-production and a large scale production within CTA.

On the pattern of black hole information release

NASA Astrophysics Data System (ADS)

Park, I. Y.; James, F.

2014-03-01

We propose a step towards a resolution to black hole information paradox by analyzing scattering amplitudes of a complex scalar field around a Schwarzschild black hole. The scattering cross-section reveals much information on the incoming state but exhibits flux loss at the same time. The flux loss should be temporary, and indicate mass growth of the black hole. The black hole should Hawking-radiate subsequently, thereby, compensating for the flux loss. By examining the purity issue, we comment on the possibility that information bleaching may be the key to the paradox.

The time delay in strong gravitational lensing with Gauss-Bonnet correction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Man, Jingyun; Cheng, Hongbo, E-mail: jingyunman@mail.ecust.edu.cn, E-mail: hbcheng@ecust.edu.cn

2014-11-01

The time delay between two relativistic images in the strong gravitational lensing governed by Gauss-Bonnet gravity is studied. We make a complete analytical derivation of the expression of time delay in presence of Gauss-Bonnet coupling. With respect to Schwarzschild, the time delay decreases as a consequence of the shrinking of the photon sphere. As the coupling increases, the second term in the time delay expansion becomes more relevant. Thus time delay in strong limit encodes some new information about geometry in five-dimensional spacetime with Gauss-Bonnet correction.

Black hole evaporation in conformal gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bambi, Cosimo; Rachwał, Lesław; Modesto, Leonardo

We study the formation and the evaporation of a spherically symmetric black hole in conformal gravity. From the collapse of a spherically symmetric thin shell of radiation, we find a singularity-free non-rotating black hole. This black hole has the same Hawking temperature as a Schwarzschild black hole with the same mass, and it completely evaporates either in a finite or in an infinite time, depending on the ensemble. We consider the analysis both in the canonical and in the micro-canonical statistical ensembles. Last, we discuss the corresponding Penrose diagram of this physical process.

Strong lensing of a regular black hole with an electrodynamics source

NASA Astrophysics Data System (ADS)

Manna, Tuhina; Rahaman, Farook; Molla, Sabiruddin; Bhadra, Jhumpa; Shah, Hasrat Hussain

2018-05-01

In this paper we have investigated the gravitational lensing phenomenon in the strong field regime for a regular, charged, static black holes with non-linear electrodynamics source. We have obtained the angle of deflection and compared it to a Schwarzschild black hole and Reissner Nordström black hole with similar properties. We have also done a graphical study of the relativistic image positions and magnifications. We hope that this method may be useful in the detection of non-luminous bodies like this current black hole.

Research Investigation Directed Toward Extending the Useful Range of the Electromagnetic Spectrum.

DTIC Science & Technology

1985-12-31

0.33) or a Schwarzschild reflector (N.A. ..- - 1.25, x 36) directly onto the GaAs (100) substrate housed in a stainless steel, 4-window cell. The cell...Department of Energy under contract .. DE-AC-02-78ER04940. (1) G. Karl , P. Kruus and J. Polanyl, J. Chem. Phys. 46,224, (1967). .- (2) G. Karl , P. Kruus, J...Chem. 39, 2244, (1961). (7) G. Karl and J. Polanyl, J. Chem Phys. 38, 271, (1963). (8) H. Okabe, Photochemistrv-of Small Molecules, New York, J

Workshop on Repetitive Opening Switches, held 28-30 January 1981, Tamarron, Colorado

DTIC Science & Technology

1981-04-20

have to be clever experimentalists and try out our ideas, such as the laser diverter described in t-he next paper by Karl Schoenbach. Thank you. :1 63...34Kinetics of E-Beam Ex- cited XeCL," 33rd Gaseous Electronics Conf., Univ of Oklahoma, Oct. 1980, Abstract FB-3. 10. M. Kruskal, M. Schwarzschild , Proc. hcy...International 1si0 e Rear 2700 Merced Street 10 15a3o San Leandro, CA 94577 Pittsburgh, PA 15235 ,415/357-4610 412/256-7552 . -Kr~stiansen Karl Freytag E

Entropy in the interior of a higher-dimensional black hole

NASA Astrophysics Data System (ADS)

Yang, Jian-Zhi; Liu, Wen-Biao

2018-07-01

Recently Christodoulou and Rovelli brought out a sensible description for the black hole volume as the largest volume. Later the entropy related to this volume in a 4-dimensional Schwarzschild black hole was investigated, which showed that such entropy is proportional to the surface area of the black hole. We will probe into these issues in the context of higher-dimensional case. It is found that the proportion between this entropy and the Bekenstein-Hawking entropy will go down through dramatic change along with the increase of spacetime dimension.

Surface evaluation of the grazing incidence mirrors for the Extreme Ultraviolet Explorer

NASA Technical Reports Server (NTRS)

Green, James; Finley, David S.; Bowyer, Stuart; Malina, Roger F.

1987-01-01

The EUV scattering from the Wolter-Schwarzschild type I short wavelength scanner mirror aboard the Extreme Ultraviolet Explorer is measured, and the results are used to evaluate the surface microroughness of the mirror. It is found that the most likely values for the mirror surface are sigma = 20 A, and rho = 40 microns. These results are consistent with previous estimates, but with a higher degree of certainty. The full-scale simulation presented here allows over 99 percent of the light distribution to be reasonably modeled.

Self-force calculations with matched expansions and quasinormal mode sums

DOE Office of Scientific and Technical Information (OSTI.GOV)

Casals, Marc; Dolan, Sam; Ottewill, Adrian C.

2009-06-15

Accurate modeling of gravitational wave emission by extreme-mass ratio inspirals is essential for their detection by the LISA mission. A leading perturbative approach involves the calculation of the self-force acting upon the smaller orbital body. In this work, we present the first application of the Poisson-Wiseman-Anderson method of 'matched expansions' to compute the self-force acting on a point particle moving in a curved spacetime. The method employs two expansions for the Green function, which are, respectively, valid in the 'quasilocal' and 'distant past' regimes, and which may be matched together within the normal neighborhood. We perform our calculation in amore » static region of the spherically symmetric Nariai spacetime (dS{sub 2}xS{sup 2}), in which scalar-field perturbations are governed by a radial equation with a Poeschl-Teller potential (frequently used as an approximation to the Schwarzschild radial potential) whose solutions are known in closed form. The key new ingredients in our study are (i) very high order quasilocal expansions and (ii) expansion of the distant past Green function in quasinormal modes. In combination, these tools enable a detailed study of the properties of the scalar-field Green function. We demonstrate that the Green function is singular whenever x and x{sup '} are connected by a null geodesic, and apply asymptotic methods to determine the structure of the Green function near the null wave front. We show that the singular part of the Green function undergoes a transition each time the null wave front passes through a caustic point, following a repeating fourfold sequence {delta}({sigma}), 1/{pi}{sigma}, -{delta}({sigma}), -1/{pi}{sigma}, etc., where {sigma} is Synge's world function. The matched-expansion method provides insight into the nonlocal properties of the self-force. We show that the self-force generated by the segment of the worldline lying outside the normal neighborhood is not negligible. We apply the matched-expansion method to compute the scalar self-force acting on a static particle on the Nariai spacetime, and validate against an alternative method, obtaining agreement to six decimal places. We conclude with a discussion of the implications for wave propagation and self-force calculations. On black hole spacetimes, any expansion of the Green function in quasinormal modes must be augmented by a branch-cut integral. Nevertheless, we expect the Green function in Schwarzschild spacetime to inherit certain key features, such as a fourfold singular structure manifesting itself through the asymptotic behavior of quasinormal modes. In this way, the Nariai spacetime provides a fertile testing ground for developing insight into the nonlocal part of the self-force on black hole spacetimes.« less

The variability of accretion on to Schwarzschild black holes from turbulent magnetized discs

NASA Astrophysics Data System (ADS)

Armitage, Philip J.; Reynolds, Christopher S.

2003-05-01

We use global magnetohydrodynamic simulations, in a pseudo-Newtonian potential, to investigate the temporal variability of accretion discs around Schwarzschild black holes. We use the vertically averaged magnetic stress in the simulated disc as a proxy for the rest-frame dissipation, and compute the observed emission by folding this through the transfer function describing the relativistic beaming, light bending and time delays near a non-rotating black hole. The temporal power spectrum of the predicted emission from individual annuli in the disc is described by a broken power law, with indices of ~-3.5 at high frequency and ~0 to -1 at low frequency. Integrated over the disc, the power spectrum is approximated by a single power law with an index of -2. Increasing inclination boosts the relative power at frequencies around ~0.3fms, where fms is the orbital frequency at the marginally stable orbit, but no evidence is found for sharp quasi-periodic oscillations in the light curve. Assuming that fluorescent iron line emission locally tracks the continuum flux, we compute simulated broad iron line profiles. We find that relativistic beaming of the non-axisymmetric emission profile, induced by turbulence, produces high-amplitude variability in the iron line profile. We show that this substructure within the broad iron line profile can survive averaging over a number of orbital periods, and discuss the origin of the anomalous X-ray spectral features, recently reported by Turner et al. for the Seyfert galaxy NGC 3516, in the context of turbulent disc models.

A Clue to the Extent of Convective Mixing Inside Massive Stars: The Surface Hydrogen Abundances of Luminous Blue Variables and Hydrogen-Poor Wolf-Rayet Stars

NASA Technical Reports Server (NTRS)

Stothers, Richard B.; Chin, Chao-wen

1999-01-01

Interior layers of stars that have been exposed by surface mass loss reveal aspects of their chemical and convective histories that are otherwise inaccessible to observation. It must be significant that the surface hydrogen abundances of luminous blue variables (LBVs) show a remarkable uniformity, specifically X(sub surf) = 0.3 - 0.4, while those of hydrogen-poor Wolf-Rayet (WN) stars fall, almost without exception, below these values, ranging down to X(sub surf) = 0. According to our stellar model calculations, most LBVs are post-red-supergiant objects in a late blue phase of dynamical instability, and most hydrogen-poor WN stars are their immediate descendants. If this is so, stellar models constructed with the Schwarzschild (temperature-gradient) criterion for convection account well for the observed hydrogen abundances, whereas models built with the Ledoux (density-gradient) criterion fail. At the brightest luminosities, the observed hydrogen abundances of LBVs are too large to be explained by any of our highly evolved stellar models, but these LBVs may occupy transient blue loops that exist during an earlier phase of dynamical instability when the star first becomes a yellow supergiant. Independent evidence concerning the criterion for convection, which is based mostly on traditional color distributions of less massive supergiants on the Hertzsprung-Russell diagram, tends to favor the Ledoux criterion. It is quite possible that the true criterion for convection changes over from something like the Ledoux criterion to something like the Schwarzschild criterion as the stellar mass increases.

The statistical mechanics of relativistic orbits around a massive black hole

NASA Astrophysics Data System (ADS)

Bar-Or, Ben; Alexander, Tal

2014-12-01

Stars around a massive black hole (MBH) move on nearly fixed Keplerian orbits, in a centrally-dominated potential. The random fluctuations of the discrete stellar background cause small potential perturbations, which accelerate the evolution of orbital angular momentum by resonant relaxation. This drives many phenomena near MBHs, such as extreme mass-ratio gravitational wave inspirals, the warping of accretion disks, and the formation of exotic stellar populations. We present here a formal statistical mechanics framework to analyze such systems, where the background potential is described as a correlated Gaussian noise. We derive the leading order, phase-averaged 3D stochastic Hamiltonian equations of motion, for evolving the orbital elements of a test star, and obtain the effective Fokker-Planck equation for a general correlated Gaussian noise, for evolving the stellar distribution function. We show that the evolution of angular momentum depends critically on the temporal smoothness of the background potential fluctuations. Smooth noise has a maximal variability frequency {{ν }max }. We show that in the presence of such noise, the evolution of the normalized angular momentum j=\\sqrt{1-{{e}2}} of a relativistic test star, undergoing Schwarzschild (in-plane) general relativistic precession with frequency {{ν }GR}/{{j}2}, is exponentially suppressed for j\\lt {{j}b}, where {{ν }GR}/jb2˜ {{ν }max }, due to the adiabatic invariance of the precession against the slowly varying random background torques. This results in an effective Schwarzschild precession-induced barrier in angular momentum. When jb is large enough, this barrier can have significant dynamical implications for processes near the MBH.

How the Hawking radiation affect quantum Fisher information of Dirac particles in the background of a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Huang, ChunYu; Ma, Wen-chao; Wang, Dong; Ye, Liu

2018-01-01

In this work, the effect of Hawking radiation on the quantum Fisher information (QFI) of Dirac particles is investigated in the background of a Schwarzschild black hole. Interestingly, it has been verified that the QFI with respect to the weight parameter θ of a target state is always independent of the Hawking temperature T. This implies that if we encode the information on the weight parameter, then we can affirm that the corresponding accuracy of the parameter estimation will be immune to the Hawking effect. Besides, it reveals that the QFI with respect to the phase parameter φ exhibits a decay behavior with the increase in the Hawking temperature T and converges to a nonzero value in the limit of infinite Hawking temperature T. Remarkably, it turns out that the function F_φ on θ =π \\big /4 symmetry was broken by the influence of the Hawking radiation. Finally, we generalize the case of a three-qubit system to a case of a N-qubit system, i.e., |ψ > _{1,2,3,\\ldots ,N} =(cos θ | 0 > ^{⊗ N}+sin θ e^{iφ }| 1 > ^{⊗ N}) and obtain an interesting result: the number of particles in the initial state does not affect the QFI F_θ , nor the QFI F_φ . However, with the increasing number of particles located near the event horizon, F_φ will be affected by Hawking radiation to a large extent, while F_θ is still free from disturbance resulting from the Hawking effects.

The effect of non-sphericity on mass and anisotropy measurements in dSph galaxies with Schwarzschild method

NASA Astrophysics Data System (ADS)

Kowalczyk, Klaudia; Łokas, Ewa L.; Valluri, Monica

2018-05-01

In our previous work we confirmed the reliability of the spherically symmetric Schwarzschild orbit-superposition method to recover the mass and velocity anisotropy profiles of spherical dwarf galaxies. Here, we investigate the effect of its application to intrinsically non-spherical objects. For this purpose we use a model of a dwarf spheroidal galaxy formed in a numerical simulation of a major merger of two discy dwarfs. The shape of the stellar component of the merger remnant is axisymmetric and prolate which allows us to identify and measure the bias caused by observing the spheroidal galaxy along different directions, especially the longest and shortest principal axis. The modelling is based on mock data generated from the remnant that are observationally available for dwarfs: projected positions and line-of-sight velocities of the stars. In order to obtain a reliable tool while keeping the number of parameters low we parametrize the total mass distribution as a radius-dependent mass-to-light ratio with just two free parameters we aim to constrain. Our study shows that if the total density profile is known, the true, radially increasing anisotropy profile can be well recovered for the observations along the longest axis whereas the data along the shortest axis lead to the inference of an incorrect, isotropic model. On the other hand, if the density profile is derived from the method as well, the anisotropy is always underestimated but the total mass profile is well recovered for the data along the shortest axis whereas for the longest axis the mass content is overestimated.

Black Hole Entropy Calculated via Wavefunction Approximations on a Schwarzschild Spacetime

DTIC Science & Technology

2015-05-18

dimension of μA is kg2m2s−2 which is the expected dimension . The μ2B has an extra unit of length in the numerator but is also divided by another factor...phenomena. The two ideas were General Relativity (GR) and Quantum Mechanics (QM). General relativity describes physics on large scales with masses the size...operator ̂L = ̂r × ̂p. These operators can be written in three dimensions in a compact way by using the del operator4 ∇ = ∂xî+ ∂y ĵ + ∂zk̂, ̂p

Corrected black hole thermodynamics in Damour-Ruffini’s method with generalized uncertainty principle

NASA Astrophysics Data System (ADS)

Zhou, Shiwei; Chen, Ge-Rui

Recently, some approaches to quantum gravity indicate that a minimal measurable length lp ˜ 10-35 should be considered, a direct implication of the minimal measurable length is the generalized uncertainty principle (GUP). Taking the effect of GUP into account, Hawking radiation of massless scalar particles from a Schwarzschild black hole is investigated by the use of Damour-Ruffini’s method. The original Klein-Gordon equation is modified. It is obtained that the corrected Hawking temperature is related to the energy of emitting particles. Some discussions appear in the last section.

Bending of light in quantum gravity.

PubMed

Bjerrum-Bohr, N E J; Donoghue, John F; Holstein, Barry R; Planté, Ludovic; Vanhove, Pierre

2015-02-13

We consider the scattering of lightlike matter in the presence of a heavy scalar object (such as the Sun or a Schwarzschild black hole). By treating general relativity as an effective field theory we directly compute the nonanalytic components of the one-loop gravitational amplitude for the scattering of massless scalars or photons from an external massive scalar field. These results allow a semiclassical computation of the bending angle for light rays grazing the Sun, including long-range ℏ contributions. We discuss implications of this computation, in particular, the violation of some classical formulations of the equivalence principle.

Radiative Efficiency of Collisionless Accretion

NASA Astrophysics Data System (ADS)

Gruzinov, Andrei V.

1998-07-01

The radiative efficiency, η≡L/Ṁc2, of a slowly accreting black hole is estimated using a two-temperature model of accretion. The radiative efficiency depends on the magnetic field strength near the Schwarzschild radius. For weak magnetic fields, i.e., β-1 ≡ B2/8πp <~ 10-3, the low efficiency η ~ 10-4 that is assumed in some theoretical models is achieved. For β-1 > 10-3, a significant fraction of viscous heat is dissipated by electrons and radiated away resulting in η > 10-4. At equipartition magnetic fields, β-1 ~ 1, we estimate η ~ 10-1.

Using 3D Spectroscopy to Probe the Orbital Structure of Composite Bulges

NASA Astrophysics Data System (ADS)

Erwin, Peter; Saglia, Roberto; Thomas, Jens; Fabricius, Maximilian; Bender, Ralf; Rusli, Stephanie; Nowak, Nina; Beckman, John E.; Vega Beltrán, Juan Carlos

2015-02-01

Detailed imaging and spectroscopic analysis of the centers of nearby S0 and spiral galaxies shows the existence of ``composite bulges'', where both classical bulges and disky pseudobulges coexist in the same galaxy. As part of a search for supermassive black holes in nearby galaxy nuclei, we obtained VLT-SINFONI observations in adaptive-optics mode of several of these galaxies. Schwarzschild dynamical modeling enables us to disentangle the stellar orbital structure of the different central components, and to distinguish the differing contributions of kinematically hot (classical bulge) and kinematically cool (pseudobulge) components in the same galaxy.

Gravitation. [Book on general relativity

NASA Technical Reports Server (NTRS)

Misner, C. W.; Thorne, K. S.; Wheeler, J. A.

1973-01-01

This textbook on gravitation physics (Einstein's general relativity or geometrodynamics) is designed for a rigorous full-year course at the graduate level. The material is presented in two parallel tracks in an attempt to divide key physical ideas from more complex enrichment material to be selected at the discretion of the reader or teacher. The full book is intended to provide competence relative to the laws of physics in flat space-time, Einstein's geometric framework for physics, applications with pulsars and neutron stars, cosmology, the Schwarzschild geometry and gravitational collapse, gravitational waves, experimental tests of Einstein's theory, and mathematical concepts of differential geometry.

On non-linear magnetic-charged black hole surrounded by quintessence

NASA Astrophysics Data System (ADS)

Nam, Cao H.

2018-06-01

We derive a non-linear magnetic-charged black hole surrounded by quintessence, which behaves asymptotically like the Schwarzschild black hole surrounded by quintessence but at the short distances like the dS geometry. The horizon properties of this black hole are investigated in detail. The thermodynamics of the black hole is studied in the local and global views. Finally, by calculating the heat capacity and the free energy, we point to that the black hole may undergo a thermal phase transition, between a larger unstable black hole and a smaller stable black hole, at a critical temperature.