Rindler-like Horizon in Spherically Symmetric Spacetime
NASA Astrophysics Data System (ADS)
Yang, Jinbo; He, Tangmei; Zhang, Jingyi
2016-02-01
In this paper, the Rindler-like horizon in a spherically symmetric spacetime is proposed. It is showed that just like the Rindler horizon in Minkowski spacetimes, there is also a Rindler-like horizon to a family of special observers in general spherically symmetric spacetimes. The entropy of this type of horizon is calculated with the thin film brick-wall model. The significance of entropy is discussed. Our results imply some connection between Bekeinstein-Hawking entropy and entanglement entropy.
Rindler-like Horizon in Spherically Symmetric Spacetime
NASA Astrophysics Data System (ADS)
Yang, Jinbo; He, Tangmei; Zhang, Jingyi
2016-07-01
In this paper, the Rindler-like horizon in a spherically symmetric spacetime is proposed. It is showed that just like the Rindler horizon in Minkowski spacetimes, there is also a Rindler-like horizon to a family of special observers in general spherically symmetric spacetimes. The entropy of this type of horizon is calculated with the thin film brick-wall model. The significance of entropy is discussed. Our results imply some connection between Bekeinstein-Hawking entropy and entanglement entropy.
Quantum singularities in spherically symmetric, conformally static spacetimes
NASA Astrophysics Data System (ADS)
Helliwell, T. M.; Konkowski, D. A.
2013-05-01
A definition of quantum singularity for the case of static spacetimes has recently been extended to conformally static spacetimes. Here the theory behind quantum singularities in conformally static spacetimes is reviewed and then applied to a class of spherically symmetric, conformally static spacetimes, including as special cases those studied by Roberts, by Fonarev, and by Husain et al. We use solutions of the generally coupled, massless Klein-Gordon equation as test fields. In this way we find the ranges of metric parameters and coupling coefficients for which classical timelike singularities in these spacetimes are healed quantum mechanically.
Particles' Tunneling in Spherically Symmetric Spacetimes with Dark Matter
NASA Astrophysics Data System (ADS)
Li, Guo-Ping; Zhou, Yun-Gang; Zu, Xiao-Tao
2013-11-01
Applying the Hamilton-Jacobi method, we investigate particles’ tunneling behavior in a spherically symmetric spacetime with dark matter. The tunneling rate and Hawking temperature at the event horizon are obtained. The result shows that the dark matter parameter β has an important influence on the Hawking temperature and the tunneling rate.
Static spherically symmetric space-times with six Killing vectors
Qadir, A.; Ziad, M.
1988-11-01
It had been proved earlier that spherically symmetric, static space-times have ten, seven, six, or four independent Killing vectors (KV's), but there are no cases in between. The case of six KV's is investigated here. It is shown that the space-time corresponds to a hyperboloid cross a sphere, reminiscent of Kaluza--Klein theory, with a compactification from four down to two dimensions. In effect, there is a unique metric for this space-time corresponding to a uniform mass distribution over all space.
Kodama time: Geometrically preferred foliations of spherically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Abreu, Gabriel; Visser, Matt
2010-08-01
In a general time-dependent (3+1)-dimensional spherically symmetric spacetime, the so-called Kodama vector is a naturally defined geometric quantity that is timelike outside the evolving horizon and so defines a preferred class of fiducial observers. However the Kodama vector does not by itself define any preferred notion of time. We first extract as much information as possible by invoking the “warped product” structure of spherically symmetric spacetime to study the Kodama vector, and the associated Kodama energy flux, in a coordinate-independent manner. Using this formalism we construct a general class of conservation laws, generalizing Kodama’s energy flux. We then demonstrate that a preferred time coordinate—which we shall call Kodama time—can be introduced by taking the additional step of applying the Clebsch decomposition theorem to the Kodama vector. We thus construct a geometrically preferred coordinate system for any time-dependent spherically symmetric spacetime, and explore its properties. We study the geometrically preferred fiducial observers, and demonstrate that it is possible to define and calculate a generalized notion of surface gravity that is valid throughout the entire evolving spacetime. Furthermore, by building and suitably normalizing a set of radial null geodesics, we can show that this generalized surface gravity passes several consistency tests and has a physically appropriate static limit.
Kodama time: Geometrically preferred foliations of spherically symmetric spacetimes
Abreu, Gabriel; Visser, Matt
2010-08-15
In a general time-dependent (3+1)-dimensional spherically symmetric spacetime, the so-called Kodama vector is a naturally defined geometric quantity that is timelike outside the evolving horizon and so defines a preferred class of fiducial observers. However the Kodama vector does not by itself define any preferred notion of time. We first extract as much information as possible by invoking the 'warped product' structure of spherically symmetric spacetime to study the Kodama vector, and the associated Kodama energy flux, in a coordinate-independent manner. Using this formalism we construct a general class of conservation laws, generalizing Kodama's energy flux. We then demonstrate that a preferred time coordinate - which we shall call Kodama time - can be introduced by taking the additional step of applying the Clebsch decomposition theorem to the Kodama vector. We thus construct a geometrically preferred coordinate system for any time-dependent spherically symmetric spacetime, and explore its properties. We study the geometrically preferred fiducial observers, and demonstrate that it is possible to define and calculate a generalized notion of surface gravity that is valid throughout the entire evolving spacetime. Furthermore, by building and suitably normalizing a set of radial null geodesics, we can show that this generalized surface gravity passes several consistency tests and has a physically appropriate static limit.
Maximal slicing of D-dimensional spherically symmetric vacuum spacetime
Nakao, Ken-ichi; Abe, Hiroyuki; Yoshino, Hirotaka; Shibata, Masaru
2009-10-15
We study the foliation of a D-dimensional spherically symmetric black-hole spacetime with D{>=}5 by two kinds of one-parameter families of maximal hypersurfaces: a reflection-symmetric foliation with respect to the wormhole slot and a stationary foliation that has an infinitely long trumpetlike shape. As in the four-dimensional case, the foliations by the maximal hypersurfaces avoid the singularity irrespective of the dimensionality. This indicates that the maximal slicing condition will be useful for simulating higher-dimensional black-hole spacetimes in numerical relativity. For the case of D=5, we present analytic solutions of the intrinsic metric, the extrinsic curvature, the lapse function, and the shift vector for the foliation by the stationary maximal hypersurfaces. These data will be useful for checking five-dimensional numerical-relativity codes based on the moving puncture approach.
Notes on entropy force in general spherically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Cai, Rong-Gen; Cao, Li-Ming; Ohta, Nobuyoshi
2010-04-01
In a recent paper [arXiv:1001.0785], Verlinde has shown that the Newton gravity appears as an entropy force. In this paper we show how gravity appears as entropy force in Einstein’s equation of gravitational field in a general spherically symmetric spacetime. We mainly focus on the trapping horizon of the spacetime. We find that when matter fields are absent, the change of entropy associated with the trapping horizon indeed can be identified with an entropy force. When matter fields are present, we see that heat flux of matter fields also leads to the change of entropy. Applying arguments made by Verlinde and Smolin, respectively, to the trapping horizon, we find that the entropy force is given by the surface gravity of the horizon. The cases in the untrapped region of the spacetime are also discussed.
Horizons versus singularities in spherically symmetric space-times
Bronnikov, K. A.; Elizalde, E.; Odintsov, S. D.; Zaslavskii, O. B.
2008-09-15
We discuss different kinds of Killing horizons possible in static, spherically symmetric configurations and recently classified as 'usual', 'naked', and 'truly naked' ones depending on the near-horizon behavior of transverse tidal forces acting on an extended body. We obtain the necessary conditions for the metric to be extensible beyond a horizon in terms of an arbitrary radial coordinate and show that all truly naked horizons, as well as many of those previously characterized as naked and even usual ones, do not admit an extension and therefore must be considered as singularities. Some examples are given, showing which kinds of matter are able to create specific space-times with different kinds of horizons, including truly naked ones. Among them are fluids with negative pressure and scalar fields with a particular behavior of the potential. We also discuss horizons and singularities in Kantowski-Sachs spherically symmetric cosmologies and present horizon regularity conditions in terms of an arbitrary time coordinate and proper (synchronous) time. It turns out that horizons of orders 2 and higher occur in infinite proper times in the past or future, but one-way communication with regions beyond such horizons is still possible.
Evolution of linear perturbations in spherically symmetric dust spacetimes
NASA Astrophysics Data System (ADS)
February, S.; Larena, J.; Clarkson, C.; Pollney, D.
2014-09-01
We present results from a numerical code implementing a new method to solve the master equations describing the evolution of linear perturbations in a spherically symmetric but inhomogeneous background. This method can be used to simulate several configurations of physical interest, such as relativistic corrections to structure formation, the lensing of gravitational waves (GWs) and the evolution of perturbations in a cosmological void model. This paper focuses on the latter problem, i.e. structure formation in a Hubble scale void in the linear regime. This is considerably more complicated than linear perturbations of a homogeneous and isotropic background because the inhomogeneous background leads to coupling between density perturbations and rotational modes of the spacetime geometry, as well as GWs. Previous analyses of this problem ignored this coupling in the hope that the approximation does not affect the overall dynamics of structure formation in such models. We show that for a giga-parsec void, the evolution of the density contrast is well approximated by the previously studied decoupled evolution only for very large-scale modes. However, the evolution of the gravitational potentials within the void is inaccurate at more than the 10% level, and is even worse on small scales.
Charged seven-dimensional spacetimes with spherically symmetric extra dimensions
De Felice, Antonio; Ringeval, Christophe
2009-06-15
We derive exact solutions of the seven-dimensional Einstein-Maxwell equations for a spacetime exhibiting Poincare invariance along four dimensions and spherical symmetry in the extra dimensions. Such topology generically arises in the context of braneworld models. Our solutions generalize previous results on Ricci-flat spacetimes admitting the two-sphere and are shown to include wormhole configurations. A regular coordinate system suitable to describe the whole spacetime is singled out, and we discuss the physical relevance of the derived solutions.
Spherically symmetric static spacetimes in vacuum f(T) gravity
Ferraro, Rafael; Fiorini, Franco
2011-10-15
We show that Schwarzschild geometry remains as a vacuum solution for those four-dimensional f(T) gravitational theories behaving as ultraviolet deformations of general relativity. In the gentler context of three-dimensional gravity, we also find that the infrared-deformed f(T) gravities, like the ones used to describe the late cosmic speed up of the Universe, have as the circularly symmetric vacuum solution a Deser-de Sitter or a Banados, Teitelboim and Zanelli-like spacetime with an effective cosmological constant depending on the infrared scale present in the function f(T).
Quantum resolution of timelike singularities in spherically symmetric, self-similar spacetimes
NASA Astrophysics Data System (ADS)
Konkowski, Deborah; Helliwell, Thomas; Williams, Jon
2015-04-01
A definition of quantum singularity for the case of static spacetimes has recently been extended to conformally static spacetimes. Here the theory behind quantum singularities in conformally static spacetimes is reviewed, and then applied to a class of spherically symmetric, self-similar spacetimes. We use solutions of the massless Klein-Gordon equation as test fields. In this way we find the ranges of metric parameters for which classical timelike singularities in these spacetimes are resolved quantum mechanically, in the sense that the Hamiltonian operator is essentially self-adjoint, so the evolution of quantum wave packets lacks the usual ambiguity associated with scattering off singulartities.
Slowly decaying waves on spherically symmetric spacetimes and ultracompact neutron stars
NASA Astrophysics Data System (ADS)
Keir, Joe
2016-07-01
We prove that, in a class of spherically symmetric spacetimes exhibiting stable trapping of null geodesics, linear waves cannot (uniformly) decay faster than logarithmically. When these linear waves are treated as a model for nonlinear perturbations, this slow decay is highly suggestive of nonlinear instability. We also prove that, in a large class of asymptotically flat, spherically symmetric spacetimes, logarithmic decay actually holds as a uniform upper bound. In the presence of stable trapping, this result is therefore the best one can obtain. In addition, we provide an application of these results to ultracompact neutron stars, suggesting that all stars with r\\lt 3M might be unstable.
Regularization of geodesics in static spherically symmetric Kerr-Schild spacetimes
NASA Astrophysics Data System (ADS)
Galindo, Pablo; Mars, Marc
2015-04-01
We describe a method to analyze causal geodesics in static and spherically symmetric spacetimes of Kerr-Schild form which, in particular, allows for a detailed study of the geodesics in the vicinity of the central singularity by means of a regularization procedure based on a generalization of the McGehee regularization for the motion of Newtonian point particles moving in a power-law potential. The McGehee regularization was used by Belbruno and Pretorius [1] to perform a dynamical system regularization of the central singularity of the motion of massless test particles in the Schwarzschild spacetime. Our generalization allows us to consider causal (timelike or null) geodesics in any static and spherically symmetric spacetime of Kerr-Schild form. As an example, we apply these results to causal geodesics in the Schwarzschild and Reissner-Nordstrom spacetimes.
Dualities and geometrical invariants for static and spherically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Seidel, Paola Terezinha; Cabral, Luís Antonio
2016-04-01
In this work, we consider spinless particles in curved spacetime and symmetries related to extended isometries. We search for solutions of a generalized Killing equation whose structure entails a general class of Killing tensors. The conserved quantities along particle’s geodesic are associated with a dual description of the spacetime metric. In the Hamiltonian formalism, some conserved quantities generate a dual description of the metric. The Killing tensors belonging to the conserved objects imply in a nontrivial class of dual metrics even for a Schwarzschild metric in the original spacetime. From these metrics, we construct geometrical invariants for classes of dual spacetimes to explore their singularity structure. A nontrivial singularity behavior is obtained in the dual sector.
Gravitational waves from gauge-invariant perturbations of spherically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Lasky, Paul
2009-10-01
One difficulty associated with perturbations of spherical collapse models in General Relativity is attributed to the junction conditions required at the interface of the interior matter-filled region and the exterior vacuum region. This implies extracting information about gravitational waves at spacelike infinity is also a difficult task. In this talk, I present a method which eliminates the need for junction conditions in both the background and perturbed spacetimes, thereby allowing relatively simple modelling of gravitational waveforms. This is achieved by using a recently developed method that enables a single line element to be expressed for the entire spherically symmetric background spacetime. Perturbing this spacetime in a gauge-invariant manner implies junction conditions are not required at any stage of the perturbation. Wave equations are derived for the Newman-Penrose Weyl scalars which hold in both the matter filled regions of the spacetime as well as the vacuum exterior regions.
Tomita, Kenji
2010-03-15
On the basis of the Gerlach-Sengupta theory of gauge-invariant perturbations, a formula of the integrated Sachs-Wolfe effect for a central observer is derived on general spherically symmetric spacetimes. It will be useful for comparative studies of theoretical and observational aspects of the integrated Sachs-Wolfe effect in the Lemaitre-Tolman-Bondi cosmological models which have been noticed by explaining the apparent acceleration without cosmological constant.
Spherically symmetric cosmological spacetimes with dust and radiation — numerical implementation
Lim, Woei Chet; Regis, Marco; Clarkson, Chris E-mail: regis@to.infn.it
2013-10-01
We present new numerical cosmological solutions of the Einstein Field Equations. The spacetime is spherically symmetric with a source of dust and radiation approximated as a perfect fluid. The dust and radiation are necessarily non-comoving due to the inhomogeneity of the spacetime. Such a model can be used to investigate non-linear general relativistic effects present during decoupling or big-bang nucleosynthesis, as well as for investigating void models of dark energy with isocurvature degrees of freedom. We describe the full evolution of the spacetime as well as the redshift and luminosity distance for a central observer. After demonstrating accuracy of the code, we consider a few example models, and demonstrate the sensitivity of the late time model to the degree of inhomogeneity of the initial radiation contrast.
Optimal choices of reference for a quasilocal energy: Spherically symmetric spacetimes
Wu, Ming-Fan; Chen, Chiang-Mei; Liu, Jian-Liang; Nester, James M.
2011-10-15
For a given timelike displacement vector, the covariant Hamiltonian quasilocal energy expression requires a proper choice of reference spacetime. We propose a program for determining the reference by embedding a neighborhood of the two-sphere boundary in the dynamic spacetime into a Minkowski reference, so that the two-sphere is embedded isometrically, and then extremizing the energy to determine the embedding variables. Applying this idea to Schwarzschild spacetime, we found that for each given future timelike displacement vector our program gives a unique energy value. The static observer measures the maximal energy. Applied to the Friedmann-Lemaitre-Robertson-Walker spacetime, we find that the maximum energy value is non-negative; the associated displacement vector is the unit dual mean curvature vector; and the expansion of the two-sphere boundary matches that of its reference image. For these spherically symmetric cases the reference determined by our program is equivalent to isometrically matching the geometry at the two-sphere boundary and taking the displacement vector to be orthogonal to the spacelike constant coordinate time hypersurface, like the timelike Killing vector of the Minkowski reference.
Spherically symmetric, static spacetimes in a tensor-vector-scalar theory
Giannios, Dimitrios
2005-05-15
Recently, a relativistic gravitation theory has been proposed [J. D. Bekenstein, Phys. Rev. D 70, 083509 (2004)] that gives the modified Newtonian dynamics in the weak acceleration regime. The theory is based on three dynamic gravitational fields and succeeds in explaining a large part of extragalactic and gravitational lensing phenomenology without invoking dark matter. In this work, I consider the strong gravity regime of TeVeS. I study spherically symmetric, static, and vacuum spacetimes relevant for a nonrotating black hole or the exterior of a star. Two branches of solutions are identified: in the first, the vector field is aligned with the time direction, while in the second, the vector field has a nonvanishing radial component. I show that in the first branch of solutions the {beta} and {gamma} parametrized post-Newtonian (PPN) coefficients in TeVeS are identical to these of general relativity, while in the second the {beta} PPN coefficient differs from unity, violating observational determinations of it (for the choice of the free function F of the theory made in Bekenstein's paper). For the first branch of solutions, I derive analytic expressions for the physical metric and discuss their implications. Applying these solutions to the case of black holes, it is shown that they violate causality (since they allow for superluminal propagation of metric, vector, and scalar waves) in the vicinity of the event horizon and/or that they are characterized by negative energy density carried by the fields.
NASA Astrophysics Data System (ADS)
Chakrabarti, Soumya; Banerjee, Narayan
2016-05-01
The gravitational collapse of a spherical distribution, in a class of f ( R) theories of gravity, where f ( R) is a power function of R , is discussed. The spacetime is assumed to admit a homothetic Killing vector. In the collapsing modes, some of the situations indeed hit a singularity, but they are all covered with an apparent horizon. Some peculiar cases are observed where the collapsing body settles to a constant radius at a given value of the radial coordinate.
NASA Astrophysics Data System (ADS)
Galindo, Pablo; Mars, Marc
2014-12-01
The McGehee regularization is a method to study the singularity at the origin of the dynamical system describing a point particle in a plane moving under the action of a power-law potential. It was used by Belbruno and Pretorius (2011 Class. Quantum Grav. 28 195007) to perform a dynamical system regularization of the singularity at the center of the motion of massless test particles in the Schwarzschild spacetime. In this paper, we generalize the McGehee transformation so that we can regularize the singularity at the origin of the dynamical system describing the motion of causal geodesics (timelike or null) in any stationary and spherically symmetric spacetime of Kerr-Schild form. We first show that the geodesics for both massive and massless particles can be described globally in the Kerr-Schild spacetime as the motion of a Newtonian point particle in a suitable radial potential and study the conditions under which the central singularity can be regularized using an extension of the McGehee method. As an example, we apply these results to causal geodesics in the Schwarzschild and Reissner-Nordström spacetimes. Interestingly, the geodesic trajectories in the whole maximal extension of both spacetimes can be described by a single two-dimensional phase space with non-trivial topology. This topology arises from the presence of excluded regions in the phase space determined by the condition that the tangent vector of the geodesic be causal and future directed.
NASA Astrophysics Data System (ADS)
Santos-Oliván, Daniel; Sopuerta, Carlos F.
2016-05-01
We present a new hybrid Cauchy-characteristic evolution scheme that is particularly suited to study gravitational collapse in spherically symmetric asymptotically (global) anti-de Sitter (AdS) spacetimes. The Cauchy evolution allows us to track the scalar field through the different round trips to the AdS boundary, while the characteristic method can bring us very close to the point of formation of an apparent horizon. We describe all the details of the method, including the transition between the two evolution schemes and the details of the numerical implementation for the case of massless scalar fields. We use this scheme to provide more numerical evidence for a recent conjecture on the power law scaling of the apparent horizon mass resulting from the collapse of subcritical configurations. We also compute the critical exponents and echoing periods for a number of critical points and confirm the expectation that their values should be the same as in the asymptotically flat case.
NASA Astrophysics Data System (ADS)
Raju, P.; Sobhanbabu, K.; Reddy, D. R. K.
2016-02-01
Five-dimensional spherically symmetric space-time filled with two minimally interacting fields, matter and holographic dark energy components, is investigated in a scalar tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A 113:467, 1986). An explicit solution of the field equations is obtained. Some physical and kinematic properties of the model are also studied.
Tortoise Coordinates and Hawking Radiation in a Dynamical Spherically Symmetric Spacetime
NASA Astrophysics Data System (ADS)
Yang, Jian; Zhao, Zheng; Tian, Gui-Hua; Liu, Wen-Biao
2009-12-01
Hawking effect from dynamical spherical Vaidya black hole, Vaidya-Bonner black hole, and Vaidya-de Sitter black hole is investigated using the improved Damour-Ruffini method. After the new tortoise coordinate transformation in which the position r of event horizon is an undetermined function and the temperature parameter κ is an undetermined constant, the Klein-Gordon equation can be written as the standard form at the event horizon, and both r and κ can be determined automatically. Then extending the outgoing wave from outside to inside of the horizon analytically, the Hawking temperature can also be obtained automatically.
Static cylindrically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Fjällborg, Mikael
2007-05-01
We prove the existence of static solutions to the cylindrically symmetric Einstein Vlasov system, and we show that the matter cylinder has finite extension in two of the three spatial dimensions. The same results are also proved for a quite general class of equations of state for perfect fluids coupled to the Einstein equations, extending the class of equations of state considered by Bicak et al (2004 Class. Quantum Grav.21 1583). We also obtain this result for the Vlasov Poisson system.
Spherically Symmetric Gravitational Fields
NASA Astrophysics Data System (ADS)
Vargas Moniz, P.
The purpose of this paper is to investigate the quantum vacua directly implied by the wave function of a gravitational configuration characterized by the presence of an apparent horizon, namely the Vaidya space-time solution. Spherical symmetry is a main feature of this configuration, with a scalar field constituting a source [a Klein-Gordon geon or Berger-Chitre-Moncrief-Nutku (BCMN) type model]. The subsequent analysis requires solving a Wheeler-DeWitt equation near the apparent horizon (following the guidelinesintroduced by A. Tomimatsu,18; M. Pollock, 19 and developed by A. Hosoya and I. Oda20,21) with the scalar field herein expanded in terms of S2 spherical harmonics: midisuperspace quantization. The main results present in this paper are as follows. It is found that the mass function characteristic of the Vaidya metric is positive definite within this quantum approach. Furthermore, the inhomogeneous matter sector determines a descrip-tion in terms of open quantum (sub)systems, namely in the form of an harmonic oscillator whose frequency depends on the mass function. For this open (sub)system, a twofold approach is employed. On the one hand, an exact invariant observable is obtained from the effective Hamiltonian for the inhomogeneous matter modes. It is shown that this invariant admits a set of discrete eigenvalues which depend on the mass function. The corresponding set of eigenstates is constructed from a particular vacuum state. On the other hand, exact solutions are found for the Schrädinger equation associated with the inhomogeneous matter modes. This paper is concluded with a discussion, where two other issues are raised: (i) the possible application to realistic black hole dynamics of the results obtained for a simplified (BCMN) model and (ii) whether such vacuum states could be related with others defined instead within scalar field theories constructed in classical backgrounds.
Wave equation on spherically symmetric Lorentzian metrics
Bokhari, Ashfaque H.; Al-Dweik, Ahmad Y.; Zaman, F. D.; Kara, A. H.; Karim, M.
2011-06-15
Wave equation on a general spherically symmetric spacetime metric is constructed. Noether symmetries of the equation in terms of explicit functions of {theta} and {phi} are derived subject to certain differential constraints. By restricting the metric to flat Friedman case the Noether symmetries of the wave equation are presented. Invertible transformations are constructed from a specific subalgebra of these Noether symmetries to convert the wave equation with variable coefficients to the one with constant coefficients.
Static spherically symmetric wormholes with isotropic pressure
NASA Astrophysics Data System (ADS)
Cataldo, Mauricio; Liempi, Luis; Rodríguez, Pablo
2016-06-01
In this paper we study static spherically symmetric wormhole solutions sustained by matter sources with isotropic pressure. We show that such spherical wormholes do not exist in the framework of zero-tidal-force wormholes. On the other hand, it is shown that for the often used power-law shape function there are no spherically symmetric traversable wormholes sustained by sources with a linear equation of state p = ωρ for the isotropic pressure, independently of the form of the redshift function ϕ (r). We consider a solution obtained by Tolman at 1939 for describing static spheres of isotropic fluids, and show that it also may describe wormhole spacetimes with a power-law redshift function, which leads to a polynomial shape function, generalizing a power-law shape function, and inducing a solid angle deficit.
Viscosity in spherically symmetric accretion
NASA Astrophysics Data System (ADS)
Ray, Arnab K.
2003-10-01
The influence of viscosity on the flow behaviour in spherically symmetric accretion has been studied here. The governing equation chosen has been the Navier-Stokes equation. It has been found that at least for the transonic solution, viscosity acts as a mechanism that detracts from the effectiveness of gravity. This has been conjectured to set up a limiting scale of length for gravity to bring about accretion, and the physical interpretation of such a length scale has been compared with the conventional understanding of the so-called `accretion radius' for spherically symmetric accretion. For a perturbative presence of viscosity, it has also been pointed out that the critical points for inflows and outflows are not identical, which is a consequence of the fact that under the Navier-Stokes prescription, there is a breakdown of the invariance of the stationary inflow and outflow solutions - an invariance that holds good under inviscid conditions. For inflows, the critical point gets shifted deeper within the gravitational potential well. Finally, a linear stability analysis of the stationary inflow solutions, under the influence of a perturbation that is in the nature of a standing wave, has indicated that the presence of viscosity induces greater stability in the system than has been seen for the case of inviscid spherically symmetric inflows.
Conformal cylindrically symmetric spacetimes in modified gravity
NASA Astrophysics Data System (ADS)
Türkog˜lu, Murat Metehan; Dog˜ru, Melis Ulu
2015-11-01
We investigate cylindrically symmetric spacetimes in the context of f(R) gravity. We firstly attain conformal symmetry of the cylindrically symmetric spacetime. We obtain solutions to use features of the conformal symmetry, field equations and their solutions for cylindrically symmetric spacetime filled with various cosmic matters such as vacuum state, perfect fluid, anisotropic fluid, massive scalar field and their combinations. With the vacuum state solutions, we show that source of the spacetime curvature is considered as Casimir effect. Casimir force for given spacetime is found using Wald’s axiomatic analysis. We expose that the Casimir force for Boulware, Hartle-Hawking and Unruh vacuum states could have attractive, repulsive and ineffective features. In the perfect fluid state, we show that matter form of the perfect fluid in given spacetime must only be dark energy. Also, we offer that potential of massive and massless scalar field are developed as an exact solution from the modified field equations. All solutions of field equations for vacuum case, perfect fluid and scalar field give a special f(R) function convenient to Λ-CDM model. In addition to these solutions, we introduce conformal cylindrical symmetric solutions in the cases of different f(R) models. Finally, geometrical and physical results of the solutions are discussed.
Spherically symmetric conformal gravity and ``gravitational bubbles''
NASA Astrophysics Data System (ADS)
Berezin, V. A.; Dokuchaev, V. I.; Eroshenko, Yu. N.
2016-01-01
The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson-Walker metrics. One of them we called the ``gravitational bubbles'', which is compact and with zero Weyl tensor. Thus, we obtained the pure vacuum curved space-times (without any material sources, including the cosmological constant) what is absolutely impossible in General Relativity. Such a phenomenon makes it easier to create the universe from ``nothing''. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly some features of non-vacuum solutions. Two of them are explicitly written, namely, the metrics à la Vaidya, and the electrovacuum space-time metrics.
Pseudo-Z symmetric space-times
Mantica, Carlo Alberto; Suh, Young Jin
2014-04-15
In this paper, we investigate Pseudo-Z symmetric space-time manifolds. First, we deal with elementary properties showing that the associated form A{sub k} is closed: in the case the Ricci tensor results to be Weyl compatible. This notion was recently introduced by one of the present authors. The consequences of the Weyl compatibility on the magnetic part of the Weyl tensor are pointed out. This determines the Petrov types of such space times. Finally, we investigate some interesting properties of (PZS){sub 4} space-time; in particular, we take into consideration perfect fluid and scalar field space-time, and interesting properties are pointed out, including the Petrov classification. In the case of scalar field space-time, it is shown that the scalar field satisfies a generalized eikonal equation. Further, it is shown that the integral curves of the gradient field are geodesics. A classical method to find a general integral is presented.
An introduction to spherically symmetric loop quantum gravity black holes
Gambini, Rodolfo; Pullin, Jorge
2015-03-26
We review recent developments in the treatment of spherically symmetric black holes in loop quantum gravity. In particular, we discuss an exact solution to the quantum constraints that represents a black hole and is free of singularities. We show that new observables that are not present in the classical theory arise in the quantum theory. We also discuss Hawking radiation by considering the quantization of a scalar field on the quantum spacetime.
Onthe static and spherically symmetric gravitational field
NASA Astrophysics Data System (ADS)
Gottlieb, Ioan; Maftei, Gheorghe; Mociutchi, Cleopatra
Starting from a generalization of Einstein 's theory of gravitation, proposed by one of the authors (Cleopatra Mociutchi), the authors study a particular spherical symmetric case. Among other one obtain the compatibility conditions for the existence of the static and spherically symmetruic gravitational filed in the case of extended Einstein equation.
On gauge choice of spherically symmetric 3-branes
NASA Astrophysics Data System (ADS)
Wang, Anzhong
2005-12-01
The gauge choice for a spherically symmetric 3-brane embedded in a D-dimensional bulk with arbitrary matter fields on and off the brane is studied. It is shown that Israel's junction conditions across the brane severely restrict the dependence of the matter fields on the spacetime coordinates. As examples, a scalar field or a Yang Mills potential can be only either time dependent or radial-coordinate dependent for the chosen gauge, while for a perfect fluid it must be co-moving.
Stability of spherically symmetric solutions in modified theories of gravity
Seifert, Michael D.
2007-09-15
In recent years, a number of alternative theories of gravity have been proposed as possible resolutions of certain cosmological problems or as toy models for possible but heretofore unobserved effects. However, the implications of such theories for the stability of structures such as stars have not been fully investigated. We use our 'generalized variational principle', described in a previous work [M. D. Seifert and R. M. Wald, Phys. Rev. D 75, 084029 (2007)], to analyze the stability of static spherically symmetric solutions to spherically symmetric perturbations in three such alternative theories: Carroll et al.'s f(R) gravity, Jacobson and Mattingly's 'Einstein-aether theory', and Bekenstein's TeVeS theory. We find that in the presence of matter, f(R) gravity is highly unstable; that the stability conditions for spherically symmetric curved vacuum Einstein-aether backgrounds are the same as those for linearized stability about flat spacetime, with one exceptional case; and that the 'kinetic terms' of vacuum TeVeS theory are indefinite in a curved background, leading to an instability.
Spherically symmetric solutions in a FRW background
NASA Astrophysics Data System (ADS)
Moradpour, H.; Riazi, N.
2015-02-01
We impose perfect fluid concept along with slow expansion approximation to derive new solutions which, considering non-static spherically symmetric metrics, can be treated as Black Holes (BHs). We will refer to these solutions as Quasi BHs. Mathematical and physical features such as Killing vectors, singularities, and mass have been studied. Their horizons and thermodynamic properties have also been investigated. In addition, relationship with other related works (including McVittie's) are described.
Spherically symmetric thick branes cosmological evolution
NASA Astrophysics Data System (ADS)
Bernardini, A. E.; Cavalcanti, R. T.; da Rocha, Roldão
2015-01-01
Spherically symmetric time-dependent solutions for the 5D system of a scalar field canonically coupled to gravity are obtained and identified as an extension of recent results obtained by Ahmed et al. (JHEP 1404:061. arXiv:1312.3576 [hep-th], 2014). The corresponding cosmology of models with regularized branes generated by such a 5D scalar field scenario is also investigated. It has been shown that the anisotropic evolution of the warp factor and consequently the Hubble like parameter are both driven by the radial coordinate on the brane, which leads to an emergent thick brane-world scenario with spherically symmetric time dependent warp factor. Meanwhile, the separability of variables depending on fifth dimension, , which is exhibited by the equations of motion, allows one to recover the extra dimensional profiles obtained in Ahmed et al. (2014), namely the extra dimensional part of the scale (warp) factor and the scalar field dependence on . Therefore, our results are mainly concerned with the time dependence of a spherically symmetric warp factor. Besides evincing possibilities for obtaining asymmetric stable brane-world scenarios, the extra dimensional profiles here obtained can also be reduced to those ones investigated in Ahmed et al. (2014).
Static spherically symmetric wormholes in f( R, T) gravity
NASA Astrophysics Data System (ADS)
Zubair, M.; Waheed, Saira; Ahmad, Yasir
2016-08-01
In this work, we explore wormhole solutions in f( R, T) theory of gravity, where R is the scalar curvature and T is the trace of stress-energy tensor of matter. To investigate this, we consider a static spherically symmetric geometry with matter contents as anisotropic, isotropic, and barotropic fluids in three separate cases. By taking into account the Starobinsky f( R) model, we analyze the behavior of energy conditions for these different kinds of fluids. It is shown that the wormhole solutions can be constructed without exotic matter in few regions of space-time. We also give the graphical illustration of the results obtained and discuss the equilibrium picture for the anisotropic case only. It is concluded that the wormhole solutions with anisotropic matter are realistic and stable in this theory of gravity.
Spherically symmetric solutions in covariant Horava-Lifshitz gravity
Alexandre, Jean; Pasipoularides, Pavlos
2011-04-15
We study the most general case of spherically symmetric vacuum solutions in the framework of the covariant Horava-Lifshitz gravity, for an action that includes all possible higher order terms in curvature which are compatible with power-counting normalizability requirement. We find that solutions can be separated into two main classes: (i) solutions with nonzero radial shift function, and (ii) solutions with zero radial shift function. In the case (ii), spherically symmetric solutions are consistent with observations if we adopt the view of Horava and Melby-Tomson [P. Horava and C. M. Melby-Thompson, Phys. Rev. D 82, 064027 (2010).], according to which the auxiliary field A can be considered as a part of an effective general relativistic metric, which is valid only in the IR limit. On the other hand, in the case (i), consistency with observations implies that the field A should be independent of the spacetime geometry, as the Newtonian potential arises from the nonzero radial shift function. Also, our aim in this paper is to discuss and compare these two alternative but different assumptions for the auxiliary field A.
Spherically Symmetric Solutions of Light Galileon
NASA Astrophysics Data System (ADS)
Momeni, D.; Houndjo, M. J. S.; Güdekli, E.; Rodrigues, M. E.; Alvarenga, F. G.; Myrzakulov, R.
2016-02-01
We have been studied the model of light Galileon with translational shift symmetry ϕ → ϕ + c. The matter Lagrangian is presented in the form {L}_{φ }= -η (partial φ )2+β G^{μ ν }partial _{μ }φ partial _{ν }φ . We have been addressed two issues: the first is that, we have been proven that, this type of Galileons belong to the modified matter-curvature models of gravity in type of f(R,R^{μ ν }T_{μ ν }m). Secondly, we have been investigated exact solution for spherically symmetric geometries in this model. We have been found an exact solution with singularity at r = 0 in null coordinates. We have been proven that the solution has also a non-divergence current vector norm. This solution can be considered as an special solution which has been investigated in literature before, in which the Galileon's field is non-static (time dependence). Our scalar-shift symmetrized Galileon has the simple form of ϕ = t, which it is remembered by us dilaton field.
Spherical Symmetric Gravitational Collapse in Chern-Simon Modified Gravity
NASA Astrophysics Data System (ADS)
Amir, M. Jamil; Ali, Sarfraz
2016-04-01
This paper is devoted to investigate the gravitational collapse in the framework of Chern-Simon (CS) modified gravity. For this purpose, we assume the spherically symmetric metric as an interior region and the Schwarzchild spacetime is considered as an exterior region of the star. Junction conditions are used to match the interior and exterior spacetimes. In dynamical formulation of CS modified gravity, we take the scalar field Θ as a function of radial parameter r and obtain the solution of the field equations. There arise two cases where in one case the apparent horizon forms first and then singularity while in second case the order of the formation is reversed. It means the first case results a black hole which supports the cosmic censorship hypothesis (CCH). Obviously, the second case yields a naked singularity. Further, we use Junction conditions have to calculate the gravitational mass. In non-dynamical formulation, the canonical choice of scalar field Θ is taken and it is shown that the obtained results of CS modified gravity simply reduce to those of the general relativity (GR). It is worth mentioning here that the results of dynamical case will reduce to those of GR, available in literature, if the scalar field is taken to be constant.
Spin fluids in stationary axis-symmetric space-times
NASA Astrophysics Data System (ADS)
Krisch, J. P.
1987-07-01
The relations establishing the equivalence of an ordinary perfect fluid stress-energy tensor and a spin fluid stress-energy tensor are derived for stationary axis-symmetric space-times in general relativity. Spin fluid sources for the Gödel cosmology and the van Stockum metric are given.
Spherically symmetric solutions in higher-derivative gravity
NASA Astrophysics Data System (ADS)
Lü, H.; Perkins, A.; Pope, C. N.; Stelle, K. S.
2015-12-01
Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantized gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically flat solutions of this class of theories. An important element in the analysis is the careful treatment of a Lichnerowicz-type "no-hair" theorem. From a Frobenius analysis of the asymptotic small-radius behavior, the solution space is found to split into three asymptotic families, one of which contains the classic Schwarzschild solution. These three families are carefully analyzed to determine the corresponding numbers of free parameters in each. One solution family is capable of arising from coupling to a distributional shell of matter near the origin; this family can then match onto an asymptotically flat solution at spatial infinity without encountering a horizon. Another family, with horizons, contains the Schwarzschild solution but includes also non-Schwarzschild black holes. The third family of solutions obtained from the Frobenius analysis is nonsingular and corresponds to "vacuum" solutions. In addition to the three families identified from near-origin behavior, there are solutions that may be identified as "wormholes," which can match symmetrically onto another sheet of spacetime at finite radius.
Static spherically symmetric solutions in mimetic gravity: rotation curves and wormholes
NASA Astrophysics Data System (ADS)
Myrzakulov, Ratbay; Sebastiani, Lorenzo; Vagnozzi, Sunny; Zerbini, Sergio
2016-06-01
In this work, we analyse static spherically symmetric solutions in the framework of mimetic gravity, an extension of general relativity where the conformal degree of freedom of gravity is isolated in a covariant fashion. Here we extend previous works by considering, in addition, a potential for the mimetic field. An appropriate choice of such a potential allows for the reconstruction of a number of interesting cosmological and astrophysical scenarios. We explicitly show how to reconstruct such a potential for a general static spherically symmetric space-time. A number of applications and scenarios are then explored, among which are traversable wormholes. Finally, we analytically reconstruct potentials, which leads to solutions to the equations of motion featuring polynomial corrections to the Schwarzschild space-time. Accurate choices for such corrections could provide an explanation for the inferred flat rotation curves of spiral galaxies within the mimetic gravity framework, without the need for particle dark matter.
Nontrivial static, spherically symmetric vacuum solution in a nonconservative theory of gravity
NASA Astrophysics Data System (ADS)
Oliveira, A. M.; Velten, H. E. S.; Fabris, J. C.
2016-06-01
We analyze the vacuum static spherically symmetric spacetime for a specific class of nonconservative theories of gravity based on Rastall's theory. We obtain a new vacuum solution which has the same structure as the Schwarzschild-de Sitter solution in the general relativity theory obtained with a cosmological constant playing the role of source. We further discuss the structure (in particular, the coupling to matter fields) and some cosmological aspects of the underline nonconservative theory.
Influence of a plasma on the shadow of a spherically symmetric black hole
NASA Astrophysics Data System (ADS)
Perlick, Volker; Tsupko, Oleg Yu.; Bisnovatyi-Kogan, Gennady S.
2015-11-01
We analytically calculate the influence of a plasma on the shadow of a black hole (or of another compact object). We restrict to spherically symmetric and static situations, where the shadow is circular. The plasma is assumed to be nonmagnetized and pressureless. We derive the general formulas for a spherically symmetric plasma density on an unspecified spherically symmetric and static spacetime. Our main result is an analytical formula for the angular size of the shadow. As a plasma is a dispersive medium, the radius of the shadow depends on the photon frequency. The effect of the plasma is significant only in the radio regime. The formalism applies not only to black holes but also, e.g., to wormholes. As examples for the underlying spacetime model, we consider the Schwarzschild spacetime and the Ellis wormhole. In particular, we treat the case that the plasma is in radial free fall from infinity onto a Schwarzschild black hole. We find that for an observer far away from a Schwarzschild black hole, the plasma has a decreasing effect on the size of the shadow. The perspectives of actually observing the influence of a plasma on the shadows of supermassive black holes are discussed.
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.
Weakly regular T2-symmetric spacetimes. The future causal geometry of Gowdy spacetimes
NASA Astrophysics Data System (ADS)
LeFloch, Philippe G.; Smulevici, Jacques
2016-01-01
We investigate the future asymptotic behavior of Gowdy spacetimes on T3, when the metric satisfies weak regularity conditions, so that the metric coefficients (in suitable coordinates) are only in the Sobolev space H1 or have even weaker regularity. The authors recently introduced this class of spacetimes in the broader context of T2-symmetric spacetimes and established the existence of a global foliation by spacelike hypersurfaces when the time function is chosen to be the area of the surfaces of symmetry. In the present paper, we identify the global causal geometry of these spacetimes and, in particular, establish that weakly regular Gowdy spacetimes are future timelike geodesically complete. This result extends a theorem by Ringström for metrics with sufficiently high regularity. We emphasize that our proof of the energy decay is based on an energy functional inspired by the Gowdy-to-Ernst transformation. In order to establish the geodesic completeness property, we prove a higher regularity property concerning the metric coefficients along timelike curves and we provide a novel analysis of the geodesic equation for Gowdy spacetimes, which does not require high-order regularity estimates. Even when sufficient regularity is assumed, our proof provides an alternative and shorter proof of the energy decay and of the geodesic completeness property for Gowdy spacetimes.
Killing and Noether Symmetries of Plane Symmetric Spacetime
NASA Astrophysics Data System (ADS)
Shamir, M. Farasat; Jhangeer, Adil; Bhatti, Akhlaq Ahmad
2013-09-01
This paper is devoted to investigate the Killing and Noether symmetries of static plane symmetric spacetime. For this purpose, five different cases have been discussed. The Killing and Noether symmetries of Minkowski spacetime in cartesian coordinates are calculated as a special case and it is found that Lie algebra of the Lagrangian is 10 and 17 dimensional respectively. The symmetries of Taub's universe, anti-deSitter universe, self similar solutions of infinite kind for parallel perfect fluid case and self similar solutions of infinite kind for parallel dust case are also explored. In all the cases, the Noether generators are calculated in the presence of gauge term. All these examples justify the conjecture that Killing symmetries form a subalgebra of Noether symmetries (Bokhari et al. in Int. J. Theor. Phys. 45:1063, 2006).
Morris-Thorne wormholes in static pseudospherically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Cataldo, Mauricio; Liempi, Luis; Rodríguez, Pablo
2015-06-01
In this paper, we study classical general relativistic static wormhole configurations with pseudospherical symmetry. We show that, in addition to the hyperbolic wormhole solutions discussed by Lobo and Mimoso in [Phys. Rev. D 82, 044034 (2010)], there exists another wormhole class, which is a truly pseudospherical counterpart of spherical Morris-Thorne wormhole (contrary to the Lobo-Mimoso wormhole class), since all constraints originally defined by Morris and Thorne for spherically symmetric wormholes are satisfied. We show that, for both classes of hyperbolic wormholes, the energy density, at the throat, is always negative, while the radial pressure is positive, contrary to the spherically symmetric Morris-Thorne wormhole. Specific hyperbolic wormholes are constructed and discussed by imposing different conditions for the radial and lateral pressures, or by considering restricted choices for the redshift and the shape functions. In particular, we show that a hyperbolic wormhole cannot be sustained at the throat by phantom energy and that there are pseudospherically symmetric wormholes supported by matter with isotropic pressure and characterized by space sections with an angle deficit (or excess).
Concircular vector fields for plane-symmetric static spacetimes
NASA Astrophysics Data System (ADS)
Ali, Ahmad Tawfik; Khan, Suhail
2016-04-01
In this paper, we investigate concircular vector fields (CVFs) of static plane symmetric four-dimensional Lorentzian manifold. Ten conformal Killing equations and their general form of conformal Killing vector fields (CKVFs) are derived along with their conformal factor. These CKVFs are then placed into the conformal Ricci collineation equations to obtain the final form of CVFs. The existence of concircular symmetry imposes restrictions on the metric functions. The conditions imposing restrictions on these metric functions are obtained as a set of integrability conditions. It is shown that plane-symmetric static spacetimes admit four, six, seven or fifteen-dimensional concircular vector fields. Analysis of our results are also given in the light of some established results in the literature.
All static spherically symmetric anisotropic solutions of Einstein's equations
Herrera, L.; Di Prisco, A.; Ospino, J.
2008-01-15
An algorithm recently presented by Lake to obtain all static spherically symmetric perfect fluid solutions is extended to the case of locally anisotropic fluids (principal stresses unequal). As expected, the new formalism requires the knowledge of two functions (instead of one) to generate all possible solutions. To illustrate the method some known cases are recovered.
Five dimensional spherically symmetric cosmological model in Brans-Dicke theory of gravitation
NASA Astrophysics Data System (ADS)
Rao, V. U. M.; Jaysudha, V.
2015-08-01
In this paper, we consider the spherically symmetric space-time in five dimensions in Brans-Dicke (Phys. Rev. 124:925, 1961) theory of gravitation in the presence of perfect fluid distribution. A determinate solution of the highly non-linear field equations is presented using (i) relation between metric potentials and (ii) an equation of state which represents disordered radiation in five dimensional universe. The solution obtained describes five dimensional radiating model in Brans-Dicke theory. Some physical and kinematical properties of the model are also discussed.
NASA Astrophysics Data System (ADS)
Reddy, D. R. K.; Raju, P.; Sobhanbabu, K.
2016-04-01
Five dimensional spherically symmetric space-time filled with two minimally interacting fields; matter and holographic dark energy components is investigated in a scalar tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124:925, 1961). To obtain a determinate solution of the highly non-linear field equations we have used (i) a relation between metric potentials and (ii) an equation of state which represents disordered radiation in five dimensional universe. The solution obtained represents a minimally interacting and radiating holographic dark energy model in five dimensional universe. Some physical and Kinematical properties of the model are, also, studied.
Study of striations in a spherically symmetric hydrogen discharge
NASA Astrophysics Data System (ADS)
Lowell Morgan, W.; Childs, Montgomery W.
2015-10-01
Experiments on a high power spherically symmetric positive corona discharge in molecular hydrogen are reported upon. These are collisional plasmas in the H2 pressure range of about 0.75 Torr to 3 Torr. Applied voltages ranged up to 600 V on the anode with currents ranging up to 3 A. As others have observed in prior published experiments going back to 1997, we have observed spherically symmetric striations or double layers. Others have observed such striations in O2, CO2, and in mixtures of N2 and acetone or methanol, or benzene. Like H2 all these gases, except N2 itself, readily dissociate and form negative ions by dissociative attachment with electrons. We propose that the striations are instabilities arising from copious formation of negative ions that modify the radial space charge and electric field distributions in such high aspect ratio spherical discharges.
Magnetospheric energy principle for spherically symmetric monopolar magnetospheres.
Miura, Akira
2013-05-24
A new magnetospheric energy principle is developed for spherically symmetric monopolar magnetospheres with open straight field lines. The principle is based on the self-adjointness of the force operator, which ensures energy conservation in the unperturbed magnetospheric plasma volume. A Neuman-type boundary condition for the perpendicular displacement at the ionosphere yields a negative contribution to the potential energy variation. This contribution makes high-mode-number incompressible field-line-bending modes unstable owing to the plasma displacement over the spherical ionospheric surface. PMID:23745887
General static spherically symmetric solutions in Horava gravity
Capasso, Dario; Polychronakos, Alexios P.
2010-04-15
We derive the equations describing a general static spherically symmetric configuration for the softly broken Horava gravity introduced by A. Kehagias and K. Sfetsos with nonzero shift field and no-projectability condition. These represent 'hedgehog' versions of black holes with radial 'hair' arising from the shift field. For the case of the standard de Witt kinetic term ({lambda}=1) there is an infinity of solutions that exhibit a deformed version of reparametrization invariance away from the general relativistic limit. Special solutions also arise in the anisotropic conformal point {lambda}=(1/3). Moreover we obtain an implicit general expression for the solutions with N{sub r}=0 and generic {lambda}. In this context we study the presence of horizons for standard matter and the related Hawking temperature, generalizing the corresponding relations in the usual static spherically symmetric case.
Implications of the Cosmological Constant for Spherically Symmetric Mass Distributions
NASA Astrophysics Data System (ADS)
Zubairi, Omair; Weber, Fridolin
2013-04-01
In recent years, scientists have made the discovery that the expansion rate of the Universe is increasing rather than decreasing. This acceleration leads to an additional term in Albert Einstein's field equations which describe general relativity and is known as the cosmological constant. This work explores the aftermath of a non-vanishing cosmological constant for relativistic spherically symmetric mass distributions, which are susceptible to change against Einstein's field equations. We introduce a stellar structure equation known as the Tolman-Oppenhiemer-Volkoff (TOV) equation modified for a cosmological constant, which is derived from Einstein's modified field equations. We solve this modified TOV equation for these spherically symmetric mass distributions and obtain stellar properties such as mass and radius and investigate changes that may occur depending on the value of the cosmological constant.
NASA Astrophysics Data System (ADS)
Barnich, Glenn; Troessaert, Cédric; Tempo, David; Troncoso, Ricardo
2016-04-01
The theory of massive gravity proposed by Bergshoeff, Hohm and Townsend is considered in the special case of the pure irreducibly fourth-order quadratic Lagrangian. It is shown that the asymptotically locally flat black holes of this theory can be consistently deformed to "black flowers" that are no longer spherically symmetric. Moreover, we construct radiating spacetimes settling down to these black flowers in the far future. The generic case can be shown to fit within a relaxed set of asymptotic conditions as compared to the ones of general relativity at null infinity, while the asymptotic symmetries remain the same. Conserved charges as surface integrals at null infinity are constructed following a covariant approach, and their algebra represents BMS3 , but without central extensions. For solutions possessing an event horizon, we derive the first law of thermodynamics from these surface integrals.
Stability of Schwarzschild-AdS for the Spherically Symmetric Einstein-Klein-Gordon System
NASA Astrophysics Data System (ADS)
Holzegel, Gustav; Smulevici, Jacques
2013-01-01
In this paper, we study the global behavior of solutions to the spherically symmetric coupled Einstein-Klein-Gordon (EKG) system in the presence of a negative cosmological constant. For the Klein-Gordon mass-squared satisfying a ≥ -1 (the Breitenlohner-Freedman bound being a > -9/8), we prove that the Schwarzschild-AdS spacetimes are asymptotically stable: Small perturbations of Schwarzschild-AdS initial data again lead to regular black holes, with the metric on the black hole exterior approaching, at an exponential rate, a Schwarzschild-AdS spacetime. The main difficulties in the proof arise from the lack of monotonicity for the Hawking mass and the asymptotically AdS boundary conditions, which render even (part of) the orbital stability intricate. These issues are resolved in a bootstrap argument on the black hole exterior, with the redshift effect and weighted Hardy inequalities playing the fundamental role in the analysis. Both integrated decay and pointwise decay estimates are obtained. As a corollary of our estimates on the Klein-Gordon field, one obtains in particular exponential decay in time of spherically-symmetric solutions to the linear Klein-Gordon equation on Schwarzschild-AdS.
Constraints on a spherically symmetric 5-d braneworld
NASA Astrophysics Data System (ADS)
Capistrano, A. J. S.
2013-12-01
We study the effect of the extrinsic curvature within the context of braneworld with constant curvature and the restrictions on a spherically symmetric geometry embedded in a 5-d bulk. As a counterexample, we recover the Schwarzschild-de Sitter black hole but with umbilical points. In a second case we find the correct geometrical structure of a black hole but the Newtonian gravity cannot be restored implying that a higher dynamical embedding must be considered.
Gyroid phase of fluids with spherically symmetric competing interactions.
Edelmann, Markus; Roth, Roland
2016-06-01
We study the phase diagram of a fluid with spherically symmetric competing pair interactions that consist of a short-ranged attraction and a longer-ranged repulsion in addition to a hard core. To this end we perform free minimizations of three-dimensional triple periodic structures within the framework of classical density functional theory. We compare our results to those from Landau theory. Our main finding is that the double gyroid phase can exist as a thermodynamically stable phase. PMID:27415247
Dzhunushaliev, Vladimir; Folomeev, Vladimir; Singleton, Douglas; Myrzakulov, Ratbay
2010-08-15
In this paper we investigate wormhole and spherically symmetric solutions in four-dimensional gravity plus a matter source consisting of a ghost scalar field with a sine-Gordon potential. For the wormhole solutions we also include the possibility of electric and/or magnetic charges. For both types of solutions we perform a linear stability analysis and show that the wormhole solutions are stable and that when one turns on the electric and/or magnetic field the solution remains stable. The linear stability analysis of the spherically symmetric solutions indicates that they can be stable or unstable depending on one of the parameters of the system. This result for the spherically symmetric solution is nontrivial since a previous investigation of four-dimensional gravity plus a ghost scalar field with a {lambda}{phi}{sup 4} interaction found only unstable spherically symmetric solutions. Both the wormhole and spherically symmetric solutions presented here asymptotically go to anti-de Sitter space-time.
The Dirac-Hestenes Equation for Spherical Symmetric Potentials in the Spherical and Cartesian Gauges
NASA Astrophysics Data System (ADS)
da Rocha, Roldão; Rodrigues, Waldyr A.
In this paper, using the apparatus of the Clifford bundle formalism, we show how straightforwardly solve in Minkowski space-time the Dirac-Hestenes equation — which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation — by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that, contrary to what is expected at a first sight, the solution of the Dirac-Hestenes equation in both gauges has exactly the same mathematical difficulty.
Spherically symmetric high-velocity plasma expansions into background gases
NASA Technical Reports Server (NTRS)
Tan, T.-H.; Borovsky, J. E.
1986-01-01
Spherically symmetric plasmas with high expansion velocities have been produced by irradiating targets with eight beams from the Helios CO2 laser in the presence of gases at various pressures. Attention was given to the properties of the target-emitted ions in order to obtain information about the ion-acceleration mechanisms in plasma expansions. Photoionization of the ambient gases by the soft X-ray emission from the laser-irradiated targets produced background plasmas, permitting plasma counterstreaming experiments to be performed in spherical geometry. Successful laser-target coupling in the presence of back-ground gases is obtained; modification of the ion acceleration in accordance with isothermal-expansion models is observed; and an absence of collective coupling between collisionless counterstreaming plasmas is found.
Static spherically symmetric solutions in f(G) gravity
NASA Astrophysics Data System (ADS)
Sharif, M.; Fatima, H. Ismat
2016-05-01
We investigate interior solutions for static spherically symmetric metric in the background of f(G) gravity. We use the technique of conformal Killing motions to solve the field equations with both isotropic and anisotropic matter distributions. These solutions are then used to obtain density, radial and tangential pressures for power-law f(G) model. For anisotropic case, we assume a linear equation-of-state and investigate solutions for the equation-of-state parameter ω = ‑1.5. We check physical validity of the solutions through energy conditions and also examine its stability. Finally, we study equilibrium configuration using Tolman-Oppenheimer-Volkoff equation.
Corrected Entropy of a General Spherically Symmetric Black Hole
NASA Astrophysics Data System (ADS)
He, Tang-mei; Yang, Jin-bo; Wu, Feng-jie
2012-07-01
Adopting the tortoise coordinates transformation in the advanced Eddington coordinates and applying the generalized law of thermodynamics, we discuss the corrected entropy of a general spherically symmetric black hole beyond the semi-classical limit. We give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Two examples are explicitly worked out. The conclusion is that the corrected entropy includes a logarithmically term and an inverse term to the Bekenstein-Hawking entropy, which is the same form as that of the static and the stationary black holes discussed by using the loop quantum gravity and the string theory.
Electrostatic spherically symmetric configurations in gravitating nonlinear electrodynamics
NASA Astrophysics Data System (ADS)
Diaz-Alonso, J.; Rubiera-Garcia, D.
2010-03-01
We perform a study of the gravitating electrostatic spherically symmetric (G-ESS) solutions of Einstein field equations minimally coupled to generalized nonlinear Abelian gauge models in three space dimensions. These models are defined by Lagrangian densities which are general functions of the gauge field invariants, restricted by some physical conditions of admissibility. They include the class of nonlinear electrodynamics supporting electrostatic spherically symmetric (ESS) nontopological soliton solutions in absence of gravity. We establish that the qualitative structure of the G-ESS solutions of admissible models is fully characterized by the asymptotic and central-field behaviors of their ESS solutions in flat space (or, equivalently, by the behavior of the Lagrangian densities in vacuum and on the point of the boundary of their domain of definition, where the second gauge invariant vanishes). The structure of these G-ESS configurations for admissible models supporting divergent-energy ESS solutions in flat space is qualitatively the same as in the Reissner-Nordström case. In contrast, the G-ESS configurations of the models supporting finite-energy ESS solutions in flat space exhibit new qualitative features, which are discussed in terms of the Arnowitt-Deser-Misner mass, the charge, and the soliton energy. Most of the results concerning well-known models, such as the electrodynamics of Maxwell, Born-Infeld, and the Euler-Heisenberg effective Lagrangian of QED, minimally coupled to gravitation, are shown to be corollaries of general statements of this analysis.
Spherically Symmetric Core Collapse Supernova Simulations With Boltzmann Neutrino Transport
NASA Astrophysics Data System (ADS)
Messer, O. E. B.
2001-12-01
I will describe the results of several spherically symmetric core collapse supernova simulations performed with AGILE-BOLTZTRAN, a state-of-the-art radiation hydrodynamics code incorporating Boltzmann neutrino transport. Collapse simulations comparing two 15 M⊙ progenitor models with significant differences in initial Ye (Woosley & Weaver 1995, Heger et al. 2000) exhibit no differences in Ye at bounce, and, consequently, no difference in homologous core mass and shock formation radius. Fully dynamic simulations of core collapse, rebound, and shock propagation for 15 M⊙ and 20 M⊙ progenitor models of Nomoto & Hashimoto (1988) fail to produce explosions. In both cases, the shock stalls at 200 km, then recedes for several hundred milliseconds. The marked similarities observed in all these simulations highlight the need for both improved progenitor models and the incorporation of improved microphysics in modern supernova codes. Spherically symmetric simulations are, for the immediate future, the only computationally feasible way to investigate the nature of the explosion mechanism while including the requisite level of detailed neutrino transport. They also provide one of the few opportunities to delineate the effects of various feedback mechanisms present in the problem. This research was supported by funds from the Joint Institute for Heavy Ion Research and a DOE PECASE award, and made use of the resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098.
Electrostatic spherically symmetric configurations in gravitating nonlinear electrodynamics
Diaz-Alonso, J.; Rubiera-Garcia, D.
2010-03-15
We perform a study of the gravitating electrostatic spherically symmetric (G-ESS) solutions of Einstein field equations minimally coupled to generalized nonlinear Abelian gauge models in three space dimensions. These models are defined by Lagrangian densities which are general functions of the gauge field invariants, restricted by some physical conditions of admissibility. They include the class of nonlinear electrodynamics supporting electrostatic spherically symmetric (ESS) nontopological soliton solutions in absence of gravity. We establish that the qualitative structure of the G-ESS solutions of admissible models is fully characterized by the asymptotic and central-field behaviors of their ESS solutions in flat space (or, equivalently, by the behavior of the Lagrangian densities in vacuum and on the point of the boundary of their domain of definition, where the second gauge invariant vanishes). The structure of these G-ESS configurations for admissible models supporting divergent-energy ESS solutions in flat space is qualitatively the same as in the Reissner-Nordstroem case. In contrast, the G-ESS configurations of the models supporting finite-energy ESS solutions in flat space exhibit new qualitative features, which are discussed in terms of the Arnowitt-Deser-Misner mass, the charge, and the soliton energy. Most of the results concerning well-known models, such as the electrodynamics of Maxwell, Born-Infeld, and the Euler-Heisenberg effective Lagrangian of QED, minimally coupled to gravitation, are shown to be corollaries of general statements of this analysis.
Classification of Plane Symmetric Static Space-Times According to Their Noether Symmetries
NASA Astrophysics Data System (ADS)
Ali, Farhad; Feroze, Tooba
2013-09-01
In this paper we give a classification of plane symmetric static space-times using symmetry method. For this purpose we consider the Lagrangian corresponding to the general plane symmetric static metric in the Noether symmetry equation. This provides a system of determining equations. Solutions of this system give us classification of the plane symmetric static space-times according to their Noether symmetries. During this classification we recover all the results listed in Feroze et al. (J. Math. Phys. 42:4947, 2001) and Bashir and Ehsan (Il Nuovo Cimento B 123:1, 2008).
Non-metric gravity: II. Spherically symmetric solution, missing mass and redshifts of quasars
NASA Astrophysics Data System (ADS)
Krasnov, Kirill; Shtanov, Yuri
2008-01-01
We continue the study of the non-metric theory of gravity introduced by Krasnov (2006 Preprint hep-th/0611182) and obtain its general spherically symmetric vacuum solution. It respects the analog of the Birkhoff theorem, i.e. the vacuum spherically symmetric solution is necessarily static. As in general relativity, the spherically symmetric solution is seen to describe a black hole. The exterior geometry is essentially the same as in the Schwarzschild case, with power-law corrections to the Newtonian potential. The behaviour inside the black-hole region is different from the Schwarzschild case in that the usual spacetime singularity gets replaced by a singular surface of a new type, where all basic fields of the theory remain finite but metric ceases to exist. The theory does not admit arbitrarily small black holes: for small objects, the curvature on the would-be horizon is so strong that non-metric modifications prevent the horizon from being formed. The theory allows for modifications of gravity of a very interesting nature. We discuss three physical effects, namely (i) correction to Newton's law in the neighborhood of the source, (ii) renormalization of effective gravitational and cosmological constants at large distances from the source and (iii) additional redshift factor between spatial regions of different curvature. The first two effects can be responsible, respectively, for the observed anomaly in the acceleration of the Pioneer spacecraft and for the alleged missing mass in spiral galaxies and other astrophysical objects. The third effect can be used to propose a non-cosmological explanation of high redshifts of quasars and gamma-ray bursts.
String loops in the field of braneworld spherically symmetric black holes and naked singularities
Stuchlík, Z.; Kološ, M. E-mail: martin.kolos@fpf.slu.cz
2012-10-01
We study motion of current-carrying string loops in the field of braneworld spherically symmetric black holes and naked singularities. The spacetime is described by the Reissner-Nordström geometry with tidal charge b reflecting the non-local tidal effects coming from the external dimension; both positive and negative values of the spacetime parameter b are considered. We restrict attention to the axisymmetric motion of string loops when the motion can be fully governed by an appropriately defined effective potential related to the energy and angular momentum of the string loops. In dependence on these two constants of the motion, the string loops can be captured, trapped, or can escape to infinity. In close vicinity of stable equilibrium points at the centre of trapped states the motion is regular. We describe how it is transformed to chaotic motion with growing energy of the string loop. In the field of naked singularities the trapped states located off the equatorial plane of the system exist and trajectories unable to cross the equatorial plane occur, contrary to the trajectories in the field of black holes where crossing the equatorial plane is always admitted. We concentrate our attention to the so called transmutation effect when the string loops are accelerated in the deep gravitational field near the black hole or naked singularity by transforming the oscillatory energy to the energy of the transitional motion. We demonstrate that the influence of the tidal charge can be substantial especially in the naked singularity spacetimes with b > 1 where the acceleration to ultrarelativistic velocities with Lorentz factor γ ∼ 100 can be reached, being more than one order higher in comparison with those obtained in the black hole spacetimes.
The static spherically symmetric interior case of the non-symmetric theory of gravitation
NASA Astrophysics Data System (ADS)
Savaria, Pierre
1989-07-01
The field equations for a spherically symmetric perfect fluid in nonsymmetric gravitational theory (NGT) are cast as a set of first-order differential equations suitable for numerical integration. An analytic series solution is presented as an expansion around r = 0. It is shown how interior solutions match with the exterior one and how, at the boundary, the Euler equation for the fluid becomes the equation of motion of a test particle in the exterior metric. An expression is derived from a conserved pseudotensor for the total mass-energy of a static body in terms of its interior matter parameters.
NASA Astrophysics Data System (ADS)
Mimoso, José P.; Le Delliou, Morgan; Mena, Filipe C.
2013-08-01
We investigate spherically symmetric spacetimes with an anisotropic fluid and discuss the existence and stability of a separating shell dividing expanding and collapsing regions. We resort to a 3+1 splitting and obtain gauge invariant conditions relating intrinsic spacetime quantities to properties of the matter source. We find that the separating shell is defined by a generalization of the Tolman-Oppenheimer-Volkoff equilibrium condition. The latter establishes a balance between the pressure gradients, both isotropic and anisotropic, and the strength of the fields induced by the Misner-Sharp mass inside the separating shell and by the pressure fluxes. This defines a local equilibrium condition, but conveys also a nonlocal character given the definition of the Misner-Sharp mass. By the same token, it is also a generalized thermodynamical equation of state as usually interpreted for the perfect fluid case, which now has the novel feature of involving both the isotropic and the anisotropic stresses. We have cast the governing equations in terms of local, gauge invariant quantities that are revealing of the role played by the anisotropic pressures and inhomogeneous electric part of the Weyl tensor. We analyze a particular solution with dust and radiation that provides an illustration of our conditions. In addition, our gauge invariant formalism not only encompasses the cracking process from Herrera and co-workers but also reveals transparently the interplay and importance of the shear and of the anisotropic stresses.
Spherically symmetric model atmospheres for late-type giant stars
NASA Astrophysics Data System (ADS)
Bennett, Philip Desmond
The ATHENA computer code was developed to model the extended atmospheres of late-type giant and supergiant stars. The atmospheres are assumed to be static, spherically symmetric and in radiative and hydrostatic equilibrium. Molecular line blanketing (for now) is handled using the simplifying assumption of mean opacity. The complete linearization method of Auer and Mihalas, adapted to spherical geometry, is used to solve the model system. The radiative transfer is solved by using variable Eddington factors to close the system of moment transfer equations, and the entire system of transfer equations plus constraints is solved efficiently by arrangement into the Rybicki block matrix form. The variable Eddington factors are calculated from the full angle-dependent formal solution of the radiative transfer problem using the impact parameter method of Hummer, Kunas. We were guided by the work of Mihalas and Hummer in their development of extended models of O stars, but our method differs in the choice of the independent variable. The radius depth scale used by Mihals and Hummer was found to fail because of the strongly temperature-dependent opacities of late-type atmospheres. Instead, we were able to achieve an exact linearization of the radius. This permitted the use of the numerically well-behaved column mass or optical depth scales. The resulting formulation is analogous to the plane-parallel complete linearization method and reduces to this method in the compact atmosphere limit. Models of M giants were calculated for Teff = 3000K and 3500K with opacities of the CN, TiO, and H2O molecules included, and the results were in general agreement with other published spherical models. These models were calculated assuming radiative equilibrium. The importance of convective energy transport was estimated by calculating the convective flux that would result from the temperature structure of the models. The standard local mixing length theory was used for this purpose
Spherically symmetric Einstein-aether perfect fluid models
NASA Astrophysics Data System (ADS)
Coley, Alan A.; Leon, Genly; Sandin, Patrik; Latta, Joey
2015-12-01
We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a well-posed system of first order partial differential equations in two variables. We then introduce normalized variables. The formalism is particularly well-suited for numerical computations and the study of the qualitative properties of the models, which are also solutions of Horava gravity. We study the local stability of the equilibrium points of the resulting dynamical system corresponding to physically realistic inhomogeneous cosmological models and astrophysical objects with values for the parameters which are consistent with current constraints. In particular, we consider dust models in (β-) normalized variables and derive a reduced (closed) evolution system and we obtain the general evolution equations for the spatially homogeneous Kantowski-Sachs models using appropriate bounded normalized variables. We then analyse these models, with special emphasis on the future asymptotic behaviour for different values of the parameters. Finally, we investigate static models for a mixture of a (necessarily non-tilted) perfect fluid with a barotropic equations of state and a scalar field.
Spherically symmetric simulation of plasma liner driven magnetoinertial fusion
Samulyak, Roman; Parks, Paul; Wu Lingling
2010-09-15
Spherically symmetric simulations of the implosion of plasma liners and compression of plasma targets in the concept of the plasma jet driven magnetoinertial fusion have been performed using the method of front tracking. The cases of single deuterium and xenon liners and double layer deuterium-xenon liners compressing various deuterium-tritium targets have been investigated, optimized for maximum fusion energy gains, and compared with theoretical predictions and scaling laws of [P. Parks, Phys. Plasmas 15, 062506 (2008)]. In agreement with the theory, the fusion gain was significantly below unity for deuterium-tritium targets compressed by Mach 60 deuterium liners. The most optimal setup for a given chamber size contained a target with the initial radius of 20 cm compressed by a 10 cm thick, Mach 60 xenon liner, achieving a fusion energy gain of 10 with 10 GJ fusion yield. Simulations also showed that composite deuterium-xenon liners reduce the energy gain due to lower target compression rates. The effect of heating of targets by alpha particles on the fusion energy gain has also been investigated.
Rovibrational states of Wigner molecules in spherically symmetric confining potentials.
Cioslowski, Jerzy
2016-08-01
The strong-localization limit of three-dimensional Wigner molecules, in which repulsively interacting particles are confined by a weak spherically symmetric potential, is investigated. An explicit prescription for computation of rovibrational wavefunctions and energies that are asymptotically exact at this limit is presented. The prescription is valid for systems with arbitrary angularly-independent interparticle and confining potentials, including those involving Coulombic and screened (i.e., Yukawa/Debye) interactions. The necessary derivations are greatly simplified by explicit constructions of the Eckart frame and the parity-adapted primitive wavefunctions. The performance of the new formalism is illustrated with the three- and four-electron harmonium atoms at their strong-correlation limits. In particular, the involvement of vibrational modes with the E symmetry is readily pinpointed as the origin of the "anomalous" weak-confinement behavior of the (1)S+ state of the four-electron species that is absent in its (1)D+ companion of the strong-confinement regime. PMID:27497548
Velocity and velocity bounds in static spherically symmetric metrics
NASA Astrophysics Data System (ADS)
Arraut, Ivan; Batic, Davide; Nowakowski, Marek
2011-08-01
We find simple expressions for velocity of massless particles with dependence on the distance, r, in Schwarzschild coordinates. For massive particles these expressions give an upper bound for the velocity. Our results apply to static spherically symmetric metrics. We use these results to calculate the velocity for different cases: Schwarzschild, Schwarzschild-de Sitter and Reissner-Nordström with and without the cosmological constant. We emphasize the differences between the behavior of the velocity in the different metrics and find that in cases with naked singularity there always exists a region where the massless particle moves with a velocity greater than the velocity of light in vacuum. In the case of Reissner-Nordström-de Sitter we completely characterize the velocity and the metric in an algebraic way. We contrast the case of classical naked singularities with naked singularities emerging from metric inspired by noncommutative geometry where the radial velocity never exceeds one. Furthermore, we solve the Einstein equations for a constant and polytropic density profile and calculate the radial velocity of a photon moving in spaces with interior metric. The polytropic case of radial velocity displays an unexpected variation bounded by a local minimum and maximum.
Generation of spherically symmetric metrics in f( R) gravity
NASA Astrophysics Data System (ADS)
Amirabi, Z.; Halilsoy, M.; Mazharimousavi, S. Habib
2016-06-01
In D-dimensional spherically symmetric f( R) gravity there are three unknown functions to be determined from the fourth order differential equations. It is shown that the system remarkably may be integrated to relate two functions through the third one to provide a reduction to second order equations accompanied with a large class of potential solutions. The third function, which acts as the generator of the process, is F(R) =mathrm{d}f(R)/dR. We recall that our generating function has been employed as a scalar field with an accompanying self-interacting potential previously, which is entirely different from our approach. Reduction of f( R) theory into a system of equations seems to be efficient enough to generate a solution corresponding to each generating function. As particular examples, besides the known ones, we obtain new black hole solutions in any dimension D. We further extend our analysis to cover non-zero energy-momentum tensors. Global monopole and Maxwell sources are given as examples.
Rovibrational states of Wigner molecules in spherically symmetric confining potentials
NASA Astrophysics Data System (ADS)
Cioslowski, Jerzy
2016-08-01
The strong-localization limit of three-dimensional Wigner molecules, in which repulsively interacting particles are confined by a weak spherically symmetric potential, is investigated. An explicit prescription for computation of rovibrational wavefunctions and energies that are asymptotically exact at this limit is presented. The prescription is valid for systems with arbitrary angularly-independent interparticle and confining potentials, including those involving Coulombic and screened (i.e., Yukawa/Debye) interactions. The necessary derivations are greatly simplified by explicit constructions of the Eckart frame and the parity-adapted primitive wavefunctions. The performance of the new formalism is illustrated with the three- and four-electron harmonium atoms at their strong-correlation limits. In particular, the involvement of vibrational modes with the E symmetry is readily pinpointed as the origin of the "anomalous" weak-confinement behavior of the 1S+ state of the four-electron species that is absent in its 1D+ companion of the strong-confinement regime.
Alexandre, Jean; Pasipoularides, Pavlos
2011-10-15
In this note we examine whether spherically symmetric solutions in covariant Horava-Lifshitz gravity can reproduce Newton's Law in the IR limit {lambda}{yields}1. We adopt the position that the auxiliary field A is independent of the space-time metric [J. Alexandre and P. Pasipoularides, Phys. Rev. D 83, 084030 (2011).][J. Greenwald, V. H. Satheeshkumar, and A. Wang, J. Cosmol. Astropart. Phys. 12 (2010) 007.], and we assume, as in [A. M. da Silva, Classical Quantum Gravity 28, 055011 (2011).], that {lambda} is a running coupling constant. We show that under these assumptions, spherically symmetric solutions fail to restore the standard Newtonian physics in the IR limit {lambda}{yields}1, unless {lambda} does not run, and has the fixed value {lambda}=1. Finally, we comment on the Horava and Melby-Thompson approach [P. Horava and C. M. Melby-Thompson, Phys. Rev. D 82, 064027 (2010).] in which A is assumed as a part of the space-time metric in the IR.
Time-dependent spherically symmetric accretion onto compact X-ray sources
NASA Technical Reports Server (NTRS)
Cowie, L. L.; Ostriker, J. P.; Stark, A. A.
1978-01-01
Analytical arguments and a numerical hydrodynamic code are used to investigate spherically symmetric accretion onto a compact object, in an attempt to provide some insight into gas flows heated by an outgoing X-ray flux. It is shown that preheating of spherically symmetric accretion flows by energetic radiation from an X-ray source results in time-dependent behavior for a much wider range of source parameters than was determined previously and that there are two distinct types of instability. The results are compared with observations of X-ray bursters and transients as well as with theories on quasars and active galactic nuclei that involve quasi-spherically symmetric accretion onto massive black holes. Models based on spherically symmetric accretion are found to be inconsistent with observations of bursters and transients.
Bisnovatyi-Kogan, Gennady S.
2009-09-20
We construct numerical models of spherically symmetric Newtonian stellar clusters with anisotropic distribution functions. These models generalize solutions obtained earlier for isotropic Maxwellian distribution functions with an energy cutoff and take into account distributions with different levels of anisotropy.
Stability of spherically symmetric, charged black holes and multipole moments for stationary systems
Gursel, H.Y.
1983-01-01
This dissertation is written in two parts. Part I deals with the question of stability of a spherically symmetric, charged black hole against scalar, electromagnetic, and gravitational perturbations. It consists of two papers written in collaboration with Igor D. Novikov, Vernon D. Sandberg and A.A. Starobinsky. In these papers the dynamical evolution of these perturbations on the interior of a Reissner-Nordstrom black hole is described. The instability of the hole's Cauchy horizon is discussed in detail in terms of the energy densities of the test fields as measured by a freely falling observer approaching the Cauchy horizon. It is concluded that the Cauchy horizon of the analytically extended Reissner-Nordstrom solution is highly unstable and not a physical feature of a realistic gravitational collapse. Part II of this dissertation addresses two problems closely connected with multipole structure of stationary, asymptotically flat spacetimes. It consists of two papers written in collaboration with Kip S. Thorne. The first one shows the equivalence of the moments defined by Kip S. Thorne and the moments defined by Robert Geroch and Richard Hansen. The second proves a conjecture by Kip S. Thorne: In the limit of ''slow'' motion, general relativistic gravity produces no changes whatsoever in the classical Euler equations of rigid body motion. This conjecture is proved by giving an algorithm for generating rigidly rotating solutions of Einstein's equation from nonrotating, static solutions.
Spin Entanglement with {PT} Symmetric Hamiltonian in a Curved Static Space-Time
NASA Astrophysics Data System (ADS)
Mebarki, N.; Morchedi, A.; Aissaoui, H.
2015-11-01
Entanglement of spin systems in a curved static space-time with {PT} symmetric Hamiltonian is studied. It turns out that although a bipartite initial state is non entangled, one can generate in general a non vanishing ebit of entanglement through an elapsed proper time evolution. To be more specific an application of a pure state time evolution of a wave packet in a circular geodesic motion in a Schwarchild metric and {PT} symmetric spin Hamiltonian is considered and the corresponding von Newman entanglement entropy is studied.
G-factors of hole bound states in spherically symmetric potentials in cubic semiconductors
NASA Astrophysics Data System (ADS)
Miserev, Dmitry; Sushkov, Oleg
2016-03-01
Holes in cubic semiconductors have effective spin 3/2 and very strong spin orbit interaction. Due to these factors properties of hole bound states are highly unusual. We consider a single hole bound by a spherically symmetric potential, this can be an acceptor or a spherically symmetric quantum dot. Linear response to an external magnetic field is characterized by the bound state Lande g-factor. We calculate analytically g-factors of all bound states.
Static spherically symmetric thin shell wormhole colliding with a spherical thin shell
NASA Astrophysics Data System (ADS)
Wang, Xiaobao; Gao, Sijie
2016-03-01
We consider a static spherically symmetric thin shell wormhole that collides with another thin shell consisting of ordinary matter. By employing the geometrical constraint, which leads to the conservation of energy and momentum, we show that the state after the collision can be solved from the initial data. In the low speed approximation, the solutions are rather simple. The shell may either bounce back or pass through the wormhole. In either case, the wormhole shrinks right after the collision. In the "bouncing" case, a surprising result is that the radial speeds before and after the collision satisfy an addition law, which is independent of other parameters of the wormhole and the shell. Once the shell passes through the wormhole, we find that the shell always expands. However, the expansion rate is the same as its collapsing rate right before the collision. Finally, we find the solution for the shell moving together with the wormhole. This work sheds light on the interaction between wormholes and matter.
Exact solution for the Casimir stress in a spherically symmetric medium
NASA Astrophysics Data System (ADS)
Leonhardt, Ulf; Simpson, William M. R.
2011-10-01
We calculated the stress of the quantum vacuum, the Casimir stress, in a spherically symmetric medium, Maxwell’s fish eye, surrounded by a perfect mirror and derived an exact analytic solution. Our solution questions the idea that the Casimir force of a spherical mirror is repulsive—we found an attractive stress in the medium that diverges at the mirror.
NASA Astrophysics Data System (ADS)
Erices, Cristián; Martínez, Cristián
2015-08-01
The general stationary cylindrically symmetric solution of Einstein-massless scalar field system with a nonpositive cosmological constant is presented. It is shown that the general solution is characterized by four integration constants. Two of these essential parameters have a local meaning and characterize the gravitational field strength. The other two have a topological origin, as they define an improper coordinate transformation that provides the stationary solution from the static one. The Petrov scheme is considered to explore the effects of the scalar field on the algebraic classification of the solutions. In general, these spacetimes are of type I. However, the presence of the scalar field allows us to find a nonvacuum type O solution and a wider family of type D spacetimes, in comparison with the vacuum case. The mass and angular momentum of the solution are computed using the Regge-Teitelboim method in the case of a negative cosmological constant. In absence of a cosmological constant, the curvature singularities in the vacuum solutions can be removed by including a phantom scalar field, yielding nontrivial locally homogeneous spacetimes. These spacetimes are of particular interest, as they have all their curvature invariants constant.
NASA Astrophysics Data System (ADS)
Ali, Ahmad T.; Rahaman, F.; Mallick, A.
2016-05-01
We have studied the conformal, homothetic and Killing vectors in the context of teleparallel theory of gravitation for plane-symmetric static spacetimes. We have solved completely the non-linear coupled teleparallel conformal Killing equations. This yields the general form of teleparallel conformal vectors along with the conformal factor for all possible cases of metric functions. We have found four solutions which are divided into one Killing symmetries and three conformal Killing symmetries. One of these teleparalel conformal vectors depends on x only and other is a function of all spacetime coordinates. The three conformal Killing symmetries contain three proper homothetic symmetries where the conformal factor is an arbitrary non-zero constant.
Microphase separations of the fluids with spherically symmetric competing interactions.
Kim, Soon-Chul; Suh, Soong-Hyuck; Seong, Baek-Seok
2012-09-21
A density functional perturbation theory has been developed for studying the phase behaviors of a competing system in the spherical pores. The pore size as well as the intensity of competing interactions exerts a strong influence on the vapor-liquid, vapor-cluster, and cluster-liquid transitions of a competing system. The microdomain spacing (D) of the cluster is commensurate with the periodicity of modulation in the particle density distributions of a competing system in a spherical pore with the pore radius (R). For the cluster phase, we find that the multi-vaporlike void is formed depending on the periodicity of modulation by finite-size artifacts. For R < D, the competing system only shows the vapor-liquid transition at a high amplitude. For R > D, the vapor-cluster and cluster-liquid transitions are found at a high amplitude, whereas at a low amplitude, the cluster-liquid transition only occurs. The competing system exhibits two tricritical points, which are joined to one another by the line of second-order transitions at the low and high densities. A comparison with the result of a slit pore shows that (i) the tricritical points in a spherical pore, which has the highest symmetry, occur at a low amplitude compared with that of a slit pore because of the geometrical properties of the pores, and that (ii) the slit pore relatively shows the wide vapor-cluster and cluster-liquid coexistence regions compared with that of a spherical pore: the geometrical symmetry of a pore results in a weaker tendency for phase separation. PMID:22998277
Stability of spherically symmetric, charged black holes and multipole moments for stationary systems
NASA Astrophysics Data System (ADS)
Gursel, Yekta
This dissertation is written in two parts. Part I deals with the question of stability of a spherically symmetric, charged black hole against scalar, electromagnetic, and gravitational perturbations. It consists of two papers written in collaboration with Igor D. NoVikov, Vernon D. Sandberg and A. A. Starobinsky. In these papers we describe the dynamical evolution of these perturbations on the interior of a Reissner-Nordstrom black hole. The instability of the hole's Cauchy horizon is discussed in detail in terms of the energy densities of the test fields as measured by a freely falling observer approaching the Cauchy horizon. We conclude that the Cauchy horizon of the analytically extended Reissner-Nordstrom solution is highly unstable and not a physical feature of a realistic gravitational collapse. Part II of this dissertation addresses two problems closely connected with muitipole structure of stationary, asymptotically flat spacetimes. It consists of two papers written in collaboration with Kip S. Thorne despite the fact that his name does not appear on one of them. The first one (Paper III in this thesis) shows the equivalence of the moments defined by Kip S. Thorne and the moments defined by Robert Geroch and Richard Hansen. The second (Paper IV in this thesis) proves a conjecture by Kip S. Thorne: In the limit of "slow" motion, general relativistic gravity produces no changes whatsoever in the classical Euler equations of rigid body motion. We prove this conjecture by giving an algorithm for generating rigidly rotating solutions of Einstein's equations from nonrotating, static solutions.
Spherically symmetric black holes in f (R) gravity: is geometric scalar hair supported?
NASA Astrophysics Data System (ADS)
Cañate, Pedro; Jaime, Luisa G.; Salgado, Marcelo
2016-08-01
We critically discuss current research on black hole (BH) solutions in f (R) gravity and shed light on its geometrical and physical significance. We also investigate the meaning, existence or lack thereof of Birkhoff’s theorem (BT) in this kind of modified gravity. We then focus on the analysis and search for non-trivial (i.e. hairy) asymptotically flat (AF) BH solutions in static and spherically symmetric (SSS) spacetimes in vacuum having the property that the Ricci scalar does not vanish identically in the domain of outer communication. To do so, we provide and enforce regularity conditions at the horizon in order to prevent the presence of singular solutions there. Specifically, we consider several classes of f (R) models like those proposed recently for explaining the accelerated expansion in the Universe and which have been thoroughly tested in several physical scenarios. Finally, we report analytical and numerical evidence about the absence of geometric hair in AFSSSBH solutions in those f (R) models. First, we submit the models to the available no-hair theorems (NHTs), and in the cases where the theorems apply, the absence of hair is demonstrated analytically. In the cases where the theorems do not apply, we resort to a numerical analysis due to the complexity of the non-linear differential equations. With that aim, a code to solve the equations numerically was built and tested using well-known exact solutions. In a future investigation we plan to analyze the problem of hair in de Sitter and anti-de Sitter backgrounds.
Analytic treatment of complete geodesics in a static cylindrically symmetric conformal spacetime
NASA Astrophysics Data System (ADS)
Hoseini, Bahareh; Saffari, Reza; Soroushfar, Saheb; Grunau, Saskia; Kunz, Jutta
2016-08-01
We consider the motion of test particles and light rays in a static cylindrically symmetric conformal spacetime given by Said et al. [Phys. Rev. D 85, 104054 (2012)]. We derive the equations of motion and present their analytical solutions in terms of the Weierstrass ℘ function and the Kleinian σ function. Using parametric diagrams and effective potentials, we analyze the possible orbits and characterize them in terms of the energy and the angular momentum of the test particles. Finally, we show some examples of orbits.
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 }\
Simulating irradiance during lunar eclipses: the spherically symmetric case.
Vollmer, Michael; Gedzelman, Stanley David
2008-12-01
Irradiance during total lunar eclipses is simulated using a pinhole model. The Moon is illuminated by direct sunlight that is refracted into the Earth's shadow as it passes through the atmosphere at the terminator but is depleted by scattering by molecules, extinction by aerosol particles, absorption by ozone, and obstruction by clouds and elevated land. On a spherical, sea-level Earth, and a cloudless, molecular atmosphere with no ozone, the eclipsed Moon appears red and calculated irradiance at the center of the umbra is reduced by a factor of about 2400 from direct moonlight. Selective absorption mainly of light around 600 nm by stratospheric ozone turns the periphery of the umbra pale blue. Typical distributions of aerosol particles, ozone, mountains, and clouds around the terminator reduce irradiance by an additional factor of the order of 100. PMID:19037351
Critical collapse in the spherically symmetric Einstein-Vlasov model
NASA Astrophysics Data System (ADS)
Akbarian, Arman; Choptuik, Matthew W.
2014-11-01
We solve the coupled Einstein-Vlasov system in spherical symmetry using direct numerical integration of the Vlasov equation in phase space. Focusing on the case of massless particles we study critical phenomena in the model, finding strong evidence for generic type I behavior at the black hole threshold that parallels what has previously been observed in the massive sector. For differing families of initial data we find distinct critical solutions, so there is no universality of the critical configuration itself. However we find indications of at least a weak universality in the lifetime scaling exponent, which is yet to be understood. Additionally, we clarify the role that angular momentum plays in the critical behavior in the massless case.
NASA Astrophysics Data System (ADS)
Yadav, R. B. S.; Prasad, U.
1993-05-01
The nonstatic conformally flat spherically symmetric perfect fluid distribution in Einstein-Cartan theory is considered, and the field equations and their general solution are obtained using Hehl's approach (1974). Particular attention is given to the solution in co-moving coordinates and the explicit expressions for pressure, density, expansion, rotation, and shear and nonzero components of flow vector.
Conformally flat static spherically symmetric perfect-fluid distribution in Einstein-Cartan theory
NASA Astrophysics Data System (ADS)
Kalyanshetti, S. B.; Waghmode, B. B.
1983-06-01
We consider the static, conformally flat spherically symmetric perfect-fluid distribution in Einstein-Cartan theory and obtain the field equations. These field equations are solved by adopting Hehl's approach with the assumption that the spins of the particles composing the fluid are all aligned in the radial direction only and the reality conditions are discussed.
The general class of the vacuum spherically symmetric equations of the general relativity theory
Karbanovski, V. V. Sorokin, O. M.; Nesterova, M. I.; Bolotnyaya, V. A.; Markov, V. N. Kairov, T. V.; Lyash, A. A.; Tarasyuk, O. R.
2012-08-15
The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g{sub 00} and g{sub 22} is obtained. The properties of the found solutions are analyzed.
Existence of spherically symmetric solutions for a reduced gravity two-and-a-half layer system
NASA Astrophysics Data System (ADS)
Yao, Lei; Li, Zilai; Wang, Wenjun
2016-08-01
In this paper, we consider the well-posedness of solutions to a reduced gravity two-and-a-half layer system in oceanic fluid dynamics. By constructing suitable approximate solutions and using the method of weak convergence, we obtain the global existence of weak solutions in two-dimensional exterior spatial domain, when the initial data are large and spherically symmetric.
Jiang, Zhong-Xing; Yu, Y. Bruce
2010-01-01
Two novel, highly fluorinated macrocyclic chelators with highly branched and spherically symmetric fluorocarbon moieties have been designed and efficiently synthesized. This is achieved by conjugating a spherically symmetric fluorocarbon moiety to the macrocyclic chelator DOTA, with or without a flexible oligo-oxyethylene linker between these two parts. As a result of the spherical symmetry, all 27 fluorine atoms in each fluorinated chelator give a sharp singlet 19F NMR signal. The hydrophilicity and the 19F relaxation behavior of fluorinated chelators can be modulated by the insertion of a flexible linker between the fluorocarbon moiety and the macrocyclic linker. These chelators serve as prototypes for 1H-19F dual-nuclei magnetic resonance imaging agents. PMID:20585414
Seifert, Michael D.; Wald, Robert M.
2007-04-15
We present a general method for the analysis of the stability of static, spherically symmetric solutions to spherically symmetric perturbations in an arbitrary diffeomorphism covariant Lagrangian field theory. Our method involves fixing the gauge and solving the linearized gravitational field equations to eliminate the metric perturbation variables in terms of the matter variables. In a wide class of cases--which include f(R) gravity, the Einstein-aether theory of Jacobson and Mattingly, and Bekenstein's TeVeS theory--the remaining perturbation equations for the matter fields are second order in time. We show how the symplectic current arising from the original Lagrangian gives rise to a symmetric bilinear form on the variables of the reduced theory. If this bilinear form is positive definite, it provides an inner product that puts the equations of motion of the reduced theory into a self-adjoint form. A variational principle can then be written down immediately, from which stability can be tested readily. We illustrate our method in the case of Einstein's equation with perfect fluid matter, thereby rederiving, in a systematic manner, Chandrasekhar's variational principle for radial oscillations of spherically symmetric stars. In a subsequent paper, we will apply our analysis to f(R) gravity, the Einstein-aether theory, and Bekenstein's TeVeS theory.
The Design and Synthesis of Highly Branched and Spherically Symmetric Fluorinated Oils and Amphiles
Jiang, Zhong-Xing; Yu, Y. Bruce
2007-01-01
A new emulsifier design principle, based on concepts borrowed from protein science, is proposed. Using this principle, a class of highly branched and spherically symmetric fluorinated oils and amphiles has been designed and synthesized, for potential applications in the construction of fluorocarbon nanoparticles. The Mitsunobu reaction was employed as the key step for introducing three perfluoro-tert-butoxyl groups into pentaerythritol derivatives with excellent yields and extremely simple isolation procedures. Due to the symmetric arrangement of the fluorine atoms, each fluorinated oil or amphile molecule gives one sharp singlet 19F NMR signal. PMID:18461118
NASA Technical Reports Server (NTRS)
Gross, M. W.; Lee, M. A.; Lerche, I.
1977-01-01
Exact analytical solutions are presented for the standard time-independent spherically symmetric convection-diffusion-adiabatic deceleration equation governing the transport of cosmic rays in the interplanetary medium for the case in which particles are produced with spherical symmetry at the sun. It is assumed that the solar-wind speed is constant and radial, and that the spatial diffusion coefficient has a power-law dependence on momentum. The Green's function describing the modulation of a monoenergetic production of particles is presented. The solutions provide a useful basis for the study of time-integrated properties of energetic solar-flare particle spectra.
X-ray resonance scattering in a spherically symmetric coronal model
NASA Technical Reports Server (NTRS)
Haisch, B. M.; Claflin, E. S.
1985-01-01
In the solar corona the opacities of some of the prominent X-ray emission lines are on the order of tau of about I over typical coronal path lengths. A particular solution of the radiative transfer problem involving an extended, spherically symmetric coronal shell radiating isotropic, homogeneous emission in which single-scattering also takes place is presented and discussed. Within the context of this simplified model, it is found that scattered radiation is an important contribution to the total emergent resonance line flux and that for the He-like family of resonance (r), intercombination (i), and forbidden (f) lines, the ratio G = (f + i)/r would decrease as a function of optical depth for disk-center emission in an extended spherically symmetric corona.
Spherically symmetric self-dual Yang-Mills instantons on curved backgrounds in all even dimensions
Radu, Eugen; Tchrakian, D. H.; Yang Yisong
2008-02-15
We present several different classes of self-dual Yang-Mills instantons in all even d-dimensional backgrounds with Euclidean signature. In d=4p+2 the only solutions we found are on constant curvature dS (de Sitter) and AdS (anti-de Sitter) backgrounds and are evaluated in closed form. In d=4p an interesting class of instantons are given on black hole backgrounds. One class of solutions are (Euclidean) time-independent and spherically symmetric in d-1 dimensions, and the other class are spherically symmetric in all d dimensions. Some of the solutions in the former class are evaluated numerically, all the rest being given in closed form. Analytic proofs of existence covering all numerically evaluated solutions are given. All instantons studied have finite action and vanishing energy momentum tensor and do not disturb the geometry.
Maeda, Hideki
2006-05-15
We give a model of the higher-dimensional spherically symmetric gravitational collapse of a dust cloud including the perturbative effects of quantum gravity. The n({>=}5)-dimensional action with the Gauss-Bonnet term for gravity is considered and a simple formulation of the basic equations is given for the spacetime M{approx_equal}M{sup 2}xK{sup n-2} with a perfect fluid and a cosmological constant. This is a generalization of the Misner-Sharp formalism of the four-dimensional spherically symmetric spacetime with a perfect fluid in general relativity. The whole picture and the final fate of the gravitational collapse of a dust cloud differ greatly between the cases with n=5 and n{>=}6. There are two families of solutions, which we call plus-branch and the minus-branch solutions. A plus-branch solution can be attached to the outside vacuum region which is asymptotically anti-de Sitter in spite of the absence of a cosmological constant. Bounce inevitably occurs in the plus-branch solution for n{>=}6, and consequently singularities cannot be formed. Since there is no trapped surface in the plus-branch solution, the singularity formed in the case of n=5 must be naked. On the other hand, a minus-branch solution can be attached to the outside asymptotically flat vacuum region. We show that naked singularities are massless for n{>=}6, while massive naked singularities are possible for n=5. In the homogeneous collapse represented by the flat Friedmann-Robertson-Walker solution, the singularity formed is spacelike for n{>=}6, while it is ingoing-null for n=5. In the inhomogeneous collapse with smooth initial data, the strong cosmic censorship hypothesis holds for n{>=}10 and for n=9 depending on the parameters in the initial data, while a naked singularity is always formed for 5{<=}n{<=}8. These naked singularities can be globally naked when the initial surface radius of the dust cloud is fine-tuned, and then the weak cosmic censorship hypothesis is violated.
NASA Astrophysics Data System (ADS)
Fucci, Guglielmo; Kirsten, Klaus
2016-07-01
In this paper we analyze the spectral zeta function associated with a Laplace operator acting on scalar functions on an N-dimensional Euclidean space in the presence of a spherically symmetric background potential. The obtained analytic continuation of the spectral zeta function is then used to derive very simple results for the functional determinant of the operator and the Casimir energy of the scalar field.
On heat conduction in multicomponent, non-Maxwellian spherically symmetric solar wind plasmas
NASA Technical Reports Server (NTRS)
Cuperman, S.; Dryer, M.
1985-01-01
A generalized expression for the steady-state heat flux in multicomponent, moderately non-Maxwellian spherically symmetric plasmas is presented and discussed. The work was motivated by the inability of the simple, Fourier-type formula for the thermal conductivity to explain the observed correlations in the solar wind. The results hold for situations not far from local thermodynamic equilibrium. The generalized expression includes not only correlations that have been observed but also correlations not sought for previously.
SOLA-STAR: a one-dimensional ICED-ALE hydrodynamics program for spherically symmetric flows
Cloutman, L.D.
1980-07-01
This report describes a simple, general-purpose, and efficient algorithm for solving one-dimensional spherically symmetric, transient fluid-dynamics problems using a variation of the ICED-ALE technique. Included are the finite difference equations, three test problems that illustrate various capabilities of the program, and a complete code description, including a listing, sample data decks and output, a summary of important variable names, and hints for conversion to other operating systems.
Functional derivative of the kinetic energy functional for spherically symmetric systems.
Nagy, Á
2011-07-28
Ensemble non-interacting kinetic energy functional is constructed for spherically symmetric systems. The differential virial theorem is derived for the ensemble. A first-order differential equation for the functional derivative of the ensemble non-interacting kinetic energy functional and the ensemble Pauli potential is presented. This equation can be solved and a special case of the solution provides the original non-interacting kinetic energy of the density functional theory. PMID:21806089
Spherically symmetric analysis on open FLRW solution in non-linear massive gravity
Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin E-mail: izumi@phys.ntu.edu.tw
2012-12-01
We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity from general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.
Spherical Symmetric Perfect Fluid Collapse in f(R, T) Gravity
NASA Astrophysics Data System (ADS)
Amir, M. Jamil; Sattar, Sadia
2016-04-01
This paper contains the study of spherically symmetric perfect fluid collapse in the frame work of f(R, T) modified theory of gravity. We proceed our work by considering the non-static spherically symmetric background in the interior and static spherically symmetric background in the exterior regions of the star. The junction conditions between exterior and interior regions are presented by matching the exterior and interior regions. The field equations are solved by taking the assumptions that the Ricci scalar as well as the trace of energy-momentum tensor are to be constant, for a particular f(R, T) model. By inserting the solution of the field equations in junction conditions, we evaluate the gravitational mass of the collapsing system. Also, we discuss the apparent horizons and their time formation for different possible cases. It is concluded that the term f(R 0, T 0) behaves as a source of repulsive force and that's why it slowdowns the collapse of the matter.
NASA Astrophysics Data System (ADS)
Burikham, Piyabut; Cheamsawat, Krai; Harko, Tiberiu; Lake, Matthew J.
2016-03-01
We obtain bounds for the minimum and maximum mass/radius ratio of a stable, charged, spherically symmetric compact object in a D-dimensional space-time in the framework of general relativity, and in the presence of dark energy. The total energy, including the gravitational component, and the stability of objects with minimum mass/radius ratio is also investigated. The minimum energy condition leads to a representation of the mass and radius of the charged objects with minimum mass/radius ratio in terms of the charge and vacuum energy only. As applied to the electron in the four-dimensional case, this procedure allows one to re-obtain the classical electron radius from purely general relativistic considerations. By combining the lower mass bound, in four space-time dimensions, with minimum length uncertainty relations (MLUR) motivated by quantum gravity, we obtain an alternative bound for the maximum charge/mass ratio of a stable, gravitating, charged quantum mechanical object, expressed in terms of fundamental constants. Evaluating this limit numerically, we obtain again the correct order of magnitude value for the charge/mass ratio of the electron, as required by the stability conditions. This suggests that, if the electron were either less massive (with the same charge) or if its charge were any higher (for fixed mass), a combination of electrostatic and dark energy repulsion would destabilize the Compton radius. In other words, the electron would blow itself apart. Our results suggest the existence of a deep connection between gravity, the presence of the cosmological constant, and the stability of fundamental particles.
NASA Astrophysics Data System (ADS)
Kawai, K.; Takeuchi, N.; Geller, R. J.
2002-12-01
The existence of anisotropy has been suggested in many regions in the Earth. Determining the anisotropic seismic velocity structure of the Earth can contribute to our understanding of geodynamics and rheology. Inversion of observed seismic waveforms is a promising approach for determining the Earth's anisotropic structure, but development of computational algorithms and software for computing synthetic seismograms in anisotropic media is required. Software for computing seismic waveforms in isotropic media based on the Direct Solution Method (DSM; Geller and Ohminato 1994, GJI) has previously been developed and is being used in data analysis, but DSM software for computing synthetic seismograms for anisotropic media has not yet been developed. In this study, we derive algorithms and develop software for computing synthetics for transversely isotropic spherically symmetric media. Our derivation follows previous work for isotropic media (Takeuchi et al. 1996, GRL; Cummins et al. 1997, GJI). The displacement is represented using spherical harmonics for the lateral dependence and linear spline functions for the vertical dependence of the trial functions. The numerical operators derived using these trial functions are then replaced by optimally accurate operators (Geller and Takeuchi 1995, GJI; Takeuchi and Geller 2002, GJI, submitted). Although the number of elastic constants increases from 2 to 5, the numerical operators are basically identical to those for the isotropic case. Our derivation does not require approximations that treat the anisotropic or laterally heterogeneous structure as an infinitesimal perturbation to the isotropic structure. Only spherically symmetric models are considered in this paper, but when our methods can be extended to the 3-D case to permit computation of synthetic seismograms with the same accuracy as for spherically symmetric isotropic models. We present computational examples such as accuracy checks and also some applications to
NASA Astrophysics Data System (ADS)
Shabbir, Ghulam; Khan, Alamgeer; Amer Qureshi, M.; Kara, A. H.
2016-02-01
In this paper, we explore teleparallel conformal vector fields in non-static plane symmetric space-times in the teleparallel theory of gravitation using the direct integration technique and diagonal tetrads. This study will also cover the static plane symmetric space-times as well. In the teleparallel theory curvature of the non-static plane symmetric space-times is zero and the presence of torsion allows more symmetries. In this study after solving the integrabilty conditions it turns out that the dimension of teleparallel conformal vector fields are 5, 6, 7 or 8.
NASA Astrophysics Data System (ADS)
Sen, K. K., Wilson, S. J.
The advancement of observational techniques over the years has led to the discovery of a large number of stars exhibiting complex spectral structures, thus necessitating the search for new techniques and methods to study radiative transfer in such stars with moving envelopes. This led to the introduction of the concept of "photon escape probability" and the wisdom of expressing the transfer equations in "comoving frames" (CMF). Radiative transfer problems in spherically moving media form a branch of mathematical physics which uses mathematics of a very distinctive kind. Radiative Transfer in Moving Media records the basic mathematical methodologies, both analytical and numerical, developed for solving radiation transfer problems in spherically symmetric moving media, in the consideration of macroscopic velocity fields only. Part I contains the basic notions of radiation-matter interaction in participating media and constructs the relevant transfer equations to be solved in the subsequent chapters. Part II considers the basic mathematical methods for solving the transfer problems in extensive moving atmospheres when it is observed in the lab frame. Part III introduces the analytical and numerical methods for solving radiative transfer problems in spherically symmetric moving atmospheres when expressed in the comoving frame. This book is addressed to graduate students and researchers in Astrophysics, in particular to those studying radiative transfer in stellar atmospheres.
Beyond Extreme Ultra Violet (BEUV) Radiation from Spherically symmetrical High-Z plasmas
NASA Astrophysics Data System (ADS)
Yoshida, Kensuke; Fujioka, Shinsuke; Higashiguchi, Takeshi; Ugomori, Teruyuki; Tanaka, Nozomi; Kawasaki, Masato; Suzuki, Yuhei; Suzuki, Chihiro; Tomita, Kentaro; Hirose, Ryouichi; Eshima, Takeo; Ohashi, Hayato; Nishikino, Masaharu; Scally, Enda; Nshimura, Hiroaki; Azechi, Hiroshi; O'Sullivan, Gerard
2016-03-01
Photo-lithography is a key technology for volume manufacture of high performance and compact semiconductor devices. Smaller and more complex structures can be fabricated by using shorter wavelength light in the photolithography. One of the most critical issues in development of the next generation photo-lithography is to increase energy conversion efficiency (CE) from laser to shorter wavelength light. Experimental database of beyond extreme ultraviolet (BEUV) radiation was obtained by using spherically symmetrical high-Z plasmas generated with spherically allocated laser beams. Absolute energy and spectra of BEUV light emitted from Tb, Gd, and Mo plasmas were measured with a absolutely calibrated BEUV calorimeter and a transmission grating spectrometer. 1.0 x 1012 W/cm2 is the optimal laser intensity to produced efficient BEUV light source plasmas with Tb and Gd targets. Maximum CE is achieved at 0.8% that is two times higher than the published CEs obtained with planar targets.
A fully general relativistic numerical simulation code for spherically symmetric matter
NASA Astrophysics Data System (ADS)
Park, Dong-Ho; Cho, Inyong; Kang, Gungwon; Lee, Hyung Mok
2013-02-01
We present a fully general relativistic open-source code that can be used for simulating a system of spherically symmetric perfect fluid matter. It is based on the Arnowitt-Deser-Misner 3+1 formalism with maximal slicing and isotropic spatial coordinates. For hydrodynamic matter High Resolution Shock Capturing (HRSC) schemes with a monotonized central-difference limiter and approximated Riemann solvers are used in the Eulerian viewpoint. The accuracy and the convergence of our numerical code are verified by performing several test problems. These include a relativistic blast wave, relativistic spherical accretion of matter into a black hole, Tolman-Oppenheimer-Volkoff (TOV) stars and Oppenheimer-Snyder (OS) dust collapses. In particular, a dynamical code test is done for the OS collapse by explicitly performing numerical coordinate transformations between our coordinate 8system and the one used for the analytic solution. Finally, some TOV star solutions are presented for the Eddington-inspired Born-Infeld gravity theory.
Complete synthetic seismograms up to 2 Hz for transversely isotropic spherically symmetric media
NASA Astrophysics Data System (ADS)
Kawai, Kenji; Takeuchi, Nozomu; Geller, Robert J.
2006-02-01
We use the direct solution method (DSM) with optimally accurate numerical operators to calculate complete (including both body and surface waves) three-component synthetic seismograms for transversely isotropic (TI), spherically symmetric media, up to 2 Hz. We present examples of calculations for both deep (600 km) and shallow (5 km) sources. Such synthetics should be useful in forward and inverse studies of earth structure. In order to make these calculations accurately and efficiently the vertical grid spacing, maximum angular order, and cut-off depth must be carefully and systematically chosen.
Static spherically symmetric Kerr-Schild metrics and implications for the classical double copy
NASA Astrophysics Data System (ADS)
Ridgway, Alexander K.; Wise, Mark B.
2016-08-01
We discuss the physical interpretation of stress-energy tensors that source static spherically symmetric Kerr-Schild metrics. We find that the sources of such metrics with no curvature singularities or horizons do not simultaneously satisfy the weak and strong energy conditions. Sensible stress-energy tensors usually satisfy both of them. Under most circumstances, these sources are not perfect fluids and contain shear stresses. We show that for these systems the classical double copy associates the electric charge density to the Komar energy density. In addition, we demonstrate that the stress-energy tensors are determined by the electric charge density and their conservation equations.
Static spherically-symmetric perfect fluids with pressure equal to energy density
NASA Astrophysics Data System (ADS)
Yadav, R. B. S.; Saini, S. L.
1991-12-01
An exact, static, and spherically-symmetric solution is presented of Einstein's field equations for a homogeneous perfect fluid core surrounded by a field of Zel'dovich's fluid which is asymptotically homaloidal. The equation of state for the fluid is taken as p = p, which describes several important cases, e.g., radiation, relativistic degenerate Fermi gas, and probably very dense baryon matter. If the fluid satisfies p = p and if in addition its motion is irrotational, then such a source has the same stress energy tensor as that of a massless scalar field.
NASA Astrophysics Data System (ADS)
Huan Wei, Yi
2004-02-01
The fundamental axisymmetric field equations of Einstein Maxwell dilation (EMD) theory with electric fields are simplified to Ernst-like and Laplace equations; all the solutions in the low-energy limit of string theory are generalized to the current case. On the basis of the work of Wei et al (2002 Class. Quantum Grav. 19 6469), the TS-like class of solutions and the class of solutions given in terms of two harmonics are further analysed and discussed, particularly the spherically symmetric solutions.
Axi-symmetric patterns of active polar filaments on spherical and composite surfaces
NASA Astrophysics Data System (ADS)
Srivastava, Pragya; Rao, Madan
2014-03-01
Experiments performed on Fission Yeast cells of cylindrical and spherical shapes, rod-shaped bacteria and reconstituted cylindrical liposomes suggest the influence of cell geometry on patterning of cortical actin. A theoretical model based on active hydrodynamic description of cortical actin that includes curvature-orientation coupling predicts spontaneous formation of acto-myosin rings, cables and nodes on cylindrical and spherical geometries [P. Srivastava et al, PRL 110, 168104(2013)]. Stability and dynamics of these patterns is also affected by the cellular shape and has been observed in experiments performed on Fission Yeast cells of spherical shape. Motivated by this, we study the stability and dynamics of axi-symmetric patterns of active polar filaments on the surfaces of spherical, saddle shaped and conical geometry and classify the stable steady state patterns on these surfaces. Based on the analysis of the fluorescence images of Myosin-II during ring slippage we propose a simple mechanical model for ring-sliding based on force balance and make quantitative comparison with the experiments performed on Fission Yeast cells. NSF Grant DMR-1004789 and Syracuse Soft Matter Program.
Spherically Symmetric Trapping Horizons, the Misner-Sharp Mass and Black Hole Evaporation
NASA Astrophysics Data System (ADS)
Nielsen, Alex B.; Yeom, Dong-Han
We discuss some of the issues relating to information loss and black hole thermodynamics in the light of recent work on local black hole horizons. Understood in terms of pure states evolving into mixed states, the possibility of information loss in black holes is closely related to the global causal structure of space-time, as is the existence of event horizons. However, black holes need not be defined by event horizons, and in fact we argue that in order to have a fully unitary evolution for black holes, they should be defined in terms of something else, such as a trapping horizon. The Misner-Sharp mass in spherical symmetry shows very simply how trapping horizons can give rise to black hole thermodynamics, Hawking radiation and singularities. We show how the Misner-Sharp mass can also be used to give insights into the process of collapse and evaporation of locally defined black holes.
Most general spherically symmetric M2-branes and type-IIB strings
Wang Zhaolong; Lue, H.
2009-09-15
We obtain the most general spherically symmetric M2-branes and type-IIB strings, with R{sup 1,2}xSO(8) and R{sup 1,1}xSO(8) isometries, respectively. We find that there are 12 different classes of M2-branes, and we study their curvature properties. In particular, we obtain new smooth M2-brane wormholes that connect two asymptotic regions: one is flat and the other can be either flat or AdS{sub 4}xS{sup 7}. We find that these wormholes are traversable with certain timelike trajectories. We also obtain the most general Ricci-flat solutions in five dimensions with R{sup 1,1}xSO(3) isometries.
Calculation of the fast ion tail distribution for a spherically symmetric hot spot
McDevitt, C. J.; Tang, X.-Z.; Guo, Z.; Berk, H. L.
2014-10-15
The fast ion tail for a spherically symmetric hot spot is computed via the solution of a simplified Fokker-Planck collision operator. Emphasis is placed on describing the energy scaling of the fast ion distribution function in the hot spot as well as the surrounding cold plasma throughout a broad range of collisionalities and temperatures. It is found that while the fast ion tail inside the hot spot is significantly depleted, leading to a reduction of the fusion yield in this region, a surplus of fast ions is observed in the neighboring cold plasma region. The presence of this surplus of fast ions in the neighboring cold region is shown to result in a partial recovery of the fusion yield lost in the hot spot.
Kawakami, Hayato; Mitsuda, Eiji; Nambu, Yasusada; Tomimatsu, Akira
2009-07-15
In considering the gravitational collapse of matter, it is an important problem to clarify what kind of conditions leads to the formation of naked singularity. For this purpose, we apply the 1+3 orthonormal frame formalism introduced by Uggla et al. to the spherically symmetric gravitational collapse of a perfect fluid. This formalism allows us to construct an autonomous system of evolution and constraint equations for scale-invariant dynamical variables normalized by the volume expansion rate of the timelike orthonormal frame vector. We investigate the asymptotic evolution of such dynamical variables towards the formation of a central singularity and present a conjecture that the steep spatial gradient for the normalized density function is a characteristic of the naked singularity formation.
Rigorous bounds for Rényi entropies of spherically symmetric potentials
NASA Astrophysics Data System (ADS)
Sánchez-Moreno, Pablo; Zozor, Steeve; Dehesa, Jesús S.
2011-03-01
The Rényi and Shannon entropies are information-theoretic measures which have enabled to formulate the position-momentum uncertainty principle in a much more adequate and stringent way than the (variance-based) Heisenberg-like relation. Moreover, they are closely related to various energetic density-functionals of quantum systems. Here we find sharp upper bounds to these quantities in terms of the second order moment
Spherically symmetric vacuum solutions arising from trace dynamics modifications to gravitation
NASA Astrophysics Data System (ADS)
Adler, Stephen L.; Ramazanoğlu, Fethi M.
2015-12-01
We derive the equations governing static, spherically symmetric vacuum solutions to the Einstein equations, as modified by the frame-dependent effective action (derived from trace dynamics) that gives an alternative explanation of the origin of "dark energy". We give analytic and numerical results for the solutions of these equations, first in polar coordinates, and then in isotropic coordinates. General features of the static case are that: (i) there is no horizon, since g00 is nonvanishing for finite values of the polar radius, and only vanishes (in isotropic coordinates) at the internal singularity, (ii) the Ricci scalar R vanishes identically, and (iii) there is a physical singularity at cosmological distances. The large distance singularity may be an artifact of the static restriction, since we find that the behavior at large distances is altered in a time-dependent solution using the McVittie Ansatz.
Calculation of the fast ion tail distribution for a spherically symmetric hot spot
NASA Astrophysics Data System (ADS)
McDevitt, C. J.; Tang, X.-Z.; Guo, Z.; Berk, H. L.
2014-10-01
The fast ion tail for a spherically symmetric hot spot is computed via the solution of a simplified Fokker-Planck collision operator. Emphasis is placed on describing the energy scaling of the fast ion distribution function in the hot spot as well as the surrounding cold plasma throughout a broad range of collisionalities and temperatures. It is found that while the fast ion tail inside the hot spot is significantly depleted, leading to a reduction of the fusion yield in this region, a surplus of fast ions is observed in the neighboring cold plasma region. The presence of this surplus of fast ions in the neighboring cold region is shown to result in a partial recovery of the fusion yield lost in the hot spot.
Corrêa da Silva, Thales M. Pakter, Renato; Rizzato, Felipe B.; Levin, Yan
2015-02-15
The effect of an initial envelope mismatch on the transport of bunched spherically symmetric beams is investigated. A particle-core model is used to estimate the maximum radius that halo particles can reach. The theory is used to obtain an empirical formula that provides the halo size as a function of system parameters. Taking into account, the incompressibility property of the Vlasov dynamics and the resulting Landau damping, an explicit form for the final stationary distribution attained by the beam is proposed. The distribution is fully self-consistent, presenting no free fitting parameters. The theory is used to predict the relevant beam transport properties, such as the final particle density distribution, the emittance growth, and the fraction of particles that will be expelled to form halo. The theoretical results are compared to the explicit N-particle dynamics simulations, showing a good agreement.
Yan, Zhenyu; Buldyrev, Sergey V; Giovambattista, Nicolas; Debenedetti, Pablo G; Stanley, H Eugene
2006-05-01
We investigate the equation of state, diffusion coefficient, and structural order of a family of spherically symmetric potentials consisting of a hard core and a linear repulsive ramp. This generic potential has two characteristic length scales: the hard and soft core diameters. The family of potentials is generated by varying their ratio, lambda. We find negative thermal expansion (thermodynamic anomaly) and an increase of the diffusion coefficient upon isothermal compression (dynamic anomaly) for 0< or =lambda<6/7. As in water, the regions where these anomalies occur are nested domes in the (T, p) or (T, P) planes , with the thermodynamic anomaly dome contained entirely within the dynamic anomaly dome. We calculate translational and orientational order parameters (t and Q6), and project equilibrium state points onto the (t, Q6) plane, or order map. The order map evolves from waterlike behavior to hard-sphere-like behavior upon varying lambda between 4/7 and 6/7. Thus, we traverse the range of liquid behavior encompassed by hard spheres (lanbda=1) and waterlike (lambda approximately 4/7) with a family of tunable spherically symmetric potentials by simply varying the ratio of hard to soft-core diameters. Although dynamic and thermodynamic anomalies occur almost across the entire range 0< or=lambda< or=1, waterlike structural anomalies (i.e., decrease in both t and Q6 upon compression and strictly correlated T and Q6 in the anomalous region) occur only around lambda=4/7. Waterlike anomalies in structure, dynamics and thermodynamics arise solely due to the existence of two length scales, with their ratio lambda being the single control parameter, orientation-dependent interactions being absent by design. PMID:16802925
NASA Technical Reports Server (NTRS)
Ratkiewicz, R.; Barnes, A.; Molvik, G. A.; Spreiter, J. R.; Stahara, S. S.; Cuzzi, Jeffery N. (Technical Monitor)
1995-01-01
Large-scale fluctuations in the solar wind plasma upstream of the heliospheric termination shock (TS) will cause inward and outward motions of the shock. Using numerical techniques, we extend an earlier strictly one-dimensional (planar) analytic gas dynamic model to spherical symmetry to investigate the features of global behavior of shock motion. Our starting point is to establish a steady numerical solution of the gasdynamic equations describing the interaction between the solar wind and the interstellar medium. We then introduce disturbances of the solar wind dynamic pressure at an inner boundary, and follow the subsequent evolution of the system, especially the motion of the termination shock. Our model solves spherically symmetric gasdynamic equations as an initial-boundary value problem. The equations in conservative form are solved using a fully implicit Total Variation Diminishing (TVD) upwind scheme with Roe-type Riemann solver. Boundary conditions are given by the solar wind parameters on an inner spherical boundary, where they are allowed to vary with time for unsteady calculations, and by a constant pressure (roughly simulating the effect of the local interstellar medium) on an outer boundary. We find that immediately after the interaction, the shock moves with speeds given by the earlier analogous analytic models. However, as the termination shock propagates it begins to slow down, seeking a new equilibrium position. In addition, the disturbance transmitted through the TS, either a shock or rarefaction wave, will encounter the heliopause boundary and be reflected back. The reflected signal will encounter the TS, causing it to oscillate. The phenomenon may be repeated for a number of reflections, resulting in a "ringing" of the outer heliosphere.
An introduction to curved space-times.
NASA Astrophysics Data System (ADS)
Williams, R. M.
1991-07-01
These lectures focus on understanding relativity from a geometrical viewpoint, based on the use of space-time diagrams and without the tools of tensor calculus. After a brief discussion of flat space-times, curved space-times are introduced and it is shown how many of their properties may be deduced from their metric interval. The space-time around a spherically symmetric star and its possible collapse to form a black hole is described. Finally, some simple cosmological models are discussed, with emphasis on their causal properties and the existence of horizons. The titles of the lectures are: I. Flat space-times. II. Curved space-times. III. Spherical stars and stellar collapse. IV. Some simple cosmological models.
NASA Astrophysics Data System (ADS)
Lozowski, E. P.; D'Amours, R.
1980-08-01
A model of spherical hailstone growth thermodynamics is presented, and used to examine the validity of the continuous growth and heat balance assumptions frequently employed in the `classical' hail growth models. The model is similar to the spherically symmetric model formulated by Macklin and Payne (1969), but solutions to the model equations are obtained by means of finite-difference numerical methods. In the model, we do not try to simulate the discrete accretion process of individual drops. Instead, we attempt to identify the implications of the discrete, time-dependent nature of the icing process, by examining the accretion of a thin uniform layer of supercooled water over the entire surface of the sphere. The heat transfer equations both with the air and within the hailstone axe then solved assuming radial symmetry. By the addition of several such layers, the finite growth of a spherical hailstone can be simulated. In the present paper, only growth in constant ambient conditions is considered. It is shown that there are large internal heat fluxes during the interval between the accretion of successive layers (typically 1 s), which cause the temperatures near the surface to oscillate several degrees above and below their time-mean value. Nevertheless, the time-averaged temperature over an accretion cycle is almost uniform throughout the hailstone and, when the environmental conditions are constant, is approximately equal to the equilibrium surface temperature predicted by the `classical' models. As the hailstone grows under constant environmental conditions, it continually adapts to the classical equilibrium temperature, warming up almost uniformly throughout. The time scale for this adjustment to a quasi-equilibrium state is found to be of the order of the internal diffusive time scale R2/k. It is speculated therefore that if the environmental conditions change slowly (over time scales large compared with R2/k) the hailstone thermodynamics will be adequately
Cyclic and heteroclinic flows near general static spherically symmetric black holes
NASA Astrophysics Data System (ADS)
Ahmed, Ayyesha K.; Azreg-Aïnou, Mustapha; Faizal, Mir; Jamil, Mubasher
2016-05-01
We investigate the Michel-type accretion onto a static spherically symmetric black hole. Using a Hamiltonian dynamical approach, we show that the standard method employed for tackling the accretion problem has masked some properties of the fluid flow. We determine new analytical solutions that are neither transonic nor supersonic as the fluid approaches the horizon(s); rather, they remain subsonic for all values of the radial coordinate. Moreover, the three-velocity vanishes and the pressure diverges on the horizon(s), resulting in a flow-out of the fluid under the effect of its own pressure. This is in favor of the earlier prediction that pressure-dominant regions form near the horizon. This result does not depend on the form of the metric and it applies to a neighborhood of any horizon where the time coordinate is timelike. For anti-de Sitter-like {f}(R) black holes we discuss the stability of the critical flow and determine separatrix heteroclinic orbits. For de Sitter-like {f}(R) black holes, we construct polytropic cyclic, non-homoclinic, physical flows connecting the two horizons. These flows become non-relativistic for Hamiltonian values higher than the critical value, allowing for a good estimate of the proper period of the flow.
NASA Astrophysics Data System (ADS)
Xu, Limei; Buldyrev, Sergey V.; Angell, C. Austen; Stanley, H. Eugene
2006-09-01
Using molecular dynamics simulations, we study the Jagla model of a liquid which consists of particles interacting via a spherically symmetric two-scale potential with both repulsive and attractive ramps. This potential displays anomalies similar to those found in liquid water, namely expansion upon cooling and an increase of diffusivity upon compression, as well as a liquid-liquid (LL) phase transition in the region of the phase diagram accessible to simulations. The LL coexistence line, unlike in tetrahedrally coordinated liquids, has a positive slope, because of the Clapeyron relation, corresponding to the fact that the high density phase (HDL) is more ordered than low density phase (LDL). When we cool the system at constant pressure above the critical pressure, the thermodynamic properties rapidly change from those of LDL-like to those of HDL-like upon crossing the Widom line. The temperature dependence of the diffusivity also changes rapidly in the vicinity of the Widom line, namely the slope of the Arrhenius plot sharply increases upon entering the HDL domain. The properties of the glass transition are different in the two phases, suggesting that the less ordered phase is fragile, while the more ordered phase is strong, which is consistent with the behavior of tetrahedrally coordinated liquids such as water silica, silicon, and BeF2 .
Ziegler, Andy; Koehler, Thomas; Nielsen, Tim; Proksa, Roland
2006-12-15
In cone-beam transmission tomography the measurements are performed with a divergent beam of x-rays. The reconstruction with iterative methods is an approach that offers the possibility to reconstruct the corresponding images directly from these measurements. Another approach based on spherically symmetric basis functions (blobs) has been reported with results demonstrating a better image quality for iterative reconstruction algorithms. When combining the two approaches (i.e., using blobs in iterative cone-beam reconstruction of divergent rays) the problem of blob sampling without introducing aliasing must be addressed. One solution to this problem is to select a blob size large enough to ensure a sufficient sampling, but this prevents a high resolution reconstruction, which is not desired. Another solution is a heuristic low-pass filtering, which removes this aliasing, but neglects the different contributions of blobs to the absorption depending on the spatial position in the volume and, therefore, cannot achieve the best image quality. This article presents a model of sampling the blobs which is motivated by the beam geometry. It can be used for high resolution reconstruction and can be implemented efficiently.
Geodesic completeness in a wormhole spacetime with horizons
NASA Astrophysics Data System (ADS)
Olmo, Gonzalo J.; Rubiera-Garcia, D.; Sanchez-Puente, A.
2015-08-01
The geometry of a spacetime containing a wormhole generated by a spherically symmetric electric field is investigated in detail. These solutions arise in high-energy extensions of general relativity formulated within the Palatini approach and coupled to Maxwell electrodynamics. Even though curvature divergences generically arise at the wormhole throat, we find that these spacetimes are geodesically complete. This provides an explicit example where curvature divergences do not imply spacetime singularities.
Numerical relativity for D dimensional axially symmetric space-times: Formalism and code tests
NASA Astrophysics Data System (ADS)
Zilhão, Miguel; Witek, Helvi; Sperhake, Ulrich; Cardoso, Vitor; Gualtieri, Leonardo; Herdeiro, Carlos; Nerozzi, Andrea
2010-04-01
The numerical evolution of Einstein’s field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modeling black hole production in TeV gravity scenarios, to analysis of the stability of exact solutions, and to tests of cosmic censorship. In order to investigate these questions, we extend numerical relativity to more general space-times than those investigated hitherto, by developing a framework to study the numerical evolution of D dimensional vacuum space-times with an SO(D-2) isometry group for D≥5, or SO(D-3) for D≥6. Performing a dimensional reduction on a (D-4) sphere, the D dimensional vacuum Einstein equations are rewritten as a 3+1 dimensional system with source terms, and presented in the Baumgarte, Shapiro, Shibata, and Nakamura formulation. This allows the use of existing 3+1 dimensional numerical codes with small adaptations. Brill-Lindquist initial data are constructed in D dimensions and a procedure to match them to our 3+1 dimensional evolution equations is given. We have implemented our framework by adapting the Lean code and perform a variety of simulations of nonspinning black hole space-times. Specifically, we present a modified moving puncture gauge, which facilitates long-term stable simulations in D=5. We further demonstrate the internal consistency of the code by studying convergence and comparing numerical versus analytic results in the case of geodesic slicing for D=5, 6.
What spherically symmetric viscosity structure produces the same PGR as a realistic 3D Earth?
NASA Astrophysics Data System (ADS)
Paulson, A.; Zhong, S.; Wahr, J.
2003-04-01
Observations of isostatic adjustment of the earth's surface due to transient loading provide important constraints on the mantle viscosity structure. However, most studies of this response have assumed a spherically symmetric (1D) earth. This study is motivated by the following question: when a one-dimensional viscosity model is derived from post-glacial rebound (PGR) observations, how does this 1D structure correspond to the three-dimensional structure of the earth? Using the 3D spherical finite element software CitcomSVE [Zhong et al., 2002], we are able to compute the earth's response to realistic glacial loading when the earth has a truly 3D viscosity structure. The loading is provided by the ICE-3G deglaciation history [Tushingham &Peltier, 1991]. The 3D viscosity structure is constructed by first selecting a priori a radial average viscosity (for example, ( 1021 \\: {Pa \\cdot s}) in the upper mantle and (2 × 1021 \\: {Pa \\cdot s}) in the lower mantle). The lateral variations about this radial structure are derived from seismic shear-velocity tomography models by converting velocities to temperature, then temperature to viscosity. The seismic tomography models used are S20RTS [Ritsema et al., 1999] and NA00 [Van der Lee, 2002]. From the computed isostatic response, we measure typical PGR observables: relative sea level change (RSLC) and (dot{J2}). These measurements are then treated as synthetic data, and we search for 1D (radially stratified) viscosity models, forced with the same glaciation history, that will best fit these synthetic PGR observations. We find that for sites near the center of a large glacial load (e.g., southern Hudson Bay), a local average of the 3D viscosity structure provides a reasonable 1D proxy. For sites along the periphery of the glacial load (e.g., Boston), it is much more difficult to find a 1D model that can reproduce the 3D observations. We also approach the problem by running an ensemble of 1D viscosity models, and finding
The Spherically Symmetric Gravitational Collapse of a Clump of Solids in a Gas
NASA Astrophysics Data System (ADS)
Shariff, Karim; Cuzzi, Jeffrey N.
2015-05-01
In the subject of planetesimal formation, several mechanisms have been identified that create dense particle clumps in the solar nebula. The present work is concerned with the gravitational collapse of such clumps, idealized as being spherically symmetric. Fully nonlinear simulations using the two-fluid model are carried out (almost) up to the time when a central density singularity forms. We refer to this as the collapse time. The end result of the study is a parametrization of the collapse time, in order that it may be compared with timescales for various disruptive effects to which clumps may be subject in a particular situation. An important effect that determines the collapse time is that as the clump compresses, it also compresses the gas due to drag. This increases gas pressure, which retards particle collapse and can lead to oscillation in the size and density of the clump. In the limit of particles perfectly coupled to the gas, the characteristic ratio of gravitational force to gas pressure becomes relevant and defines a two-phase Jeans parameter, {{J}t}, which is the classical Jeans parameter with the speed of sound replaced by an effective wave speed in the coupled two-fluid medium. The parameter {{J}t} remains useful even away from the perfect coupling limit because it makes the simulation results insensitive to the initial density ratio of particles to gas (Φ0) as a separate parameter. A simple ordinary differential equation model is developed. It takes the form of two coupled non-linear oscillators and reproduces key features of the simulations. Finally, a parametric study of the time to collapse is performed and a formula (fit to the simulations) is developed. In the incompressible limit {{J}t}\\to 0, collapse time equals the self-sedimentation time, which is inversely proportional to the Stokes number. As {{J}t} increases, the collapse time decreases with {{J}t} and eventually becomes approximately equal to the dynamical time. Values of collapse
Nonsymmetric trapped surfaces in the Schwarzschild and Vaidya spacetimes
NASA Astrophysics Data System (ADS)
Schnetter, Erik; Krishnan, Badri
2006-01-01
Marginally trapped surfaces (MTSs) are commonly used in numerical relativity to locate black holes. For dynamical black holes, it is not known generally if this procedure is sufficiently reliable. Even for Schwarzschild black holes, Wald and Iyer constructed foliations which come arbitrarily close to the singularity but do not contain any MTSs. In this paper, we review the Wald-Iyer construction, discuss some implications for numerical relativity, and generalize to the well-known Vaidya spacetime describing spherically symmetric collapse of null dust. In the Vaidya spacetime, we numerically locate non spherically symmetric trapped surfaces which extend outside the standard spherically symmetric trapping horizon. This shows that MTSs are common in this spacetime and that the event horizon is the most likely candidate for the boundary of the trapped region.
NASA Technical Reports Server (NTRS)
Wang, Tongjiang; Davila, Joseph M.
2014-01-01
Determining the coronal electron density by the inversion of white-light polarized brightness (pB) measurements by coronagraphs is a classic problem in solar physics. An inversion technique based on the spherically symmetric geometry (spherically symmetric inversion, SSI) was developed in the 1950s and has been widely applied to interpret various observations. However, to date there is no study of the uncertainty estimation of this method. We here present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 solar radius as a model, which is reconstructed by a tomography method from STEREO/COR1 observations during the solar minimum in February 2008 (Carrington Rotation, CR 2066).We first show in theory and observation that the spherically symmetric polynomial approximation (SSPA) method and the Van de Hulst inversion technique are equivalent. Then we assess the SSPA method using synthesized pB images from the 3D density model, and find that the SSPA density values are close to the model inputs for the streamer core near the plane of the sky (POS) with differences generally smaller than about a factor of two; the former has the lower peak but extends more in both longitudinal and latitudinal directions than the latter. We estimate that the SSPA method may resolve the coronal density structure near the POS with angular resolution in longitude of about 50 deg. Our results confirm the suggestion that the SSI method is applicable to the solar minimum streamer (belt), as stated in some previous studies. In addition, we demonstrate that the SSPA method can be used to reconstruct the 3D coronal density, roughly in agreement with the reconstruction by tomography for a period of low solar activity (CR 2066). We suggest that the SSI method is complementary to the 3D tomographic technique in some cases, given that the development of the latter is still an ongoing research effort.
NASA Astrophysics Data System (ADS)
Nguyen, Lu Trong Khiem
2016-07-01
A finite difference formula based on the predictor-corrector technique is presented to integrate the cylindrically and spherically symmetric sine-Gordon equations numerically. Based on various numerical observations, one property of the waves of kink type is conjectured and used to explain their returning effect. Several numerical experiments are carried out and they are in excellent agreement with the existing results. In addition, the corresponding modulation solution for the two-dimensional ring-shaped kink is extended to that in three-dimension. Both numerical and theoretical aspects are utilized to verify the reliability of the proposed numerical scheme and thus the analytical modulation solutions.
NASA Astrophysics Data System (ADS)
Liang, Jun; Zhang, Fang-Hui; Zhang, Wei; Zhang, Jing
2014-01-01
By utilizing the improved Damour-Ruffini method with a new tortoise transformation, we study the Hawking radiation of Dirac particles from a general dynamical spherically symmetric black hole. In the improved Damour-Ruffini method, the position of the event horizon of the black hole is an undetermined function, and the temperature parameter κ is an undetermined constant. By requiring the Dirac equation to be the standard wave equation near the event horizon of the black hole, κ can be determined automatically. Therefore, the Hawking temperature can be obtained. The result is consistent with that of the Hawking radiation of scalar particles.
NASA Astrophysics Data System (ADS)
Burikham, Piyabut; Cheamsawat, Krai; Harko, Tiberiu; Lake, Matthew J.
2015-09-01
The existence of both a minimum mass and a minimum density in nature, in the presence of a positive cosmological constant, is one of the most intriguing results in classical general relativity. These results follow rigorously from the Buchdahl inequalities in four-dimensional de Sitter space. In this work, we obtain the generalized Buchdahl inequalities in arbitrary space-time dimensions with Λ ≠ 0 and consider both the de Sitter and the anti-de Sitter cases. The dependence on D, the number of space-time dimensions, of the minimum and maximum masses for stable spherical objects is explicitly obtained. The analysis is then extended to the case of dark energy satisfying an arbitrary linear barotropic equation of state. The Jeans instability of barotropic dark energy is also investigated, for arbitrary D, in the framework of a simple Newtonian model with and without viscous dissipation, and we determine the dispersion relation describing the dark energy-matter condensation process, along with estimates of the corresponding Jeans mass (and radius). Finally, the quantum mechanical implications of the mass limits are investigated, and we show that the existence of a minimum mass scale naturally leads to a model in which dark energy is composed of a `sea' of quantum particles, each with an effective mass proportional to Λ ^{1/4}.
(n+1)-dimensional spherically symmetric expanding structures in R2-gravity
NASA Astrophysics Data System (ADS)
Ebrahimi, Esmaeil
2015-05-01
In this work, we consider higher-dimensional structures in R2-gravity in an expanding background. We assume a Ricci scalar constant background and use this assumption as the basic constraint to find solutions. Two classes of solutions are presented in which every one includes naked singularity and wormhole geometries. Both classes of solutions show inflationary phase of expansion favored by recent acceleration of the universe. Traversability of the wormhole solutions is discussed. The possibility of satisfying or violating the weak energy condition (WEC) for wormholes is explored. For one class of solutions, particular choices of constants result in wormholes which satisfy the WEC all over the spacetime.
Generalized Vaidya spacetime for cubic gravity
NASA Astrophysics Data System (ADS)
Ruan, Shan-Ming
2016-03-01
We present a kind of generalized Vaidya solution of a new cubic gravity in five dimensions whose field equations in spherically symmetric spacetime are always second order like the Lovelock gravity. We also study the thermodynamics of its spherically symmetric apparent horizon and get its entropy expression and generalized Misner-Sharp energy. Finally, we present the first law and second law hold in this gravity. Although all the results are analogous to those in Lovelock gravity, we in fact introduce the contribution of a new cubic term in five dimensions where the cubic Lovelock term is just zero.
NASA Astrophysics Data System (ADS)
Lee, Kuo-Wei
2016-09-01
We prove the existence and uniqueness of the Dirichlet problem for the spacelike, spherically symmetric, constant mean curvature equation with symmetric boundary data in the extended Schwarzschild spacetime. As an application, we completely solve the CMC foliation conjecture which is proposed by Malec and Murchadha (2003 Phys. Rev. D 68 124019).
NASA Astrophysics Data System (ADS)
Momeni, Davood; Chattopadhyay, Surajit; Myrzakulov, Ratbay
2015-05-01
In this paper, we study the Ehlers' transformation (sometimes called gravitational duality rotation) for reciprocal static metrics. First, we introduce the concept of reciprocal metric. We prove a theorem which shows how we can construct a certain new static solution of Einstein field equations using a seed metric. Later, we investigate the family of stationary spacetimes of such reciprocal metrics. The key here is a theorem from Ehlers', which relates any static vacuum solution to a unique stationary metric. The stationary metric has a magnetic charge. The spacetime represents Newman-Unti-Tamburino (NUT) solutions. Since any stationary spacetime can be decomposed into a 1 + 3 time-space decomposition, Einstein field equations for any stationary spacetime can be written in the form of Maxwell's equations for gravitoelectromagnetic fields. Further, we show that this set of equations is invariant under reciprocal transformations. An additional point is that the NUT charge changes the sign. As an instructive example, by starting from the reciprocal Schwarzschild as a spherically symmetric solution and reciprocal Morgan-Morgan disk model as seed metrics we find their corresponding stationary spacetimes. Starting from any static seed metric, performing the reciprocal transformation and by applying an additional Ehlers' transformation we obtain a family of NUT spaces with negative NUT factor (reciprocal NUT factors).
NASA Astrophysics Data System (ADS)
Yao, Yuqi; Wang, Yao; Barbour, Randall L.; Graber, Harry L.; Chang, Jenghwa
1996-02-01
We present analytic expressions for the amplitude and phase of photon-density waves in strongly scattering, spherically symmetric, two-layer media containing a spherical object. This layered structure is a crude model of multilayered tissues whose absorption and scattering coefficients lie within a range reported in the literature for most tissue types. The embedded object simulates a pathology, such as a tumor. The normal-mode-series method is employed to solve the inhomogeneous Helmholtz equation in spherical coordinates, with suitable boundary conditions. By comparing the total field at points in the outer layer at a fixed distance from the origin when the object is present and when it is absent, we evaluate the potential sensitivity of an optical imaging system to inhomogeneities in absorption and scattering. For four types of background media with different absorption and scattering properties, we determine the modulation frequency that achieves an optimal compromise between signal-detection reliability and sensitivity to the presence of an object, the minimum detectable object radius, and the smallest detectable change in the absorption and scattering coefficients for a fixed object size. Our results indicate that (1) enhanced sensitivity to the object is achieved when the outer layer is more absorbing or scattering than the inner layer; (2) sensitivity to the object increases with the modulation frequency, except when the outer layer is the more absorbing; (3) amplitude measurements are proportionally more sensitive to a change in absorption, phase measurements are proportionally more sensitive to a change in scattering, and phase measurements exhibit a much greater capacity for distinguishing an absorption perturbation from a scattering perturbation.
Cioslowski, Jerzy; Albin, Joanna
2013-09-14
Energies E(N) of assemblies of equicharged particles subject to spherically symmetric power-law confining potentials vary in a convoluted fashion with the particle totalities N. Accurate rigorous upper bounds to these energies, which are amenable to detailed mathematical analysis, are found to comprise terms with smooth, oscillatory, and fluctuating dependences on N. The smooth energy component is obtained as a power series in N(-2/3) with the first two terms corresponding to the bulk and Madelung energies. The oscillatory component possesses the large-N asymptotics given by a product of N(1/(λ + 1)), where λ is the power-law exponent, and a function periodic in N(1/3). The amplitude of the fluctuating component, which originates mostly from the irregular dependence of the Thomson energy E(Th)(n) on n, also scales like N(1/(λ + 1)). PMID:24050343
NASA Astrophysics Data System (ADS)
Berberian, John Edwin
1999-01-01
A new framework is presented for analysing the spherically symmetric Einstein field equations for a zero-mass scalar field. The framework consists of a coordinate system (p, q), where the coordinate p is the scalar field, and q is a coordinate chosen to be orthogonal to p. This idea allows for a reduction of the field equations into a system of two first order partial differential equations for the areal metric function gqq and a mass function m . The metric coefficients in this coordinate system then take on values which are simply related to the scalars of the problem: 1->f˙1 ->f,gq q and-via the field equations-the scalar curvature R as well. The scalar field coordinate system is shown to have many advantages. Many of the known exact solutions (e.g. static, Roberts) are represented simply, and new self- similar solutions are derived. The framework is then applied to the problem of matching spherically symmetric scalar-tensor vacuum solutions to a homogeneous and isotropic dust solution (e.g. scalar- tensor Einstein-Straus swiss cheese solutions, scalar- tensor Oppenheimer-Snyder dust ball collapse). Scalar field coordinates are shown to be ideal for such an application. We derive the necessary matching conditions in scalar field coordinates, and show how they imply a natural extension of the Schücking condition for spherically symmetric vacuum in general relativity. The problem of finding a vacuum solution which matches a given homogeneous and isotropic solution is examined. It is found that the matching conditions are sufficient to guarantee local existence and uniqueness of the vacuum solution if it is assumed that the scalar field has neither maxima nor minima on the matching interface. In order to find explicit matched solutions, criteria are developed to screen known exact vacuum solutions for matchability, and procedures are given for determining the details of the homogeneous and isotropic solution (curvature constant, comoving radial coordinate of the
NASA Astrophysics Data System (ADS)
Wang, Wenli; Hawkins, William; Gagnon, Daniel
2004-06-01
A single photon emission computed tomography (SPECT) rotating slat collimator with strip detector acquires distance-weighted plane integral data, along with the attenuation factor and distance-dependent detector response. In order to image a 3D object, the slat collimator device has first to spin around its axis and then rotate around the object to produce 3D projection measurements. Compared to the slice-by-slice 2D reconstruction for the parallel-hole collimator and line integral data, a more complex 3D reconstruction is needed for the slat collimator and plane integral data. In this paper, we propose a 3D RBI-EM reconstruction algorithm with spherically-symmetric basis function, also called 'blobs', for the slat collimator. It has a closed and spherically symmetric analytical expression for the 3D Radon transform, which makes it easier to compute the plane integral than the voxel. It is completely localized in the spatial domain and nearly band-limited in the frequency domain. Its size and shape can be controlled by several parameters to have desired reconstructed image quality. A mathematical lesion phantom study has demonstrated that the blob reconstruction can achieve better contrast-noise trade-offs than the voxel reconstruction without greatly degrading the image resolution. A real lesion phantom study further confirmed this and showed that a slat collimator with CZT detector has better image quality than the conventional parallel-hole collimator with NaI detector. The improvement might be due to both the slat collimation and the better energy resolution of the CZT detector.
Spherically symmetric systems of fields and black holes. II. Apparent horizon in canonical formalism
Hajicek, P.
1984-09-15
We study the action of a two-dimensional model of gravity found in the preceding paper. We transform the action to the first-order Arnowitt-Deser-Misner form, and work out the generalized momenta and super-Hamiltonians. We propose to foliate the spacetime in such a way that the inside of the apparent horizon will be cut away. In the classical theory, no loss of information for the development of states from scrI/sup -/ to scrI/sup +/ can result, but in the corresponding quantum theory, some such losses could occur if a black hole evaporates. We study the boundary conditions for the fields at the apparent horizon which are implied by such a foliation, and calculate the corresponding surface correction to the Hamiltonian by the method of Regge and Teitelboim. We generalize the so-called Berger-Chitre-Moncrief-Nutku gauge in such a way that the fields cannot violate the boundary conditions. In this gauge, we perform an explicit total reduction of the canonical formalism so that only the true dynamical variables appear in the Hamiltonian. The reduced Hamiltonian splits into a black hole and a field part.
Spherically symmetric systems of fields and black holes. II. Apparent horizon in canonical formalism
NASA Astrophysics Data System (ADS)
Hajicek, P.
1984-09-01
We study the action of a two-dimensional model of gravity found in the preceding paper. We transform the action to the first-order Arnowitt-Deser-Misner form, and work out the generalized momenta and super-Hamiltonians. We propose to foliate the spacetime in such a way that the inside of the apparent horizon will be cut away. In the classical theory, no loss of information for the development of states from I- to I+ can result, but in the corresponding quantum theory, some such losses could occur if a black hole evaporates. We study the boundary conditions for the fields at the apparent horizon which are implied by such a foliation, and calculate the corresponding surface correction to the Hamiltonian by the method of Regge and Teitelboim. We generalize the socalled Berger-Chitre-Moncrief-Nutku gauge in such a way that the fields cannot violate the boundary conditions. In this gauge, we perform an explicit total reduction of the canonical formalism so that only the true dynamical variables appear in the Hamiltonian. The reduced Hamiltonian splits into a black hole and a field part.
NASA Astrophysics Data System (ADS)
Bradford, R. A. W.
2015-10-01
Stationary, static, spherically symmetric solutions of the Maxwell-Dirac system, treated as classical fields, have been found which are localised and normalisable. The solutions apply to any bound energy eigenvalue in the range 0 < E < m, where m is the bare mass in the Dirac equation. A point charge of any magnitude and either sign may be placed at the origin and the solutions remain well behaved and bound. However, no such central charge is necessary to result in a bound solution. As found previously by Radford, the magnetic flux density is equal to that of a monopole at the origin. However, no monopole is present, the magnetic flux being a result of the dipole moment distribution of the Dirac field. The Dirac field magnetic dipole moment is aligned with the magnetic flux density and so the resulting magnetic self-energy is negative. It is this which results in the states being bound (E < m). The case which omits any central point charge is therefore a self-sustaining bound state solution of the Maxwell-Dirac system which is localised, normalisable, and requires no arbitrarily added "external" features (i.e., it is a soliton). As far as the author is aware, this is the first time that such an exact solution with a positive energy eigenvalue has been reported. However, the solution is not unique since the energy eigenvalue is arbitrary within the range 0 < E < m. The stability of the solution has not been addressed.
Chang Yiren; Hsu Long; Chi Sien
2006-06-01
Since their invention in 1986, optical tweezers have become a popular manipulation and force measurement tool in cellular and molecular biology. However, until recently there has not been a sophisticated model for optical tweezers on trapping cells in the ray-optics regime. We present a model for optical tweezers to calculate the optical force upon a spherically symmetric multilayer sphere representing a common biological cell. A numerical simulation of this model shows that not only is the magnitude of the optical force upon a Chinese hamster ovary cell significantly three times smaller than that upon a polystyrene bead of the same size, but the distribution of the optical force upon a cell is also much different from that upon a uniform particle, and there is a 30% difference in the optical trapping stiffness of these two cases. Furthermore, under a small variant condition for the refractive indices of any adjacent layers of the sphere, this model provides a simple approximation to calculate the optical force and the stiffness of an optical tweezers system.
NASA Astrophysics Data System (ADS)
Alexiewicz, W.; Grygiel, K.
2008-10-01
The graphical analysis of the influence of the rotational diffusion tensor anisotropy and the orientation of the permanent dipole moment on the linear and nonlinear dielectric relaxation is shown. The solution of Smoluchowski-Debye rotational diffusion equation for rigid, and noninteracting polar, symmetric-top molecules, in the "weak molecular reorientation approximation", was used. In order to highlight the influence of the symmetric shape of molecule, in comparison with classical, spherical-top Smoluchowski rotational diffusion, we present sets of Argand-type plots and three-dimensional Cole-Cole diagrams for linear and nonlinear electric susceptibilities. The results indicate that, in describing the nonlinear dielectric relaxation, the simplest spherical-top rotational diffusion model may be a sufficient approximation in some special cases only.
Spherically symmetric nonlinear structures
NASA Astrophysics Data System (ADS)
Calzetta, Esteban A.; Kandus, Alejandra
1997-02-01
We present an analytical method to extract observational predictions about the nonlinear evolution of perturbations in a Tolman universe. We assume no a priori profile for them. We solve perturbatively a Hamilton-Jacobi equation for a timelike geodesic and obtain the null one as a limiting case in two situations: for an observer located in the center of symmetry and for a noncentered one. In the first case we find expressions to evaluate the density contrast and the number count and luminosity distance versus redshift relationships up to second order in the perturbations. In the second situation we calculate the CMBR anisotropies at large angular scales produced by the density contrast and by the asymmetry of the observer's location, up to first order in the perturbations. We develop our argument in such a way that the formulas are valid for any shape of the primordial spectrum.
Is the shell-focusing singularity of Szekeres space-time visible?
Nolan, Brien C; Debnath, Ujjal
2007-11-15
The visibility of the shell-focusing singularity in Szekeres space-time--which represents quasispherical dust collapse--has been studied on numerous occasions in the context of the cosmic censorship conjecture. The various results derived have assumed that there exist radial null geodesics in the space-time. We show that such geodesics do not exist in general, and so previous results on the visibility of the singularity are not generally valid. More precisely, we show that the existence of a radial geodesic in Szekeres space-time implies that the space-time is axially symmetric, with the geodesic along the polar direction (i.e. along the axis of symmetry). If there is a second nonparallel radial geodesic, then the space-time is spherically symmetric, and so is a Lemaitre-Tolman-Bondi space-time. For the case of the polar geodesic in an axially symmetric Szekeres space-time, we give conditions on the free functions (i.e. initial data) of the space-time which lead to visibility of the singularity along this direction. Likewise, we give a sufficient condition for censorship of the singularity. We point out the complications involved in addressing the question of visibility of the singularity both for nonradial null geodesics in the axially symmetric case and in the general (nonaxially symmetric) case, and suggest a possible approach.
Spinning bodies in curved spacetime
NASA Astrophysics Data System (ADS)
d'Ambrosi, G.; Satish Kumar, S.; van de Vis, J.; van Holten, J. W.
2016-02-01
We study the motion of neutral and charged spinning bodies in curved spacetime in the test-particle limit. We construct equations of motion using a closed covariant Poisson-Dirac bracket formulation that allows for different choices of the Hamiltonian. We derive conditions for the existence of constants of motion and apply the formalism to the case of spherically symmetric spacetimes. We show that the periastron of a spinning body in a stable orbit in a Schwarzschild or Reissner-Nordstrøm background not only precesses but also varies radially. By analyzing the stability conditions for circular motion we find the innermost stable circular orbit (ISCO) as a function of spin. It turns out that there is an absolute lower limit on the ISCOs for increasing prograde spin. Finally we establish that the equations of motion can also be derived from the Einstein equations using an appropriate energy-momentum tensor for spinning particles.
Exact Relativistic Newtonian Representation of Gravitational static Spacetime Geometries
NASA Astrophysics Data System (ADS)
Ghosh, Shubhrangshu; Sarkar, Tamal; Bhadra, Arunava
2016-09-01
We construct a self-consistent relativistic Newtonian analogue corresponding to gravitational static spherical symmetric spacetime geometries, starting directly from a generalized scalar relativistic gravitational action in a Newtonian framework, which gives geodesic equations of motion identical to those of the parent metric. Consequently, the derived velocity-dependent relativistic scalar potential, which is a relativistic generalization of the Newtonian gravitational potential, exactly reproduces the relativistic gravitational features corresponding to any static spherical symmetric spacetime geometry in its entirety, including all the experimentally tested gravitational effects in the weak field up to the present. This relativistic analogous potential is expected to be quite useful in studying a wide range of astrophysical phenomena, especially in strong field gravity.
Quantized Space-Time and Black Hole Entropy
NASA Astrophysics Data System (ADS)
Ma, Meng-Sen; Li, Huai-Fan; Zhao, Ren
2014-06-01
On the basis of Snyder’s idea of quantized space-time, we derive a new generalized uncertainty principle and a new modified density of states. Accordingly, we obtain a corrected black hole entropy with a logarithmic correction term by employing the new generalized uncertainty principle. In addition, we recalculate the entropy of spherically symmetric black holes using statistical mechanics. Because of the use of the minimal length in quantized space-time as a natural cutoff, the entanglement entropy we obtained does not have the usual form A/4 but has a coefficient dependent on the minimal length, which shows differences between black hole entropy in quantized space-time and that in continuous space-time.
Black holes in loop quantum gravity: the complete space-time.
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. PMID:18999656
Quantum singularity structure of a class of continuously self-similar spacetimes
NASA Astrophysics Data System (ADS)
Konkowski, Deborah; Helliwell, Thomas; Wiliams, Jon
2016-03-01
The dynamical, classical timelike singularity in a class of continuously self-similar, conformally-static, spherically-symmetric, power-law spacetimes is probed using massless scalar test fields. Ranges of metric parameters for which these classical singularities may be resolved quantum mechanically are determined; however, the wave operator is shown to be not essentially self-adjoint using Weyl's limit point-limit circle criterion. Thus, unfortunately, in this class of spacetimes the wave packet evolution still has the usual ambiguity associated with scattering off singularities. These spacetimes are not healed quantum mechanically.
On the Static Spacetime of a Single Point Charge
NASA Astrophysics Data System (ADS)
Tahvildar-Zadeh, A. Shadi
Among all electromagnetic theories which (a) are derivable from a Lagrangian, (b) satisfy the dominant energy condition, and (c) in the weak field limit coincide with classical linear electromagnetics, we identify a certain subclass with the property that the corresponding spherically symmetric, asymptotically flat, electrostatic spacetime metric has the mildest possible singularity at its center, namely, a conical singularity on the time axis. The electric field moreover has a point defect on the time axis, its total energy is finite, and is equal to the ADM mass of the spacetime. By an appropriate scaling of the Lagrangian, one can arrange the total mass and total charge of these spacetimes to have any chosen values. For small enough mass-to-charge ratio, these spacetimes have no horizons and no trapped null geodesics. We also prove the uniqueness of these solutions in the spherically symmetric class, and we conclude by performing a qualitative study of the geodesics and test-charge trajectories of these spacetimes.
Midisuperspace quantization: Possibilities for fractional and emergent spacetime dimensions
NASA Astrophysics Data System (ADS)
Tibrewala, Rakesh
2016-06-01
Recently, motivated by certain loop quantum gravity-inspired corrections, it was shown that for spherically symmetric midisuperspace models infinitely many second-derivative theories of gravity exist (as revealed by the presence of three arbitrary functions in the corresponding Lagrangian/Hamiltonian) and not just those allowed by spherically symmetric general relativity. This freedom can be interpreted as the freedom to accommodate certain quantum gravity corrections in these models even in the absence of higher-curvature terms (at a semiclassical level, at least). For a particular choice of the arbitrary functions it is shown that the new theories map to spherically symmetric general relativity in arbitrary number of (integer) dimensions thus explicitly demonstrating that when working with midisuperspace models, one loses the information about the dimensionality of the full spacetime. In addition, it is shown that these new theories can accommodate scenarios of fractional spacetime dimensions as well as those of emergent spacetime dimensions—a possibility suggested by various approaches to quantum gravity.
Entropic force, holography and thermodynamics for static space-times
NASA Astrophysics Data System (ADS)
Konoplya, R. A.
2010-10-01
Recently Verlinde has suggested a new approach to gravity which interprets gravitational interaction as a kind of entropic force. The new approach uses the holographic principle by stating that the information is kept on the holographic screens which coincide with equipotential surfaces. Motivated by this new interpretation of gravity (but not being limited by it) we study equipotential surfaces, the Unruh-Verlinde temperature, energy and acceleration for various static space-times: generic spherically symmetric solutions, axially symmetric black holes immersed in a magnetic field, traversable spherically symmetric wormholes of an arbitrary shape function, system of two and more extremely charged black holes in equilibrium. In particular, we have shown that the Unruh-Verlinde temperature of the holographic screen reaches absolute zero on the wormhole throat independently of the particular form of the wormhole solution.
Bertrand spacetimes as Kepler/oscillator potentials
NASA Astrophysics Data System (ADS)
Ballesteros, Ángel; Enciso, Alberto; Herranz, Francisco J.; Ragnisco, Orlando
2008-08-01
Perlick's classification of (3 + 1)-dimensional spherically symmetric and static spacetimes \\big({\\cal M},\\eta=-{\\frac{1}{V}} {d} t^2+g\\big) for which the classical Bertrand theorem holds (Perlick V 1992 Class. Quantum Grav. 9 1009) is revisited. For any Bertrand spacetime ({\\cal M},\\eta) the term V(r) is proven to be either the intrinsic Kepler Coulomb or the harmonic oscillator potential on its associated Riemannian 3-manifold (M, g). Among the latter 3-spaces (M, g) we explicitly identify the three classical Riemannian spaces of constant curvature, a generalization of a Darboux space and the Iwai Katayama spaces generalizing the MIC Kepler and Taub NUT problems. The key dynamical role played by the Kepler and oscillator potentials in Euclidean space is thus extended to a wide class of three-dimensional curved spaces.
Hydrodynamics in type B warped spacetimes
Carot, J.; Nunez, L.A.
2005-10-15
We discuss certain general features of type B warped spacetimes which have important consequences on the material content they may admit and its associated dynamics. We show that, for warped B spacetimes, if shear and anisotropy are nonvanishing, they have to be proportional. We also study some of the physics related to the warping factor and of the underlying decomposable metric. Finally we explore the only possible cases compatible with a type B warped geometry which satisfy the dominant energy conditions. As an example of the above mentioned consequences we consider a radiating fluid and two nonspherically symmetric metrics which depend upon an arbitrary parameter a, such that for a=0 spherical symmetry is recovered.
Hamiltonian of a spinning test particle in curved spacetime
Barausse, Enrico; Racine, Etienne; Buonanno, Alessandra
2009-11-15
Using a Legendre transformation, we compute the unconstrained Hamiltonian of a spinning test particle in a curved spacetime at linear order in the particle spin. The equations of motion of this unconstrained Hamiltonian coincide with the Mathisson-Papapetrou-Pirani equations. We then use the formalism of Dirac brackets to derive the constrained Hamiltonian and the corresponding phase space algebra in the Newton-Wigner spin supplementary condition, suitably generalized to curved spacetime, and find that the phase space algebra (q,p,S) is canonical at linear order in the particle spin. We provide explicit expressions for this Hamiltonian in a spherically symmetric spacetime, both in isotropic and spherical coordinates, and in the Kerr spacetime in Boyer-Lindquist coordinates. Furthermore, we find that our Hamiltonian, when expanded in post-Newtonian (PN) orders, agrees with the Arnowitt-Deser-Misner canonical Hamiltonian computed in PN theory in the test particle limit. Notably, we recover the known spin-orbit couplings through 2.5PN order and the spin-spin couplings of type S{sub Kerr}S (and S{sub Kerr}{sup 2}) through 3PN order, S{sub Kerr} being the spin of the Kerr spacetime. Our method allows one to compute the PN Hamiltonian at any order, in the test particle limit and at linear order in the particle spin. As an application we compute it at 3.5PN order.
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.
Relativistic positioning in Schwarzschild space-time
NASA Astrophysics Data System (ADS)
Puchades, Neus; Sáez, Diego
2015-04-01
In the Schwarzschild space-time created by an idealized static spherically symmetric Earth, two approaches -based on relativistic positioning- may be used to estimate the user position from the proper times broadcast by four satellites. In the first approach, satellites move in the Schwarzschild space-time and the photons emitted by the satellites follow null geodesics of the Minkowski space-time asymptotic to the Schwarzschild geometry. This assumption leads to positioning errors since the photon world lines are not geodesics of any Minkowski geometry. In the second approach -the most coherent one- satellites and photons move in the Schwarzschild space-time. This approach is a first order one in the dimensionless parameter GM/R (with the speed of light c=1). The two approaches give different inertial coordinates for a given user. The differences are estimated and appropriately represented for users located inside a great region surrounding Earth. The resulting values (errors) are small enough to justify the use of the first approach, which is the simplest and the most manageable one. The satellite evolution mimics that of the GALILEO global navigation satellite system.
Resonant Dynamics and the Instability of Anti-de Sitter Spacetime.
Bizoń, Piotr; Maliborski, Maciej; Rostworowski, Andrzej
2015-08-21
We consider spherically symmetric Einstein-massless-scalar field equations with a negative cosmological constant in five dimensions and analyze the evolution of small perturbations of anti-de Sitter (AdS) spacetime using the recently proposed resonant approximation. We show that for typical initial data the solution of the resonant system develops an oscillatory singularity in finite time. This result hints at a possible route to establishing the instability of AdS under arbitrarily small perturbations. PMID:26340178
Resonant Dynamics and the Instability of Anti-de Sitter Spacetime
NASA Astrophysics Data System (ADS)
Bizoń, Piotr; Maliborski, Maciej; Rostworowski, Andrzej
2015-08-01
We consider spherically symmetric Einstein-massless-scalar field equations with a negative cosmological constant in five dimensions and analyze the evolution of small perturbations of anti-de Sitter (AdS) spacetime using the recently proposed resonant approximation. We show that for typical initial data the solution of the resonant system develops an oscillatory singularity in finite time. This result hints at a possible route to establishing the instability of AdS under arbitrarily small perturbations.
Null surfaces in static space-times
NASA Astrophysics Data System (ADS)
Vollick, Dan N.
2015-07-01
In this paper I consider surfaces in a space-time with a Killing vector ξ α that is time-like and hypersurface-orthogonal on one side of the surface. The Killing vector may be either time-like or space-like on the other side of the surface. It has been argued that the surface is null if ξ α ξ α → 0 as the surface is approached from the static region. This implies that, in a coordinate system adapted to ξ, surfaces with g tt = 0 are null. In spherically symmetric space-times the condition g rr = 0 instead of g tt = 0 is sometimes used to locate null surfaces. In this paper I examine the arguments that lead to these two different criteria and show that both arguments are incorrect. A surface ξ = const has a normal vector whose norm is proportional to ξ α ξ α . This lead to the conclusion that surfaces with ξ α ξ α = 0 are null. However, the proportionality factor generally diverges when g tt = 0, leading to a different condition for the norm to be null. In static spherically symmetric space-times this condition gives g rr = 0, not g tt = 0. The problem with the condition g rr = 0 is that the coordinate system is singular on the surface. One can either use a nonsingular coordinate system or examine the induced metric on the surface to determine if it is null. By using these approaches it is shown that the correct criteria is g tt = 0. I also examine the condition required for the surface to be nonsingular.
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
Quantum corrected spherical collapse: A phenomenological framework
Ziprick, Jonathan; Kunstatter, Gabor
2010-08-15
A phenomenological framework is presented for incorporating quantum gravity motivated corrections into the dynamics of spherically symmetric collapse. The effective equations are derived from a variational principle that guarantees energy conservation and the existence of a Birkhoff theorem. The gravitational potential can be chosen as a function of the areal radius to yield specific nonsingular static spherically symmetric solutions that generically have two horizons. For a specific choice of potential, the effective stress energy tensor violates only the dominant energy condition. The violations are maximum near the inner horizon and die off rapidly. A numerical study of the quantum corrected collapse of a spherically symmetric scalar field in this case reveals that the modified gravitational potential prevents the formation of a central singularity and ultimately yields a static, mostly vacuum, spacetime with two horizons. The matter 'piles up' on the inner horizon giving rise to mass inflation at late times. The Cauchy horizon is transformed into a null, weak singularity, but in contrast to Einstein gravity, the absence of a central singularity renders this null singularity stable.
The anti-de Sitter spacetime as a time machine
NASA Astrophysics Data System (ADS)
Ahmed, Faizuddin; Bikash Hazarika, Bidyut; Sarma, Debojit
2016-07-01
We construct an axially symmetric spacetime admitting, after a certain instant, closed timelike curves (CTCs) indicating that it is a time-machine spacetime. The spacetime, which is locally anti-de Sitter, is a four-dimensional extension of the Misner space with identical causality-violating properties. In this spacetime, CTCs evolve from a casually well-behaved initial hypersurface.
Nonlinear cosmological spherical collapse of quintessence
NASA Astrophysics Data System (ADS)
Rekier, J.; Füzfa, A.; Cordero-Carrión, I.
2016-02-01
We present a study of the fully relativistic spherical collapse in the presence of quintessence using on numerical relativity, following the method proposed by the authors in a previous article [Phys. Rev. D 91, 024025 (2015)]. We ascertain the validity of the method by studying the evolution of a spherically symmetric quintessence inhomogeneity on a de Sitter background and we find that it has an impact on the local expansion around the center of coordinates. We then proceed to compare the results of our method to those of the more largely adopted top-hat model. We find that quintessence inhomogeneities do build up under the effect that matter inhomogeneities have on the local space-time, yet remain very small due to the presence of momentum transfer from the over-dense to the background regions. We expect that these might have an even more important role in modified theories of gravitation.
Computing spacetime curvature via differential-algebraic equations
Ashby, S.F.; Lee, S.L.; Petzold, L.R.; Saylor, P.E.; Seidel, E.
1996-01-01
The equations that govern the behavior of physical systems can often solved numerically using a method of lines approach and differential-algebraic equation (DAE) solvers. For example, such an approach can be used to solve the Einstein field equations of general relativity, and thereby simulate significant astrophysical events. In this paper, we describe some preliminary work in which two model problems in general relativity are formulated, spatially discretized, and then numerically solved as a DAE. In particular, we seek to reproduce the solution to the spherically symmetric Schwarzschild spacetime. This is an important testbed calculation in numerical relativity since the solution is the steady-state for the collision of two (or more) non-rotating black holes. Moreover, analytic late-time properties of the Schwarzschild spacetime are well known and can be used the accuracy of the simulation.
Wormholes and nonsingular spacetimes in Palatini f (R ) gravity
NASA Astrophysics Data System (ADS)
Bambi, Cosimo; Cardenas-Avendano, Alejandro; Olmo, Gonzalo J.; Rubiera-Garcia, D.
2016-03-01
We reconsider the problem of f (R ) theories of gravity coupled to Born-Infeld theory of electrodynamics formulated in a Palatini approach, where metric and connection are independent fields. By studying electrovacuum configurations in a static and spherically symmetric spacetime, we find solutions which reduce to their Reissner-Nordström counterparts at large distances but undergo important nonperturbative modifications close to the center. Our new analysis reveals that the pointlike singularity is replaced by a finite-size wormhole structure, which provides a geodesically complete and thus nonsingular spacetime, despite the existence of curvature divergences at the wormhole throat. Implications of these results, in particular for the cosmic censorship conjecture, are discussed.
Doppler tracking in time-dependent cosmological spacetimes
NASA Astrophysics Data System (ADS)
Giulini, Domenico; Carrera, Matteo
I will discuss the theoretical problems associated with Doppler tracking in time dependent background geometries, where ordinary Newtonian kinematics fails. A derivation of an exact general-relativistic formula for the two-way Doppler tracking of a spacecraft in homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetimes is presented, as well as a controlled approximation in McVittie spacetimes representing an FLRW background with a single spherically-symmetric inhomogeneity (e.g. a single star or black hole). The leading-order corrections of the acceleration as compared to the Newtonian expression are calculated, which are due to retardation and cosmological expansion and which in the Solar System turn out to be significantly below the scale (nanometer per square-second) set by the Pioneer Anomaly. Last, but not least, I discuss kinematical ambiguities connected with notions of "simultaneity" and "spatial distance", which, in principle, also lead to tracking corrections.
Back reaction effects in black hole spacetimes
NASA Astrophysics Data System (ADS)
Loustó, C. O.; Sánchez, N.
1988-10-01
We solve the semiclassical Einstein equations for the static spherically symmetric case. Using expressions for the renormalized
NASA Astrophysics Data System (ADS)
Peng, Jie; Zhu, Jianhua; Li, Tong
2016-06-01
The thermal lens effect of 2.1 μm Cr, Tm, Ho: YAG (CTH:YAG) solid-state laser under high pumping power condition is analyzed, and a symmetric spherical resonator which is insensitive to thermal focal length change is proposed to improve the beam quality of Fabry-Perot (F-P) resonator. Then the gradient-reflectivity mirror is introduced as output mirror to optimize the resonator mode and beam quality. Based on the scalar diffraction theory, the Fox-Li numerical iteration method and fast Fourier transform (FFT) algorithm are used to calculate the resonator mode and output power distribution of resonators with Gaussian, super-Gaussian and parabolic gradient mirror, respectively. By comparing the cavity loss and beam quality, one can find that the symmetric spherical resonator with a super-Gaussian mirror can provide the best output beam quality, it has the minimum cavity loss of 0.1907, the minimum far-field divergence angle of 1 mrad and the maximum power in the bucket (PIB) of 89.42%.
NASA Astrophysics Data System (ADS)
Gambini, Rodolfo; Pullin, Jorge
2013-01-01
We discuss a gauge fixing of gravity coupled to a scalar field in spherical symmetry such that the Hamiltonian is an integral over space of a local density. In a previous paper, we had presented it using Ashtekar’s new variables. Here we study it in metric variables. We specify completely the initial-boundary value problem for ingoing Gaussian pulses.
Geodesics in the static Mallett spacetime
Olum, Ken D.
2010-06-15
Mallett has exhibited a cylindrically symmetric spacetime containing closed timelike curves produced by a light beam circulating around a line singularity. I analyze the static version of this spacetime obtained by setting the intensity of the light to zero. Some null geodesics can escape to infinity, but all timelike geodesics in this spacetime originate and terminate at the singularity. Freely falling matter originally at rest quickly attains relativistic velocity inward and is destroyed at the singularity.
Scalar hair on the black hole in asymptotically anti--de Sitter spacetime
Torii, Takashi; Maeda, Kengo; Narita, Makoto
2001-08-15
We examine the no-hair conjecture in asymptotically anti--de Sitter (AdS) spacetime. First, we consider a real scalar field as the matter field and assume static spherically symmetric spacetime. Analysis of the asymptotics shows that the scalar field must approach the extremum of its potential. Using this fact, it is proved that there is no regular black hole solution when the scalar field is massless or has a 'convex' potential. Surprisingly, while the scalar field has a growing mode around the local minimum of the potential, there is no growing mode around the local maximum. This implies that the local maximum is a kind of 'attractor' of the asymptotic scalar field. We give two examples of the new black hole solutions with a nontrivial scalar field configuration numerically in the symmetric or asymmetric double well potential models. We study the stability of these solutions by using the linear perturbation method in order to examine whether or not the scalar hair is physical. In the symmetric double well potential model, we find that the potential function of the perturbation equation is positive semidefinite in some wide parameter range and that the new solution is stable. This implies that the black hole no-hair conjecture is violated in asymptotically AdS spacetime.
NASA Astrophysics Data System (ADS)
Gryb, Sean
2015-04-01
The notion of reference frame is a central theoretical construct for interpreting the physical implications of spacetime diffeomorphism invariance in General Relativity. However, the alternative formulation of classical General Relativity known as Shape Dynamics suggest that a subset of spacetime diffeomorphisms—namely hypersurface deformations—are, in a precise sense, dual to spatial conformal (or Weyl) invariance. Moreover, holographic gauge/gravity dualities suggest that bulk spacetime diffeomorphism invariance can be replaced by the properties of boundary CFTs. How can these new frameworks be compatible with the traditional notion of reference frame so fundamental to our interpretation of General Relativity? In this paper, we address this question by investigating the classical case of maximally symmetric spacetimes with a positive cosmological constant. We find that it is possible to define a notion of Shape Observer that represents a conformal reference frame dual to the notion of inertial reference frame in spacetime and provide a precise dictionary relating the two notions. We explicitly calculate the Hamilton-Jacobi functional for a theory of reparametrization invariant shape configurations dual to a theory of free inertial observers in de Sitter. These Shape Observers are holographic in the sense that they are defined on the asymptotic conformal boundaries of spacetime but know about bulk physics, and show that the dual theory is conformally invariant at the classical level. This leads to a first principles derivation of an exact classical holographic correspondence that can easily be generalized to more complicated situations and may lead to insights regarding the interpretation of the conformal invariance manifest in Shape Dynamics.
Acoustic perturbations on steady spherical accretion in Schwarzschild geometry
Naskar, Tapan; Chakravarty, Nabajit; Bhattacharjee, Jayanta K.; Ray, Arnab K.
2007-12-15
The stationary background flow in the spherically symmetric infall of a compressible fluid, coupled to the space-time defined by the static Schwarzschild metric, has been subjected to linearized acoustic perturbations. The perturbative procedure is based on the continuity condition and it shows that the coupling of the flow with the geometry of space-time brings about greater stability for the flow, to the extent that the amplitude of the perturbation, treated as a standing wave, decays in time, as opposed to the amplitude remaining constant in the Newtonian limit. In qualitative terms this situation simulates the effect of a dissipative mechanism in the classical Bondi accretion flow, defined in the Newtonian construct of space and time. As a result of this approach it becomes impossible to define an acoustic metric for a conserved spherically symmetric flow, described within the framework of Schwarzschild geometry. In keeping with this view, the perturbation, considered separately as a high-frequency traveling wave, also has its amplitude reduced.
Hořava's quantum gravity illustrated by embedding diagrams of the Kehagias-Sfetsos spacetimes
NASA Astrophysics Data System (ADS)
Goluchová, Kateřina; Kulczycki, Konrad; Vieira, Ronaldo S. S.; Stuchlík, Zdeněk; Kluźniak, Włodek; Abramowicz, Marek
2015-11-01
Possible astrophysical consequences of the Hořava quantum gravity theory have been recently studied by several authors. They usually employ the Kehagias-Sfetsos (KS) spacetime which is a spherically symmetric vacuum solution of a specific version of Hořava's gravity. The KS metric has several unusual geometrical properties that in the present article we examine by means of the often used technique of embedding diagrams. We pay particular attention to the transition between naked singularity and black-hole states, which is possible along some particular sequences of the KS metrics.
Relative Locality in Curved Spacetime
NASA Astrophysics Data System (ADS)
Kowalski-Glikman, Jerzy; Rosati, Giacomo
2013-07-01
In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a nontrivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are present. So far aspects of nonlinearities in momentum space have been studied only for flat or constantly expanding (de Sitter) spacetimes, relying on their maximally symmetric nature. The extension of curved momentum space frameworks to arbitrary spacetime geometries could be relevant for the opportunities to test Planck-scale curvature/deformation of particles momentum space. As a first example of this construction we describe the particle with κ-Poincaré momentum space on a circular orbit in Schwarzschild spacetime, where the contributes of momentum space curvature turn out to be negligible. The analysis of this problem relies crucially on the solution of the soccer ball problem.
Toroidal configurations of perfect fluid in the Reissner-Nordström-(anti-)de Sitter spacetimes
Kucáková, Hana; Slaný, Petr; Stuchlík, Zdenĕk E-mail: petr.slany@fpf.slu.cz
2011-01-01
Influence of cosmological constant on toroidal fluid configurations around charged spherically symmetric black holes and naked singularities is demostrated by study of perfect-fluid tori with uniform distribution of specific angular momentum orbiting in the Reissner-Nordström-(anti-)de Sitter spacetimes. Toroidal configurations are allowed only in the spacetimes admitting existence of stable circular geodesics. Configurations with marginally closed equipotential (equipressure) surfaces crossing itself in a cusp allow accretion (through the inner cusp) and/or excretion (through the outer cusp) of matter from the toroidal configuration. Detailed classification of the Reissner-Nordström-(anti-)de Sitter spacetimes according to properties of the marginally stable tori is given. It is demonstrated that in the Reissner-Nordström-de Sitter naked-singularity spacetimes an interesting phenomenon of doubled tori can exist enabling exchange of matter between two tori in both inward and outward directions. In naked-singularity spacetimes the accretion onto the central singularity is impossible due to existence of a potential barrier.
Symmetrizing the symmetrization postulate
NASA Astrophysics Data System (ADS)
York, Michael
2000-11-01
Reasonable requirements of (a) physical invariance under particle permutation and (b) physical completeness of state descriptions [1], enable us to deduce a Symmetric Permutation Rule(SPR): that by taking care with our state descriptions, it is always possible to construct state vectors (or wave functions) that are purely symmetric under pure permutation for all particles, regardless of type distinguishability or spin. The conventional exchange antisymmetry for two identical half-integer spin particles is shown to be due to a subtle interdependence in the individual state descriptions arising from an inherent geometrical asymmetry. For three or more such particles, however, antisymmetrization of the state vector for all pairs simultaneously is shown to be impossible and the SPR makes observably different predictions, although the usual pairwise exclusion rules are maintained. The usual caveat of fermion antisymmetrization—that composite integer spin particles (with fermionic constituents) behave only approximately like bosons—is no longer necessary.
Spherical gravitational collapse in N dimensions
Goswami, Rituparno; Joshi, Pankaj S.
2007-10-15
We investigate here spherically symmetric gravitational collapse in a space-time with an arbitrary number of dimensions and with a general type I matter field, which is a broad class that includes most of the physically reasonable matter forms. We show that given the initial data for matter in terms of the initial density and pressure profiles at an initial surface t=t{sub i} from which the collapse evolves, there exist the rest of the initial data functions and classes of solutions of Einstein equations which we construct here, such that the space-time evolution goes to a final state which is either a black hole or a naked singularity, depending on the nature of initial data and evolutions chosen, and subject to validity of the weak energy condition. The results are discussed and analyzed in the light of the cosmic censorship hypothesis in black hole physics. The formalism here combines the earlier results on gravitational collapse in four dimensions in a unified treatment. Also the earlier work is generalized to higher-dimensional space-times to allow a study of the effect of the number of dimensions on the possible final outcome of the collapse in terms of either a black hole or naked singularity. No restriction is adopted on the number of dimensions, and other limiting assumptions such as self-similarity of space-time are avoided, in order to keep the treatment general. Our methodology allows us to consider to an extent the genericity and stability aspects related to the occurrence of naked singularities in gravitational collapse.
NASA Astrophysics Data System (ADS)
Siddiqui, Azad A.
2007-04-01
In this paper the concept of foliation is reviewed. The idea of spacetime foliation by hypersurfaces of zero intrinsic curvature that are orthogonal to the world-lines of observers falling freely from infinity is also presented.
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.
Gravitational shock waves of ultra-high energetic particles on curved spacetimes
NASA Astrophysics Data System (ADS)
Loustó, C. O.; Sánchez, N.
1989-03-01
We generalize the Dray and 't Hooft procedure to generate gravitational shock waves superimposed on curved background solutions of the vacuum Einstein equations in order to include sources and a non-zero cosmological constant for the backgrounds, and a charge for the shock waves (all that in D dimensions). We apply this generalization to the study of the gravitational shock wave of ultrarelativistic particles with kinetic and electromagnetic momenta p and pe in static spherically symmetric spacetimes and its effect on shifting the event horizon (the terms with p and pe give rise to different shifts). Examples of these shock waves on the Reissner-Nordstrom and the Schwarzschild-de Sitter (and Schwarzschild-anti de Sitter) spacetimes are considered. UA 336. Laboratoire associé au CNRS, Observatoire de Meudon et Ecole Normale Supérieure.
Hartle, J.B. Isaac Newton Institute for the Mathematical Sciences, University of Cambridge, Cambridge CB3 0EH )
1995-02-15
In usual quantum theory, the information available about a quantum system is defined in terms of the density matrix describing it on a spacelike surface. This definition must be generalized for extensions of quantum theory which neither require, nor always permit, a notion of state on a spacelike surface. In particular, it must be generalized for the generalized quantum theories appropriate when spacetime geometry fluctuates quantum mechanically or when geometry is fixed but not foliable by spacelike surfaces. This paper introduces a four-dimensional notion of the information available about a quantum system's boundary conditions in the various sets of decohering, coarse-grained histories it may display. This spacetime notion of information coincides with the familiar one when quantum theory [ital is] formulable in terms of states on spacelike surfaces but generalizes this notion when it cannot be so formulated. The idea of spacetime information is applied in several contexts: When spacetime geometry is fixed the information available through alternatives restricted to a fixed spacetime region is defined. The information available through histories of alternatives of general operators is compared to that obtained from the more limited coarse grainings of sum-over-histories quantum mechanics that refer only to coordinates. The definition of information is considered in generalized quantum theories. We consider as specific examples time-neutral quantum mechanics with initial and final conditions, quantum theories with nonunitary evolution, and the generalized quantum frameworks appropriate for quantum spacetime. In such theories complete information about a quantum system is not necessarily available on any spacelike surface but must be searched for throughout spacetime. The information loss commonly associated with the evolution of pure states into mixed states'' in black hole evaporation is thus not in conflict with the principles of generalized quantum mechanics.
Note on cosmological Levi-Civita spacetimes in higher dimensions
Sarioglu, Oezguer; Tekin, Bayram
2009-04-15
We find a class of solutions to cosmological Einstein equations that generalizes the four dimensional cylindrically symmetric spacetimes to higher dimensions. The AdS soliton is a special member of this class with a unique singularity structure.
Quantization of Horizon Entropy and the Thermodynamics of Spacetime
NASA Astrophysics Data System (ADS)
Skákala, Jozef
2014-06-01
This is a review of my work published in the papers of Skakala (JHEP 1201:144, 2012; JHEP 1206:094, 2012) and Chirenti et al. (Phys. Rev. D 86:124008, 2012; Phys. Rev. D 87:044034, 2013). It offers a more detailed discussion of the results than the accounts in those papers, and it links my results to some conclusions recently reached by other authors. It also offers some new arguments supporting the conclusions in the cited articles. The fundamental idea of this work is that the semiclassical quantization of the black hole entropy, as suggested by Bekenstein (Phys. Rev. D 7:2333-2346, 1973), holds (at least) generically for the spacetime horizons. We support this conclusion by two separate arguments: (1) we generalize Bekenstein's lower bound on the horizon area transition to a much wider class of horizons than only the black-hole horizon, and (2) we obtain the same entropy spectra via the asymptotic quasi-normal frequencies of some particular spherically symmetric multi-horizon spacetimes (in the way proposed by Maggiore (Phys. Rev. Lett. 100:141301, 2008)). The main result of this paper supports the conclusions derived by Kothawalla et al. (Phys. Rev. D 78:104018, 2008) and Kwon and Nam (Class. Quant. Grav. 28:035007, 2011), on the basis of different arguments.
Conformal Killing Vectors in LRS Bianchi Type V Spacetimes
NASA Astrophysics Data System (ADS)
Suhail, Khan; Tahir, Hussain; Ashfaque, H. Bokhari; Gulzar, Ali Khan
2016-03-01
In this note, we investigate conformal Killing vectors (CKVs) of locally rotationally symmetric (LRS) Bianchi type V spacetimes. Subject to some integrability conditions, CKVs up to implicit functions of (t,x) are obtained. Solving these integrability conditions in some particular cases, the CKVs are completely determined, obtaining a classification of LRS Bianchi type V spacetimes. The inheriting conformal Killing vectors of LRS Bianchi type V spacetimes are also discussed.
Light rays in a spherically symmetric medium
NASA Astrophysics Data System (ADS)
Gillespie, Daniel T.
1986-06-01
We derive from Maxwell's equations a set of three coupled first-order differential equations for high-frequency light ray trajectories in a medium whose index of refraction n(r) at any point r is a function only of r.
NASA Astrophysics Data System (ADS)
Banks, Tom
2012-10-01
The theory of holographic spacetime (HST) generalizes both string theory and quantum field theory (QFT). It provides a geometric rationale for supersymmetry (SUSY) and a formalism in which super-Poincare invariance follows from Poincare invariance. HST unifies particles and black holes, realizing both as excitations of noncommutative geometrical variables on a holographic screen. Compact extra dimensions are interpreted as finite-dimensional unitary representations of super-algebras, and have no moduli. Full field theoretic Fock spaces, and continuous moduli are both emergent phenomena of super-Poincare invariant limits in which the number of holographic degrees of freedom goes to infinity. Finite radius de Sitter (dS) spaces have no moduli, and break SUSY with a gravitino mass scaling like Λ1/4. In regimes where the Covariant Entropy Bound is saturated, QFT is not a good description in HST, and inflation is such a regime. Following ideas of Jacobson, the gravitational and inflaton fields are emergent classical variables, describing the geometry of an underlying HST model, rather than "fields associated with a microscopic string theory". The phrase in quotes is meaningless in the HST formalism, except in asymptotically flat and AdS spacetimes, and some relatives of these.
Ramond, P. . Dept. of Physics)
1993-01-01
The Wolfenstein parametrization is extended to the quark masses in the deep ultraviolet, and an algorithm to derive symmetric textures which are compatible with existing data is developed. It is found that there are only five such textures.
Ramond, P.
1993-04-01
The Wolfenstein parametrization is extended to the quark masses in the deep ultraviolet, and an algorithm to derive symmetric textures which are compatible with existing data is developed. It is found that there are only five such textures.
NASA Astrophysics Data System (ADS)
Liang, Canbin; Tian, Guihua
1994-11-01
Electromagnetic fields yielding plane symmetric metrics in higher-dimensional spacetimes are exhausted and classified. It is shown that these EM fields must fall into one of the following two cases: (i)F it =F iz =0,i=1,...,n; (ii)Ftz=0. We give the general solution to the Einstein-Maxwell equations in higher dimensions corresponding to electromagnetic fields of case (ii) withF it =F iz , which covers all even-dimensional spacetimes as well as a subcase of odd-dimensional spacetimes.
New Features of Gravitational Collapse in Anti-de Sitter Spacetimes
NASA Astrophysics Data System (ADS)
Santos-Oliván, Daniel; Sopuerta, Carlos F.
2016-01-01
Gravitational collapse of a massless scalar field in spherically symmetric anti-de Sitter (AdS) spacetimes presents a new phenomenology with a series of critical points whose dynamics is discretely self-similar as in the asymptotically flat case. Each critical point is the limit of a branch of scalar field configurations that have bounced off the AdS boundary a fixed number of times before forming an apparent horizon. We present results from a numerical study that focus on the interfaces between branches. We find that there is a mass gap between branches and that subcritical configurations near the critical point form black holes with an apparent horizon mass that follows a power law of the form MAH-Mg∝(pc-p )ξ, where Mg is the mass gap and the exponent ξ ≃0.7 appears to be universal.
Compact stars on pseudo-spheroidal spacetime compatible with observational data
NASA Astrophysics Data System (ADS)
Thomas, V. O.; Pandya, D. M.
2015-12-01
A new class of solutions for Einstein's field equations representing a static spherically symmetric anisotropic distribution of matter is obtained on the background of pseudo-spheroidal spacetime. We have prescribed the bounds of the model parameters k and p0 on the basis of the elementary criteria for physical acceptability, viz., regularity, stability and energy conditions. By taking the values of model parameters from the prescribed bounds, we have shown that our model is compatible with the observational data of a wide variety of compact stars like 4U 1820-30, PSR J1903{+}327, 4U 1608-52, Vela X-1, PSR J1614-2230, SMC X-4 and Cen X-3.
New Features of Gravitational Collapse in Anti-de Sitter Spacetimes.
Santos-Oliván, Daniel; Sopuerta, Carlos F
2016-01-29
Gravitational collapse of a massless scalar field in spherically symmetric anti-de Sitter (AdS) spacetimes presents a new phenomenology with a series of critical points whose dynamics is discretely self-similar as in the asymptotically flat case. Each critical point is the limit of a branch of scalar field configurations that have bounced off the AdS boundary a fixed number of times before forming an apparent horizon. We present results from a numerical study that focus on the interfaces between branches. We find that there is a mass gap between branches and that subcritical configurations near the critical point form black holes with an apparent horizon mass that follows a power law of the form M(AH)-M(g)∝(p(c)-p)^(ξ), where M(g) is the mass gap and the exponent ξ≃0.7 appears to be universal. PMID:26871317
Milking the spherical cow - on aspherical dynamics in spherical coordinates
NASA Astrophysics Data System (ADS)
Pontzen, Andrew; Read, Justin I.; Teyssier, Romain; Governato, Fabio; Gualandris, Alessia; Roth, Nina; Devriendt, Julien
2015-08-01
Galaxies and the dark matter haloes that host them are not spherically symmetric, yet spherical symmetry is a helpful simplifying approximation for idealized calculations and analysis of observational data. The assumption leads to an exact conservation of angular momentum for every particle, making the dynamics unrealistic. But how much does that inaccuracy matter in practice for analyses of stellar distribution functions, collisionless relaxation, or dark matter core-creation? We provide a general answer to this question for a wide class of aspherical systems; specifically, we consider distribution functions that are `maximally stable', i.e. that do not evolve at first order when external potentials (which arise from baryons, large-scale tidal fields or infalling substructure) are applied. We show that a spherically symmetric analysis of such systems gives rise to the false conclusion that the density of particles in phase space is ergodic (a function of energy alone). Using this idea we are able to demonstrate that: (a) observational analyses that falsely assume spherical symmetry are made more accurate by imposing a strong prior preference for near-isotropic velocity dispersions in the centre of spheroids; (b) numerical simulations that use an idealized spherically symmetric setup can yield misleading results and should be avoided where possible; and (c) triaxial dark matter haloes (formed in collisionless cosmological simulations) nearly attain our maximally stable limit, but their evolution freezes out before reaching it.
How Spherical Is a Cube (Gravitationally)?
ERIC Educational Resources Information Center
Sanny, Jeff; Smith, David
2015-01-01
An important concept that is presented in the discussion of Newton's law of universal gravitation is that the gravitational effect external to a spherically symmetric mass distribution is the same as if all of the mass of the distribution were concentrated at the center. By integrating over ring elements of a spherical shell, we show that the…
Symmetric spaces of exceptional groups
Boya, L. J.
2010-02-15
We address the problem of the reasons for the existence of 12 symmetric spaces with the exceptional Lie groups. The 1 + 2 cases for G{sub 2} and F{sub 4}, respectively, are easily explained from the octonionic nature of these groups. The 4 + 3 + 2 cases on the E{sub 6,7,8} series require the magic square of Freudenthal and, for the split case, an appeal to the supergravity chain in 5, 4, and 3 space-time dimensions.
Presheaves of Superselection Structures in Curved Spacetimes
NASA Astrophysics Data System (ADS)
Vasselli, Ezio
2015-04-01
We show that superselection structures on curved spacetimes that are expected to describe quantum charges affected by the underlying geometry are categories of sections of presheaves of symmetric tensor categories. When an embedding functor is given, the superselection structure is a Tannaka-type dual of a locally constant group bundle, which hence becomes a natural candidate for the role of the gauge group. Indeed, we show that any locally constant group bundle (with suitable structure group) acts on a net of C* algebras fulfilling normal commutation relations on an arbitrary spacetime. We also give examples of gerbes of C* algebras, defined by Wightman fields and constructed using projective representations of the fundamental group of the spacetime, which we propose as solutions for the problem that existence and uniqueness of the embedding functor are not guaranteed.
Region with trapped surfaces in spherical symmetry, its core, and their boundaries
NASA Astrophysics Data System (ADS)
Bengtsson, Ingemar; Senovilla, José M. M.
2011-02-01
We consider the region T in spacetime containing future-trapped closed surfaces and its boundary B, and derive some of their general properties. We then concentrate on the case of spherical symmetry, but the methods we use are general and applicable to other situations. We argue that closed trapped surfaces have a nonlocal property, “clairvoyance”, which is inherited by B. We prove that B is not a marginally trapped tube in general, and that it can have portions in regions whose whole past is flat. For asymptotically flat black holes, we identify a general past barrier, well inside the event horizon, to the location of B under physically reasonable conditions. We also define the core Z of the trapped region as that part of T which is indispensable to sustain closed trapped surfaces. We prove that the unique spherically symmetric dynamical horizon is the boundary of such a core, and we argue that this may serve to single it out. To illustrate the results, some explicit examples are discussed, namely, Robertson-Walker geometries and the imploding Vaidya spacetime.
Constraining spacetime torsion with the Moon and Mercury
March, Riccardo; Bellettini, Giovanni; Tauraso, Roberto; Dell'Agnello, Simone
2011-05-15
We report a search for new gravitational physics phenomena based on Riemann-Cartan theory of general relativity including spacetime torsion. Starting from the parametrized torsion framework of Mao, Tegmark, Guth, and Cabi, we analyze the motion of test bodies in the presence of torsion, and, in particular, we compute the corrections to the perihelion advance and to the orbital geodetic precession of a satellite. We consider the motion of a test body in a spherically symmetric field, and the motion of a satellite in the gravitational field of the Sun and the Earth. We describe the torsion field by means of three parameters, and we make use of the autoparallel trajectories, which in general differ from geodesics when torsion is present. We derive the specific approximate expression of the corresponding system of ordinary differential equations, which are then solved with methods of celestial mechanics. We calculate the secular variations of the longitudes of the node and of the pericenter of the satellite. The computed secular variations show how the corrections to the perihelion advance and to the orbital de Sitter effect depend on the torsion parameters. All computations are performed under the assumptions of weak field and slow motion. To test our predictions, we use the measurements of the Moon's geodetic precession from lunar laser ranging data, and the measurements of Mercury's perihelion advance from planetary radar ranging data. These measurements are then used to constrain suitable linear combinations of the torsion parameters.
(2+1)-dimensional gravity in Weyl integrable spacetime
NASA Astrophysics Data System (ADS)
Madriz Aguilar, J. E.; Romero, C.; Fonseca Neto, J. B.; Almeida, T. S.; Formiga, J. B.
2015-11-01
We investigate (2+1)-dimensional gravity in a Weyl integrable spacetime (WIST). We show that, unlike general relativity, this scalar-tensor theory has a Newtonian limit for any dimension n≥slant 3 and that in three dimensions the congruence of world lines of particles of a pressureless fluid has a non-vanishing geodesic deviation. We present and discuss a class of static vacuum solutions generated by a circularly symmetric matter distribution that for certain values of the parameter ω corresponds to a spacetime with a naked singularity at the center of the matter distribution. We interpret all these results as being a direct consequence of the spacetime geometry.
Black Hole Spacetimes with Killing-Yano Symmetries
NASA Astrophysics Data System (ADS)
Kubizňák, David
2010-03-01
We present a brief overview of black hole spacetimes admitting Killing-Yano tensors. In vacuum these include Kerr-NUT-(A)dS metrics and certain black brane solutions. In the presence of matter fields, (conformal) Killing-Yano symmetries are known to exist for the Plebanski-Demianski solution and (trivially) for any spacetime with spherical symmetry. Special attention is devoted to generalized Killing-Yano tensors of black holes in minimal gauged supergravity Several aspects directly related to the existence of Killing-Yano tensors--such as the Kerr-Schild form, algebraic type of spacetimes, and separability of field equations--are also briefly discussed.
Relativistic positioning: four-dimensional numerical approach in Minkowski space-time
NASA Astrophysics Data System (ADS)
Puchades, Neus; Sáez, Diego
2012-10-01
We simulate the satellite constellations of two Global Navigation Satellite Systems: Galileo (EU) and GPS (USA). Satellite motions are described in the Schwarzschild space-time produced by an idealized spherically symmetric non rotating Earth. The trajectories are then circumferences centered at the same point as Earth. Photon motions are described in Minkowski space-time, where there is a well known relation, (Coll et al. in Class. Quantum Gravit. 27:065013, 2010a), between the emission and inertial coordinates of any event. Here, this relation is implemented in a numerical code, which is tested and applied. The first application is a detailed numerical four-dimensional analysis of the so-called emission coordinate region and co-region. In a second application, a GPS (Galileo) satellite is considered as the receiver and its emission coordinates are given by four Galileo (GPS) satellites. The bifurcation problem (double localization) in the positioning of the receiver satellite is then pointed out and discussed in detail.
Newtonian analogue of static general relativistic spacetimes: An extension to naked singularities
NASA Astrophysics Data System (ADS)
Ghosh, Shubhrangshu; Sarkar, Tamal; Bhadra, Arunava
2015-10-01
We formulate a generic Newtonian-like analogous potential for static spherically symmetric general relativistic (GR) spacetime and subsequently derived proper Newtonian-like analogous potential corresponding to Janis-Newman-Winicour (JNW) and Reissner-Nordström (RN) spacetimes, both exhibiting naked singularities. The derived potentials were found to reproduce the entire GR features including the orbital dynamics of the test particle motion and the orbital trajectories, with precise accuracy. The nature of the particle orbital dynamics including their trajectory profiles in JNW and RN geometries show altogether different behaviors with distinctive traits as compared to the nature of particle dynamics in Schwarzschild geometry. Exploiting the Newtonian-like analogous potentials, we found that the radiative efficiency of a geometrically thin and optically thick Keplerian accretion disk around naked singularities corresponding to both JNW and RN geometries, in general, is always higher than that for Schwarzschild geometry. The derived potentials would thus be useful to study astrophysical processes, especially to investigate more complex accretion phenomena in active galactic nuclei (AGNs) or in x-ray binaries (XRBs) in the presence of naked singularities and thereby to explore any noticeable differences in their observational features from those in the presence of black holes (BHs) to ascertain outstanding debatable issues relating to gravity—whether the end state of gravitational collapse in our physical Universe renders BH or naked singularity.
Stress tensor from the trace anomaly in Reissner-Nordström spacetimes
NASA Astrophysics Data System (ADS)
Anderson, Paul R.; Mottola, Emil; Vaulin, Ruslan
2007-12-01
The effective action associated with the trace anomaly provides a general algorithm for approximating the expectation value of the stress tensor of conformal matter fields in arbitrary curved spacetimes. In static, spherically symmetric spacetimes, the algorithm involves solving a fourth order linear differential equation in the radial coordinate r for the two scalar auxiliary fields appearing in the anomaly action, and its corresponding stress tensor. By appropriate choice of the homogeneous solutions of the auxiliary field equations, we show that it is possible to obtain finite stress tensors on all Reissner-Nordström event horizons, including the extreme Q=M case. We compare these finite results to previous analytic approximation methods, which yield invariably an infinite stress energy on charged black hole horizons, as well as with detailed numerical calculations that indicate the contrary. The approximation scheme based on the auxiliary field effective action reproduces all physically allowed behaviors of the quantum stress tensor, in a variety of quantum states, for fields of any spin, in the vicinity of the entire family (0≤Q≤M) of RN horizons.
Stress tensor from the trace anomaly in Reissner-Nordstroem spacetimes
Anderson, Paul R.; Mottola, Emil; Vaulin, Ruslan
2007-12-15
The effective action associated with the trace anomaly provides a general algorithm for approximating the expectation value of the stress tensor of conformal matter fields in arbitrary curved spacetimes. In static, spherically symmetric spacetimes, the algorithm involves solving a fourth order linear differential equation in the radial coordinate r for the two scalar auxiliary fields appearing in the anomaly action, and its corresponding stress tensor. By appropriate choice of the homogeneous solutions of the auxiliary field equations, we show that it is possible to obtain finite stress tensors on all Reissner-Nordstroem event horizons, including the extreme Q=M case. We compare these finite results to previous analytic approximation methods, which yield invariably an infinite stress energy on charged black hole horizons, as well as with detailed numerical calculations that indicate the contrary. The approximation scheme based on the auxiliary field effective action reproduces all physically allowed behaviors of the quantum stress tensor, in a variety of quantum states, for fields of any spin, in the vicinity of the entire family (0{<=}Q{<=}M) of RN horizons.
Dyons and dyonic black holes in su (N ) Einstein-Yang-Mills theory in anti-de Sitter spacetime
NASA Astrophysics Data System (ADS)
Shepherd, Ben L.; Winstanley, Elizabeth
2016-03-01
We present new spherically symmetric, dyonic soliton and black hole solutions of the su (N ) Einstein-Yang-Mills equations in four-dimensional asymptotically anti-de Sitter spacetime. The gauge field has nontrivial electric and magnetic components and is described by N -1 magnetic gauge field functions and N -1 electric gauge field functions. We explore the phase space of solutions in detail for su (2 ) and su (3 ) gauge groups. Combinations of the electric gauge field functions are monotonic and have no zeros; in general the magnetic gauge field functions may have zeros. The phase space of solutions is extremely rich, and we find solutions in which the magnetic gauge field functions have more than fifty zeros. Of particular interest are solutions for which the magnetic gauge field functions have no zeros, which exist when the negative cosmological constant has sufficiently large magnitude. We conjecture that at least some of these nodeless solutions may be stable under linear, spherically symmetric, perturbations.
Normalized energy eigenspinors of the Dirac field on anti-de Sitter spacetime
NASA Astrophysics Data System (ADS)
Cotăescu, Ion I.
1999-12-01
I show how to derive the normalized energy eigenspinors of the free Dirac field on anti-de Sitter spacetime by using a Cartesian tetrad gauge where the separation of spherical variables can be done as in special relativity.
Asymmetrically warped spacetimes
Csaki, C.
2001-01-01
We investigate spacetimes in which the speed of light along flat 4D sections varies over the extra dimensions due to different warp factors for the space and the time coordinates ('asymmetrically warped' spacetimes). The main property of such spaces is that while the induced metric is flat, implying Lorentz invariant particle physics on a brane, bulk gravitational effects will cause apparent violations of Lorentz invariance and of causality from the brane observer's point of view. An important experimentally verifiable consequence of this is that gravitational waves may travel with a speed different from the speed of light on the brane, and possibly even faster. We find the most general spacetimes of this sort, which are given by certain types of black hole spacetimes characterized by the m a s and the charge of the black hole. We show how to satisfy the junction conditions and analyze the properties of these space-times.
Spherical and planar three-dimensional anti-de Sitter black holes
NASA Astrophysics Data System (ADS)
Zanchin, Vilson T.; Miranda, Alex S.
2004-02-01
The technique of dimensional reduction was used in a recent paper (Zanchin V T, Kleber A and Lemos J P S 2002 Phys. Rev. D 66 064022) where a three-dimensional (3D) Einstein Maxwell dilaton theory was built from the usual four-dimensional (4D) Einstein Maxwell Hilbert action for general relativity. Starting from a class of 4D toroidal black holes in asymptotically anti-de Sitter (AdS) spacetimes several 3D black holes were obtained and studied in such a context. In the present work we choose a particular case of the 3D action which presents Maxwell field, dilaton field and an extra scalar field, besides gravity field and a negative cosmological constant, and obtain new 3D static black hole solutions whose horizons may have spherical or planar topology. We show that there is a 3D static spherically symmetric solution analogous to the 4D Reissner Nordström AdS black hole, and obtain other new 3D black holes with planar topology. From the static spherical solutions, new rotating 3D black holes are also obtained and analysed in some detail.
QFT on homothetic Killing twist deformed curved spacetimes
NASA Astrophysics Data System (ADS)
Schenkel, Alexander
2011-10-01
We study the quantum field theory (QFT) of a free, real, massless and curvature coupled scalar field on self-similar symmetric spacetimes, which are deformed by an abelian Drinfel'd twist constructed from a Killing and a homothetic Killing vector field. In contrast to deformations solely by Killing vector fields, such as the Moyal-Weyl Minkowski spacetime, the equation of motion and Green's operators are deformed. We show that there is a *-algebra isomorphism between the QFT on the deformed and the formal power series extension of the QFT on the undeformed spacetime. We study the convergent implementation of our deformations for toy-models. For these models it is found that there is a *-isomorphism between the deformed Weyl algebra and a reduced undeformed Weyl algebra, where certain strongly localized observables are excluded. Thus, our models realize the intuitive physical picture that noncommutative geometry prevents arbitrary localization in spacetime.
Symmetric Novikov superalgebras
Ayadi, Imen; Benayadi, Saied
2010-02-15
We study Novikov superalgebras with nondegenerate associative supersymmetric bilinear forms which are called symmetric Novikov superalgebras. We show that Novikov symmetric superalgebras are associative superalgebras with additional condition. Several examples of symmetric Novikov superalgebras are included, in particular, examples of symmetric Novikov superalgebras which are not 2-nilpotent. Finally, we introduce some notions of double extensions in order to give inductive descriptions of symmetric Novikov superalgebras.
Conformally symmetric traversable wormholes
Boehmer, Christian G.; Harko, Tiberiu; Lobo, Francisco S. N.
2007-10-15
Exact solutions of traversable wormholes are found under the assumption of spherical symmetry and the existence of a nonstatic conformal symmetry, which presents a more systematic approach in searching for exact wormhole solutions. In this work, a wide variety of solutions are deduced by considering choices for the form function, a specific linear equation of state relating the energy density and the pressure anisotropy, and various phantom wormhole geometries are explored. A large class of solutions impose that the spatial distribution of the exotic matter is restricted to the throat neighborhood, with a cutoff of the stress-energy tensor at a finite junction interface, although asymptotically flat exact solutions are also found. Using the 'volume integral quantifier', it is found that the conformally symmetric phantom wormhole geometries may, in principle, be constructed by infinitesimally small amounts of averaged null energy condition violating matter. Considering the tidal acceleration traversability conditions for the phantom wormhole geometry, specific wormhole dimensions and the traversal velocity are also deduced.
Induction heating plant for heat treatment of spherical metal products
NASA Astrophysics Data System (ADS)
Meshcheryakov, V. N.; Titov, S. S.
2015-12-01
A control system for an induction heating plant is developed and studied to perform symmetric high-rate surface induction heating of spherical metal products with given technological parameters for heat treatment.
Electron Optics for Biologists: Physical Origins of Spherical Aberrations
ERIC Educational Resources Information Center
Geissler, Peter; Zadunaisky, Jose
1974-01-01
Reports on the physical origins of spherical aberrations in axially symmetric electrostatic lenses to convey the essentials of electon optics to those who must think critically about the resolution of the electron microscope. (GS)
Introduction to multifractional spacetimes
Calcagni, Gianluca
2012-09-24
We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display discrete symmetries in the ultraviolet and ordinary Poincare symmetries in the infrared. Under certain reasonable assumptions, field theories (including gravity) on multifractional geometries are generally argued to be perturbatively renormalizable. We also sketch the relation with other field theories of quantum gravity based on the renormalization group.
Bounce-free spherical hydrodynamic implosion
Kagan, Grigory; Tang Xianzhu; Hsu, Scott C.; Awe, Thomas J.
2011-12-15
In a bounce-free spherical hydrodynamic implosion, the post-stagnation hot core plasma does not expand against the imploding flow. Such an implosion scheme has the advantage of improving the dwell time of the burning fuel, resulting in a higher fusion burn-up fraction. The existence of bounce-free spherical implosions is demonstrated by explicitly constructing a family of self-similar solutions to the spherically symmetric ideal hydrodynamic equations. When applied to a specific example of plasma liner driven magneto-inertial fusion, the bounce-free solution is found to produce at least a factor of four improvement in dwell time and fusion energy gain.
Gravitational self-force in nonvacuum spacetimes
NASA Astrophysics Data System (ADS)
Zimmerman, Peter; Poisson, Eric
2014-10-01
The gravitational self-force has thus far been formulated in background spacetimes for which the metric is a solution to the Einstein field equations in vacuum. While this formulation is sufficient to describe the motion of a small object around a black hole, other applications require a more general formulation that allows for a nonvacuum background spacetime. We provide a foundation for such extensions, and carry out a concrete formulation of the gravitational self-force in two specific cases. In the first we consider a particle of mass m and scalar charge q moving in a background spacetime that contains a background scalar field. In the second we consider a particle of mass m and electric charge e moving in an electrovac spacetime. The self-force incorporates all couplings between the gravitational perturbations and those of the scalar or electromagnetic fields. It is expressed as a sum of local terms involving tensors defined in the background spacetime and evaluated at the current position of the particle, as well as tail integrals that depend on the past history of the particle. Because such an expression may not be a useful starting point for an explicit evaluation of the self-force, we also provide covariant expressions for the singular potentials, expressed as local expansions near the world line; these can be involved in the construction of effective extended sources for the regular potentials, or in the computation of regularization parameters when the self-force is computed as a sum over spherical-harmonic modes.
NASA Technical Reports Server (NTRS)
1997-01-01
Developed largely through a Small Business Innovation Research contract through Langley Research Center, Interactive Picture Corporation's IPIX technology provides spherical photography, a panoramic 360-degrees. NASA found the technology appropriate for use in guiding space robots, in the space shuttle and space station programs, as well as research in cryogenic wind tunnels and for remote docking of spacecraft. Images of any location are captured in their entirety in a 360-degree immersive digital representation. The viewer can navigate to any desired direction within the image. Several car manufacturers already use IPIX to give viewers a look at their latest line-up of automobiles. Another application is for non-invasive surgeries. By using OmniScope, surgeons can look more closely at various parts of an organ with medical viewing instruments now in use. Potential applications of IPIX technology include viewing of homes for sale, hotel accommodations, museum sites, news events, and sports stadiums.
Spacetime-constrained oblivious transfer
NASA Astrophysics Data System (ADS)
Pitalúa-García, Damián
2016-06-01
In 1-out-of-2 oblivious transfer (OT), Alice inputs numbers x0,x1 , Bob inputs a bit b and outputs xb. Secure OT requires that Alice and Bob learn nothing about b and xb ¯, respectively. We define spacetime-constrained oblivious transfer (SCOT) as OT in Minkowski spacetime in which Bob must output xb within Rb, where R0 and R1 are fixed spacelike separated spacetime regions. We show that unconditionally secure SCOT is impossible with classical protocols in Minkowski (or Galilean) spacetime, or with quantum protocols in Galilean spacetime. We describe a quantum SCOT protocol in Minkowski spacetime, and we show it unconditionally secure.
5D non-symmetric gravity and geodesic confinement
NASA Astrophysics Data System (ADS)
Ghosh, Suman; Shankaranarayanan, S.
2013-09-01
This work focuses on an unexplored aspect of non-symmetric geometry where only the off-diagonal metric components along the extra dimension, in a 5-dimensional spacetime, are non-symmetric. We show that the energy densities of the stationary non-symmetric models are similar to that of brane models thereby mimicking the thick-brane scenario. We find that the massive test particles are confined near the location of the brane for both growing and decaying warp factors. This feature is unique to the non-symmetric nature of our model. We have also studied the dynamical models where standard 4D FLRW brane is embedded. Our analysis shows that the non-symmetric terms deconfine energy density at the early universe while automatically confine at late times.
NASA Astrophysics Data System (ADS)
Bini, Donato; Bittencourt, Eduardo; Geralico, Andrea; Jantzen, Robert T.
2015-04-01
A general framework is developed to investigate the properties of useful choices of stationary spacelike slicings of stationary spacetimes whose congruences of timelike orthogonal trajectories are interpreted as the world lines of an associated family of observers, the kinematical properties of which in turn may be used to geometrically characterize the original slicings. On the other hand, properties of the slicings themselves can directly characterize their utility motivated instead by other considerations like the initial value and evolution problems in the 3-plus-1 approach to general relativity. An attempt is made to categorize the various slicing conditions or "time gauges" used in the literature for the most familiar stationary spacetimes: black holes and their flat spacetime limit.
Brink, Jeandrew
2010-01-15
The problem of obtaining an explicit representation for the fourth invariant of geodesic motion (generalized Carter constant) of an arbitrary stationary axisymmetric vacuum spacetime generated from an Ernst potential is considered. The coupling between the nonlocal curvature content of the spacetime as encoded in the Weyl tensor, and the existence of a Killing tensor is explored and a constructive, algebraic test for a fourth-order Killing tensor suggested. The approach used exploits the variables defined for the Baecklund transformations to clarify the relationship between Weyl curvature, constants of geodesic motion, expressed as Killing tensors, and the solution-generation techniques. A new symmetric noncovariant formulation of the Killing equations is given. This formulation transforms the problem of looking for fourth-order Killing tensors in 4D into one of looking for four interlocking two-manifolds admitting fourth-order Killing tensors in 2D.
Superradiance in spherical layered nanostructures
NASA Astrophysics Data System (ADS)
Goupalov, S. V.
2016-06-01
We propose a design of a spherically symmetric nanostructure consisting of alternate concentric semiconductor and dielectric layers. The exciton states in different semiconductor layers of such a structure interact via the common electromagnetic field of light. We show that, if the exciton states in N semiconductor layers are in resonance with one another, then a superradiant state emerges under optical excitation of such a structure. We discuss the conditions under which superradiance can be observed and show that they strongly depend on the valence-band structure of the semiconductor layers.