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.
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.
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.
Thermodynamics of spherically symmetric spacetimes in loop quantum gravity
NASA Astrophysics Data System (ADS)
Mäkelä, Jarmo
2015-06-01
The choice of the area operator in loop quantum gravity is by no means unique. In addition to the area operator commonly used in loop quantum gravity there is also an area operator introduced by Krasnov in 1998, which gives uniformly spaced area spectra for the horizons of spacetime. Using Krasnov's area operator we consider the thermodynamics of spherically symmetric spacetimes equipped with horizons in loop quantum gravity. Among other things, our approach implies, in a pretty simple manner, that every horizon of spacetime emits thermal radiation and possesses entropy which, in the natural units, is one-quarter of its area. When applied to the de Sitter spacetime loop quantum gravity provides an explanation both to the presence and the smallness of the cosmological constant.
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
Cai Ronggen; Cao Liming; Ohta, Nobuyoshi
2010-04-15
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.
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.
Self tuning scalar fields in spherically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Appleby, Stephen
2015-05-01
We search for self tuning solutions to the Einstein-scalar field equations for the simplest class of `Fab-Four' models with constant potentials. We first review the conditions under which self tuning occurs in a cosmological spacetime, and by introducing a small modification to the original theory—introducing the second and third Galileon terms—show how one can obtain de Sitter states where the expansion rate is independent of the vacuum energy. We then consider whether the same self tuning mechanism can persist in a spherically symmetric inhomogeneous spacetime. We show that there are no asymptotically flat solutions to the field equations in which the vacuum energy is screened, other than the trivial one (Minkowski space). We then consider the possibility of constructing Schwarzschild de Sitter spacetimes for the modified Fab Four plus Galileon theory. We argue that the only model that can successfully screen the vacuum energy in both an FLRW and Schwarzschild de Sitter spacetime is one containing `John' ~ Gμν ∂μphi∂νphi and a canonical kinetic term ~ ∂αphi ∂αphi. This behaviour was first observed in [1]. The screening mechanism, which requires redundancy of the scalar field equation in the `vacuum', fails for the `Paul' term in an inhomogeneous spacetime.
New second derivative theories of gravity for spherically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Tibrewala, Rakesh
2015-06-01
We present new second derivative, generally covariant theories of gravity for spherically symmetric spacetimes (the general covariance is in the t-r plane) belonging to the class where the spherically symmetric Einstein-Hilbert theory is modified by the presence of {{g}θ θ } dependent functions. In 3+1 dimensional vacuum spacetimes there is a three-fold infinity of freedom in constructing such theories, as revealed by the presence of three arbitrary {{g}θ θ } dependent functions in the Hamiltonian (matter Hamiltonian also has the corresponding freedom). This result is not a contradiction to the theorem of Hojman et al [1], which is applicable to the full theory, whereas the above conclusion is for the symmetry reduced sector of the theory (which has a much reduced phase space). In the full theory where there are no special symmetries, the result of Hojman et al will continue to hold. In the process we also show that theories where the constraint algebra is deformed by the presence of {{g}θ θ } dependent functions—as is the case in the presence of inverse triad corrections in loop quantum gravity—can always be brought to the form where they obey the standard (undeformed) constraint algebra by performing a suitable canonical transformation. We prove that theories obtained after performing canonical transformation are inequivalent to the symmetry reduced general relativity and that the resulting theories fall within the purview of the theories mentioned above.
Quasi-local energy for spherically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Wu, Ming-Fan; Chen, Chiang-Mei; Liu, Jian-Liang; Nester, James M.
2012-09-01
We present two complementary approaches for determining the reference for the covariant Hamiltonian boundary term quasi-local energy and test them on spherically symmetric spacetimes. On the one hand, we isometrically match the 2-surface and extremize the energy. This can be done in two ways, which we call programs I (without constraint) and II (with additional constraints). On the other hand, we match the orthonormal 4-frames of the dynamic and the reference spacetimes. Then, if we further specify the observer by requiring the reference displacement to be the timelike Killing vector of the reference, the result is the same as program I, and the energy can be positive, zero, or even negative. If, instead, we require that the Lie derivatives of the two-area along the displacement vector in both the dynamic and reference spacetimes to be the same, the result is the same as program II, and it satisfies the usual criteria: the energies are non-negative and vanish only for Minkowski (or anti-de Sitter) spacetime.
Relativistic electromagnetic mass models in spherically symmetric spacetime
NASA Astrophysics Data System (ADS)
Maurya, S. K.; Gupta, Y. K.; Ray, Saibal; Chatterjee, Vikram
2016-10-01
Under the static spherically symmetric Einstein-Maxwell spacetime of embedding class one we explore possibility of constructing electromagnetic mass model where mass and other physical parameters have purely electromagnetic origin (Lorentz in Proc. Acad. Sci. Amst. 6, 1904). This work is in continuation of our earlier investigation of Maurya et al. (Eur. Phys. J. C 75:389, 2015a) where we developed an algorithm and found out three new solutions of electromagnetic mass model. In the present work we consider different metric potentials ν and λ and have analyzed them in a systematic way. It is observed that some of the previous solutions related to electromagnetic mass model are nothing but special cases of the presently obtained generalized solution set. We further verify the solution set and especially show that these are extremely applicable in the case of compact stars.
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.
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).
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.
Asymptotic behavior of marginally trapped tubes in spherically symmetric black hole spacetimes
NASA Astrophysics Data System (ADS)
Williams, Catherine M.
We begin by reviewing some fundamental features of general relativity, then outline the mathematical definitions of black holes, trapped surfaces, and marginally trapped tubes, first in general terms, then rigorously in the context of spherical symmetry. We describe explicitly the reduction of Einstein's equation on a spherically symmetric 4-dimensional Lorentzian manifold to a system of partial differential equations on a subset of 2-dimensional Minkowski space. We discuss the asymptotic behavior of marginally trapped tubes in the Schwarzschild, Vaidya, and Reisner-Nordstrom solutions to Einstein's equations in spherical symmetry, as well as in Einstein-Maxwell-scalar field black hole spacetimes generated by evolving certain classes of asymptotically flat initial data. Our first main result gives conditions on a general stress-energy tensor Talphabeta in a spherically symmetric black hole spacetime that are sufficient to guarantee that the black hole will contain a marginally trapped tube which is eventually achronal, connected, and asymptotic to the event horizon. Here "general" means that the matter model is arbitrary, subject only to a certain positive energy condition. A certain matter field decay rate, known as Price law decay in the literature, is not required per se for this asymptotic result, but such decay does imply that the marginally trapped tube has finite length with respect to the induced metric. In our second main result, we give two separate applications of the first theorem to self-gravitating Higgs field spacetimes, one using weak Price law decay, the other certain strong smallness and monotonicity assumptions.
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.
A 3+1 computational scheme for dynamic spherically symmetric black hole spacetimes: Initial data
NASA Astrophysics Data System (ADS)
Thornburg, Jonathan
1999-05-01
This is the first in a series of papers describing a 3+1 computational scheme for the numerical simulation of dynamic spherically symmetric black hole spacetimes. In this paper we discuss the construction of dynamic black hole initial data slices using York's conformal-decomposition algorithm in its most general form, where no restrictions are placed on K (the trace of the extrinsic curvature) and hence the full 4-vector nonlinear York equations must be solved numerically. To construct an initial data slice, we begin with a known black hole slice (e.g. a slice of Schwarzschild or Kerr spacetime), perturb this via some Ansatz (e.g. the addition of a suitable Gaussian to one of the coordinate components of the 3-metric, extrinsic curvature, or matter field variables), apply the York decomposition (using a further Ansatz for the inner boundary conditions) to project the perturbed field variables back into the constraint hypersurface, and finally optionally apply a numerical 3-coordinate transformation to restore any desired form for the spatial coordinates (e.g. an areal radial coordinate). In comparison to other initial data algorithms, the key advantage of this algorithm is its flexibility: K is unrestricted, allowing the use of whatever slicing is most suitable for (say) a time evolution. This algorithm also offers great flexibility in controlling the physical content of the initial data, while placing no restrictions on the type of matter fields, or on spacetime's symmetries or lack thereof. We have implemented this algorithm for the spherically symmetric scalar field system. We present numerical results for a number of asymptotically flat Eddington-Finkelstein-like initial data slices containing black holes surrounded by scalar field shells, the latter with masses ranging from as low as 0.17 to as high as 17 times the black hole mass. In all cases we find that the computed slices are very accurate: Using 4th order finite differencing on smoothly nonuniform grids
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.
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.
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.
Matching a static cylindrically symmetric elastic spacetime
NASA Astrophysics Data System (ADS)
Brito, I.; Carot, J.; Mena, F. C.; Vaz, E. G. L. R.
2012-07-01
We consider a static cylindrically symmetric spacetime with elastic matter and study the matching problem of this spacetime with a suitable exterior. For the exterior, we take the Levi-Civita spacetime and its generalization including a cosmological constant, the Linet-Tian spacetime. We show that the matching is only possible with the Linet-Tian solution.
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.
NASA Astrophysics Data System (ADS)
Shabbir, Ghulam; Mahomed, F. M.; Qureshi, M. A.
2016-11-01
A study of proper projective symmetry in the most general form of non-static spherically symmetric space-time is given using direct integration and algebraic techniques. In this study, we show that when the above space-time admits proper projective symmetry it becomes a very special class of static spherically symmetric space-times.
Spherically symmetric conformal gravity and ''gravitational bubbles''
Berezin, V.A.; Dokuchaev, V.I.; Eroshenko, Yu.N. E-mail: dokuchaev@inr.ac.ru
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.
An introduction to spherically symmetric loop quantum gravity black holes
NASA Astrophysics Data System (ADS)
Gambini, Rodolfo; Pullin, Jorge
2015-03-01
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.
Geometrodynamics in a spherically symmetric, static crossflow of null dust
Horvath, Zsolt; Kovacs, Zoltan; Gergely, Laszlo A.
2006-10-15
The spherically symmetric, static space-time generated by a crossflow of noninteracting radiation streams, treated in the geometrical optics limit (null dust), is equivalent to an anisotropic fluid forming a radiation atmosphere of a star. This reference fluid provides a preferred/internal time, which is employed as a canonical coordinate. Among the advantages we encounter a new Hamiltonian constraint, which becomes linear in the momentum conjugate to the internal time (therefore yielding a functional Schroedinger equation after quantization), and a strongly commuting algebra of the new constraints.
New framework for studying spherically symmetric static solutions in f(R) gravity
Nzioki, Anne Marie; Goswami, Rituparno; Carloni, Sante; Dunsby, Peter K. S.
2010-04-15
We develop a new covariant formalism to treat spherically symmetric spacetimes in metric f(R) theories of gravity. Using this formalism we derive the general equations for a static and spherically symmetric metric in a general f(R) gravity. These equations are used to determine the conditions for which the Schwarzschild metric is the only vacuum solution with vanishing Ricci scalar. We also show that our general framework provides a clear way of showing that the Schwarzschild solution is not a unique static spherically symmetric solution, providing some insight into how the current form of Birkhoff's theorem breaks down for these theories.
Design of spherical symmetric gradient index lenses
NASA Astrophysics Data System (ADS)
Miñano, Juan C.; Grabovičkić, Dejan; Benítez, Pablo; González, Juan C.; Santamaría, Asunción
2012-10-01
Spherical symmetric refractive index distributions also known as Gradient Index lenses such as the Maxwell-Fish-Eye (MFE), the Luneburg or the Eaton lenses have always played an important role in Optics. The recent development of the technique called Transformation Optics has renewed the interest in these gradient index lenses. For instance, Perfect Imaging within the Wave Optics framework has recently been proved using the MFE distribution. We review here the design problem of these lenses, classify them in two groups (Luneburg moveable-limits and fixed-limits type), and establish a new design techniques for each type of problem.
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.
Revisiting the quantum scalar field in spherically symmetric quantum gravity
NASA Astrophysics Data System (ADS)
Borja, Enrique F.; Garay, Iñaki; Strobel, Eckhard
2012-07-01
We extend previous results in spherically symmetric gravitational systems coupled with a massless scalar field within the loop quantum gravity framework. As a starting point, we take the Schwarzschild spacetime. The results presented here rely on the uniform discretization method. We are able to minimize the associated discrete master constraint using a variational method. The trial state for the vacuum consists of a direct product of a Fock vacuum for the matter part and a Gaussian centered around the classical Schwarzschild solution. This paper follows the line of research presented by Gambini et al (2009 Class. Quantum Grav. 26 215011 (arXiv:0906.1774v1)) and a comparison between their result and the one given in this work is made.
Implications of nonlinearity for spherically symmetric accretion
NASA Astrophysics Data System (ADS)
Sen, Sourav; Ray, Arnab K.
2014-03-01
We subject the steady solutions of a spherically symmetric accretion flow to a time-dependent radial perturbation. The equation of the perturbation includes nonlinearity up to any arbitrary order and bears a form that is very similar to the metric equation of an analogue acoustic black hole. Casting the perturbation as a standing wave on subsonic solutions, and maintaining nonlinearity in it up to the second order, we get the time dependence of the perturbation in the form of a Liénard system. A dynamical systems analysis of the Liénard system reveals a saddle point in real time, with the implication that instabilities will develop in the accreting system when the perturbation is extended into the nonlinear regime. The instability of initial subsonic states also adversely affects the temporal evolution of the flow toward a final and stable transonic state.
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.
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.
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.
On projective invariants of spherically symmetric Finsler spaces in Rn
NASA Astrophysics Data System (ADS)
Sadeghzadeh, Nasrin; Hesamfar, Maedeh
2015-05-01
In this paper, we study projective invariants of spherically symmetric Finsler metrics in Rn. We find the necessary and sufficient conditions for the metrics to be Weyl, Douglas and generalized Douglas-Weyl (GDW) types. In particular, we find the necessary and sufficient condition for the metrics to be of scalar flag curvature. Also we show that two classes of GDW and Douglas spherically symmetric Finsler metrics coincide.
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).
The spherically symmetric Standard Model with gravity
NASA Astrophysics Data System (ADS)
Balasin, H.; Böhmer, C. G.; Grumiller, D.
2005-08-01
Spherical reduction of generic four-dimensional theories is revisited. Three different notions of "spherical symmetry" are defined. The following sectors are investigated: Einstein-Cartan theory, spinors, (non-)abelian gauge fields and scalar fields. In each sector a different formalism seems to be most convenient: the Cartan formulation of gravity works best in the purely gravitational sector, the Einstein formulation is convenient for the Yang-Mills sector and for reducing scalar fields, and the Newman-Penrose formalism seems to be the most transparent one in the fermionic sector. Combining them the spherically reduced Standard Model of particle physics together with the usually omitted gravity part can be presented as a two-dimensional (dilaton gravity) theory.
Spherically Symmetric Gravitational Collapse of a Dust Cloud in Third-Order Lovelock Gravity
NASA Astrophysics Data System (ADS)
Zhou, Kang; Yang, Zhan-Ying; Zou, De-Cheng; Yue, Rui-Hong
We investigate the spherically symmetric gravitational collapse of an incoherent dust cloud by considering a LTB-type spacetime in third-order Lovelock Gravity without cosmological constant, and give three families of LTB-like solutions which separately corresponding to hyperbolic, parabolic and elliptic. Notice that the contribution of high-order curvature corrections have a profound influence on the nature of the singularity, and the global structure of spacetime changes drastically from the analogous general relativistic case. Interestingly, the presence of high order Lovelock terms leads to the formation of massive, naked and timelike singularities in the 7D spacetime, which is disallowed in general relativity. Moveover, we point out that the naked singularities in the 7D case may be gravitational weak therefore may not be a serious threat to the cosmic censorship hypothesis, while the naked singularities in the D ≥ 8 inhomogeneous collapse violate the cosmic censorship hypothesis seriously.
Spherically symmetric brane in a bulk of f(R) and Gauss–Bonnet gravity
NASA Astrophysics Data System (ADS)
Chakraborty, Sumanta; SenGupta, Soumitra
2016-11-01
Effective gravitational field equations on a four-dimensional brane embedded in a five-dimensional bulk have been considered. Using the Einstein–Hilbert action along with the Gauss–Bonnet correction term, we have derived static spherically symmetric vacuum solution to the effective field equations, first order in the Gauss–Bonnet coupling parameter. The solution so obtained, has one part corresponding to general relativity with an additional correction term, proportional to the Gauss–Bonnet coupling parameter. The correction term modifies the spacetime structure, in particular, the location of the event horizon. Proceeding further, we have derived effective field equations for f(R) gravity with Gauss–Bonnet correction term and a static spherically symmetric solution has been obtained. In this case the Gauss–Bonnet term modifies both the event and cosmological horizon of the spacetime. There exists another way of obtaining the brane metric—expanding the bulk gravitational field equations in the ratio of bulk to brane curvature scale and assuming a separable bulk metric ansatz. It turns out that static, spherically symmetric solutions obtained from this perturbative method can be matched exactly, with the solutions derived earlier. This will hold for Einstein–Hilbert plus Gauss–Bonnet as well as for f(R) with the Gauss–Bonnet correction. Implications of these results are discussed.
Local existence of symmetric spinor potentials for symmetric (3,1)-spinors in Einstein space-times
NASA Astrophysics Data System (ADS)
Andersson, F.; Edgar, S. B.
2001-03-01
We investigate the possibility of existence of a symmetric potential HABA' B' = H( AB)( A' B') for a symmetric (3,1)-spinor LABCA' , e.g., a Lanczos potential of the Weyl spinor, as defined by the equation LABCA' =∇ ( AB' HBC) A' B' . We prove that in all Einstein space-times such a symmetric potential HABA' B' exists. Potentials of this type have been found earlier in investigations of some very special spinors in restricted classes of space-times. A tensor version of this result is also given. We apply similar ideas and results by Illge to Maxwell's equations in a curved space-time.
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.
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.
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.
Classification of static plane symmetric spacetime via Noether gauge symmetries
NASA Astrophysics Data System (ADS)
Jhangeer, Adil; Iftikhar, Nazish; Naz, Tayyaba
2016-07-01
In this paper, general static plane symmetric spacetime is classified with respect to Noether operators. For this purpose, Noether theorem is used which yields a set of linear partial differential equations (PDEs) with unknown radial functions A(r), B(r) and F(r). Further, these PDEs are solved by taking different possibilities of radial functions. In the first case, all radial functions are considered same, while two functions are taken proportional to each other in second case, which further discussed by taking four different relationships between A(r), B(r) and F(r). For all cases, different forms of unknown functions of radial factor r are reported for nontrivial Noether operators with non-zero gauge term. At the end, a list of conserved quantities for each Noether operator Tables 1-4 is presented.
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
Spherically symmetric black holes in minimally modified self-dual gravity
NASA Astrophysics Data System (ADS)
Ishibashi, Akihiro; Speziale, Simone
2009-09-01
We discuss spherically symmetric black holes in the modified self-dual theory of gravity recently studied by Krasnov, obtained by adding a Weyl curvature- dependent 'cosmological term' to the Plebanski lagrangian for general relativity. This type of modified gravity admits two different types of singularities: one is a true singularity for the theory where the fundamental fields of the theory, as well as the (auxiliary) spacetime metric, become singular, and the other one is a milder 'non-metric singularity' where the metric description of the spacetime breaks down but the fundamental fields themselves are regular. We first generalize this modified self-dual gravity to include Maxwell's field and then study the basic features of spherically symmetric, charged black holes, with particular focus on whether these two types of singularities are hidden or naked. We restrict our attention to minimal forms of the modification, and find that the theory exhibits 'screening' effects of the electric charge (or 'anti-screening', depending upon the sign of the modification term), in the sense that it leads to the possibility of charging the black hole more (or less) than it would be possible in general relativity without exposing a naked singularity. We also find that for any (even arbitrarily large) value of charge, true singularities of the theory appear to be either achronal (non-timelike) covered by the hypersurface of a harmless non-metric singularity or simply hidden inside at least one Killing horizon.
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.
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.
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.
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.
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
Gyroid phase of fluids with spherically symmetric competing interactions
NASA Astrophysics Data System (ADS)
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Vollmer, Andreas
2015-10-01
Stationary and axially symmetric spacetimes play an important role in astrophysics, particularly in the theory of neutron stars and black holes. The static vacuum subclass of these spacetimes is known as Weyl's class, and contains the Schwarzschild spacetime as its most prominent example. This paper is going to study the space of Killing tensor fields of valence 3 for spacetimes of Weyl's class. Killing tensor fields play a crucial role in physics since they are in correspondence to invariants of the geodesic motion (i.e. constants of the motion). It will be proven that in static and axially symmetric vacuum spacetimes the space of Killing tensor fields of valence 3 is generated by Killing vector fields and quadratic Killing tensor fields. Using this result, it will be proven that for the family of Zipoy-Voorhees metrics, valence-3 Killing tensor fields are always generated by Killing vector fields and the metric.
Decanini, Yves; Folacci, Antoine; Raffaelli, Bernard
2010-05-15
We consider a wide class of static spherically symmetric black holes of arbitrary dimension with a photon sphere (a hypersurface on which a massless particle can orbit the black hole on unstable circular null geodesics). This class includes various spacetimes of physical interest such as Schwarzschild, Schwarzschild-Tangherlini, and Reissner-Nordstroem black holes, the canonical acoustic black hole, or the Schwarzschild-de Sitter black hole. For this class of black holes, we provide general analytical expressions for the Regge poles of the S matrix associated with a massless scalar field theory. This is achieved by using third-order WKB approximations to solve the associated radial wave equation. These results permit us to obtain analytically the nonlinear dispersion relation and the damping of the 'surface waves' lying close to the photon sphere as well as, from Bohr-Sommerfeld-type resonance conditions, formulas beyond the leading-order terms for the complex frequencies corresponding to the weakly damped quasinormal modes.
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.
Bagchi, Arjun; Rama, S. Kalyana
2004-11-15
We consider scalar-tensor theories in D-dimensional spacetime, D{>=}4. They consist of a metric and a nonminimally coupled scalar field, with its nonminimal coupling characterized by a function. The probes couple minimally to the metric only. We obtain vacuum solutions--both cosmological and static spherically symmetric ones--and study their properties. We find that, as seen by the probes, there is no singularity in the cosmological solutions for a class of functions which obey certain constraints. It turns out that for the same class of functions, there are static spherically symmetric solutions which exhibit novel properties: e.g., near the 'horizon', the gravitational force as seen by the probe becomes repulsive.
Winds from T Tauri stars. I - Spherically symmetric models
NASA Technical Reports Server (NTRS)
Hartmann, Lee; Avrett, Eugene H.; Loeser, Rudolf; Calvet, Nuria
1990-01-01
Line fluxes and profiles are computed for a sequence of spherically symmetric T Tauri wind models. The calculations indicate that the H-alpha emission of T Tauri stars arises in an extended and probably turbulent circumstellar envelope at temperatures above about 8000 K. The models predict that Mg II resonance line emission should be strongly correlated with H-alpha fluxes; observed Mg II/H-alpha ratios are inconsistent with the models unless extinction corrections have been underestimated. The models predict that most of the Ca II resonance line and IR triplet emission arises in dense layers close to the star rather than in the wind. H-alpha emission levels suggest mass loss rates of about 10 to the -8th solar mass/yr for most T Tauri stars, in reasonable agreement with independent analysis of forbidden emission lines. These results should be useful for interpreting observed line profiles in terms of wind densities, temperatures, and velocity fields.
Absorbed dose from traversing spherically symmetric, Gaussian radioactive clouds.
Thompson, J M; Poston, J W
1999-06-01
If a large radioactive cloud is produced, sampling may require that an airplane traverse the cloud. A method to predict the absorbed dose to the aircrew from penetrating the radioactive cloud is needed. Dose rates throughout spherically symmetric Gaussian clouds of various sizes, and the absorbed doses from traversing the clouds, were calculated. Cloud size is a dominant parameter causing dose to vary by orders of magnitude for a given dose rate measured at some distance. A method to determine cloud size, based on dose rate readings at two or more distances from the cloud center, was developed. This method, however, failed to resolve the smallest cloud sizes from measurements made at 1,000 m to 2,000 m from the cloud center.
NASA Astrophysics Data System (ADS)
Breitenlohner, Peter; Forgács, Peter; Maison, Dieter
2006-02-01
We give a complete classification of all static, spherically symmetric solutions of the SU(2) Einstein-Yang-Mills theory with a positive cosmological constant. Our classification proceeds in two steps. We first extend solutions of the radial field equations to their maximal interval of existence. In a second step we determine the Carter-Penrose diagrams of all 4-dimensional space-times constructible from such radial pieces. Based on numerical studies we sketch a complete phase space picture of all solutions with a regular origin.
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.
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
Spherically symmetric Einstein-aether perfect fluid models
Coley, Alan A.; Latta, Joey; Leon, Genly; Sandin, Patrik E-mail: genly.leon@ucv.cl E-mail: lattaj@mathstat.dal.ca
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.
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.
Truly naked spherically symmetric and distorted black holes
NASA Astrophysics Data System (ADS)
Zaslavskii, O. B.
2007-07-01
We demonstrate the existence of spherically symmetric truly naked black holes (TNBH) for which the Kretschmann scalar is finite on the horizon but some curvature components including those responsible for tidal forces as well as the energy density ρ¯ measured by a free-falling observer are infinite. We choose a rather generic powerlike asymptotics for the metric functions and analyze possible types of a horizon depending on the behavior of curvature components in the free-falling frame. It is also shown in a general case of distorted black holes that ρ¯ and tidal forces are either both finite or both infinite. The general approach developed in the article includes previously found examples and, in particular, TNBHs with an infinite area of a horizon. The fact that the detection of singularity depends on a frame may be relevant for a more accurate definition of the cosmic censorship conjecture. TNBHs may be considered as a new example of so-called nonscalar singularities for which the scalar curvature invariants are finite but some components of the Riemann tensor may diverge in certain frames.
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.
Spherically symmetric problem on the brane and galactic rotation curves
NASA Astrophysics Data System (ADS)
Viznyuk, Alexander; Shtanov, Yuri
2007-09-01
We investigate the braneworld model with induced gravity to clarify the role of the crossover length scale ℓ in the possible explanation of the dark-matter phenomenon in astrophysics and in cosmology. Observations of the 21 cm line from neutral hydrogen clouds in spiral galaxies reveal that the rotational velocities remain nearly constant at a value υc˜10-3 10-4 in the units of the speed of light in the region of the galactic halo. Using the smallness of υc, we develop a perturbative scheme for reconstructing the metric in a galactic halo. In the leading order of expansion in υc, at the distances r≳υcℓ, our result reproduces that obtained in the Randall-Sundrum braneworld model. This inequality is satisfied in a real spiral galaxy such as our Milky Way for distances r˜3kpc, at which the rotational velocity curve becomes flat, υc˜7×10-4, if ℓ≲2Mpc. The gravitational situation in this case can be approximately described by the Einstein equations with the so-called Weyl fluid playing the role of dark matter. In the region near the gravitating body, we derive a closed system of equations for the static spherically symmetric situation under the approximation of zero anisotropic stress of the Weyl fluid. We find the Schwarzschild metric to be an approximate vacuum solution of these equations at distances r≲rgℓ23. The value ℓ≲2Mpc complies well with the solar system tests. At the same time, in cosmology, a low-density braneworld with ℓ of this order of magnitude can mimic the expansion properties of the high-density Λ+colddarkmatter (LCDM) universe at late times. Combined observations of galactic rotation curves and gravitational lensing can possibly discriminate between the higher-dimensional effects and dark matter.
Scalar self-energy for a charged particle in global monopole spacetime with a spherical boundary
NASA Astrophysics Data System (ADS)
Bezerra de Mello, E. R.; Saharian, A. A.
2012-07-01
We analyze combined effects of the geometry produced by a global monopole and a concentric spherical boundary on the self-energy of a point-like scalar charged test particle at rest. We assume that the boundary is outside the monopole’s core with a general spherically symmetric inner structure. An important quantity to this analysis is the three-dimensional Green function associated with this system. For both Dirichlet and Neumann boundary conditions obeyed by the scalar field on the sphere, the Green function presents a structure that contains contributions due to the background geometry of the spacetime and the boundary. Consequently, the corresponding induced scalar self-energy also presents a similar structure. For points near the sphere, the boundary-induced part dominates and the self-force is repulsive/attractive with respect to the boundary for Dirichlet/Neumann boundary condition. In the region outside the sphere at large distances from it, the boundary-free part in the self-energy dominates and the corresponding self-force can be either attractive or repulsive with dependence of the curvature coupling parameter for scalar field. In particular, for the minimal coupling we show the presence of a stable equilibrium point for the Dirichlet boundary condition. In the region inside the sphere, the nature of the self-force depends on the specific model for the monopole’s core. As illustrations of the general procedure adopted, we shall consider two distinct models, namely the flower-pot and the ballpoint-pen ones.
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.
NASA Astrophysics Data System (ADS)
Brihaye, Yves; Hartmann, Betti
2005-01-01
We construct solutions of an Einstein Yang Mills system including a cosmological constant in 4 + n spacetime dimensions, where the n-dimensional manifold associated with the extra dimensions is taken to be Ricci flat. Assuming the matter and metric fields to be independent of the n extra coordinates, a spherical symmetric ansatz for the fields leads to a set of coupled ordinary differential equations. We find that for n > 1 only solutions with either one non-zero Higgs field or with all Higgs fields constant and zero gauge field function (corresponding to a Wu Yang-type ansatz) exist. We give the analytic solutions available in this model. These are 'embedded' Abelian solutions with a diverging size of the manifold associated with the extra n dimensions. Depending on the choice of parameters, these latter solutions either represent naked singularities or they possess a single horizon. We also present solutions of the effective four-dimensional Einstein Yang Mills Higgs-dilaton model, where the higher-dimensional cosmological constant induces a Liouville-type potential. The solutions are non-Abelian solutions with diverging Higgs fields, which exist only up to a maximal value of the cosmological constant.
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.
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
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.
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.
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.
Spherically symmetric random walks. I. Representation in terms of orthogonal polynomials
Bender, C.M.; Cooper, F.; Meisinger, P.N.
1996-07-01
It is shown that, in general, a connection exists between orthogonal polynomials and semibounded random walks. This connection allows one to view a random walk as taking place on the set of integers that index the orthogonal polynomials. An illustration is provided by the case of spherically symmetric random walks. The correspondence between orthogonal polynomials and random walks enables one to express random-walk probabilities as weighted inner products of the polynomials. This correspondence is exploited to construct and analyze spherically symmetric random walks in {ital D}-dimensional space, where {ital D} is {ital not} restricted to be an integer. Such random walks can be described in terms of Gegenbauer (ultraspherical) polynomials. For example, Legendre polynomials can be used to represent the special case of two-dimensional spherically symmetric random walks. The weighted inner-product representation is used to calculate exact closed-form spatial and temporal moments of the probability distribution associated with the random walk. The polynomial representation of spherically symmetric random walks is then used to calculate the two-point Green{close_quote}s function for a rotationally symmetric free scalar quantum field theory. {copyright} {ital 1996 The American Physical Society.}
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
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.
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)
Shabbir, Ghulam; Khan, Suhail
In this paper we classify cylindrically symmetric static spacetimes according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the teleparallel Killing vector fields are 3, 4, 6 or 10 which are the same in numbers as in general relativity. In case of 3, 4 or 6 the teleparallel Killing vector fields are multiple of the corresponding Killing vector fields in general relativity by some function of r. In the case of 10 Killing vector fields the spacetime becomes Minkowski spacetime and all the torsion components are zero. The Killing vector fields in this case are exactly the same as in general relativity. Here we also discuss the Lie algebra in each case. It is important to note that this classification also covers the plane symmetric static spacetimes.
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.
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.
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
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.
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.
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.
Static spherically symmetric monopole solutions in the presence of a dilaton field
NASA Astrophysics Data System (ADS)
Forgács, Péter; Gyürüsi, József
1996-02-01
A numerical study of static, spherically symmetric monopole solutions of a spontaneously broken SU(2) gauge theory coupled to a dilation field is presented. Regular solutions seem to exist only up a maximal value of the dilaton coupling. In addition to the generalization of the 't Hooft-Polyakov monopole a discrete family of regular solutions is found, corresponding to radial excitations absent in the theory without dilaton.
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
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.
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.
NASA Technical Reports Server (NTRS)
Jackson, G. S.; Avedisian, C. T.
1993-01-01
The effect of initial droplet diameter on the burning rate of sooting fuels (n-heptane and 1-chloro-octane) is studied experimentally at low gravity. A 1.2 s drop tower provided a low gravity environment to minimize buoyancy and achieve spherically symmetric flames for stationary droplets. Free-floating and fiber supported droplets were burned, and both methods gave matching results for droplets of similar initial diameter.
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.
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.
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.
On Spherically Symmetric Motions Of a Viscous Compressible Barotropic and Selfgravitating Gas
NASA Astrophysics Data System (ADS)
Ducomet, Bernard; Nečasová, Šárka; Vasseur, Alexis
2011-06-01
We consider the Cauchy problem for the equations of spherically symmetric motions in {mathbb {R}^3}, of a selfgravitating barotropic gas, with possibly non monotone pressure law, in two different situations: in the first one we suppose that the viscosities μ( ρ), and λ( ρ) are density-dependent and satisfy the Bresch-Desjardins condition, in the second one we consider constant densities. In the two cases, we prove that the problem admits a global weak solution, provided that the polytropic index γ satisfy γ > 1.
SPHERICALLY SYMMETRIC NLTE MODEL ATMOSPHERES OF HOT HYDROGEN-HELIUM FIRST STARS
Kubat, Jiri
2012-12-15
We present results of our calculations of NLTE model stellar atmospheres for hot Population III stars composed of hydrogen and helium. We use our own computer code for the calculation of spherically symmetric NLTE model atmospheres in hydrostatic and radiative equilibrium. The model atmospheres are then used for the calculation of emergent fluxes. These fluxes serve to evaluate the flow of high-energy photons for energies higher than ionization energies of hydrogen and helium, the so-called ionizing photon fluxes. We also present the time evolution of the ionizing photon fluxes.
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.
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.
Podolsky, Jiri; Svarc, Robert
2010-06-15
We investigate motion of test particles in exact spacetimes with an expanding impulsive gravitational wave which propagates in a Minkowski, a de Sitter, or an anti-de Sitter universe. Using the continuous form of these metrics we derive explicit junction conditions and simple refraction formulas for null, timelike, and spacelike geodesics crossing a general impulse of this type. In particular, we present a detailed geometrical description of the motion of test particles in a special class of axially symmetric spacetimes in which the impulse is generated by a snapped cosmic string.
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.
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.
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.
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.
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
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.
Scattering of P and S waves by a spherically symmetric inclusion
NASA Astrophysics Data System (ADS)
Korneev, Valeri A.; Johnson, Lane R.
1996-10-01
Scattering of an arbitrary elastic wave incident upon a spherically symmetric inclusion is considered and solutions are developed in terms of the spherical vector system of Petrashen, which produces results in terms of displacements rather than displacement potentials and in a form suitable for accurate numerical computations. Analytical expressions for canonical scattering coefficients are obtained for both the cases of incident P waves and incident S waves. Calculations of energy flux in the scattered waves lead to elastic optical theorems for both P and S waves, which relate the scattering cross sections to the amplitude of the scattered fields in the forward direction. The properties of the solutions for a homogeneous elastic sphere, a sphere filled by fluid, and a spherical cavity are illustrated with scattering cross sections that demonstrate important differences between these types of obstacles. A general result is that the frequency dependence of the scattering is defined by the wavelength of the scattered wave rather than the wavelength of the incident wave. This is consistent with the finding that the intensity of the P→S scattering is generally much stronger than the S→P scattering. When averaged over all scattering angles, the mean intensity of the P→S converted waves is 2V {p/2}/V{s/4}times the mean intensity of the S→P converted waves, and this ratio is independent of frequency. The exact solutions reduce to simple and easily used expressions in the case of the low frequency (Rayleigh) approximation and the low contrast (Rayleigh-Born) approximation. The case of energy absorbing inclusions can also be obtained by assigning complex values to the elastic parameters, which leads to the result that an increase in attenuation within the inclusion causes an increased scattering cross section with a marked preference for scattered S waves. The complete generality of the results is demonstrated by showing waves scattered by the earth's core in the
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 .
Physical properties of an exact spherically symmetric solution with shear in general relativity
NASA Astrophysics Data System (ADS)
Knutsen, Henning
1992-12-01
The properties of an exact spherically symmetric perfect fluid solution obtained in non-comoving coordinates are examined. This solution contains shear, and the pressure and the density are positive in the interior of the fluid. Their respective gradients with respect to comoving radial coordinate are equal and negative, and the speed of sound in this fluid is less than the speed of light in vacuum and is increasing outwards. There is a singularity at the center of the fluid since the pressure and the density become infinite there, though their ratio becomes unity. This singularity is naked, since there does not exist a trapped surface in the fluid outside this singularity. The circumference is an increasing function of radical comoving coordinate, and the mass function is positive and is increasing outwards. There are no tidal forces in radial direction, but the tidal forces normal to this direction are non-vanishing. We also give the kinematic quantities for this fluid. However, it is not possible to match this solution with an exterior vacuum Schwarzschild solution. Moreover, the dominant energy condition produces imaginary values for the sound speed.
Trapped surfaces in spherical stars
Bizon, P.; Malec, E.; O'Murchadha, N.
1988-09-05
We give necessary and sufficient conditions for the existence of trapped surfaces in spherically symmetric spacetimes. These conditions show that the formation of trapped surfaces depends on both the degree of concentration and the average flow of the matter. The result can be considered as a partial validation of the cosmic-censorship hypothesis.
Numerical relativity for D dimensional axially symmetric space-times: Formalism and code tests
Zilhao, Miguel; Herdeiro, Carlos; Witek, Helvi; Nerozzi, Andrea; Sperhake, Ulrich; Cardoso, Vitor; Gualtieri, Leonardo
2010-04-15
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.
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.
Shendeleva, Margarita L; Molloy, John A
2006-09-20
We report on the development of Monte Carlo software that can model media with spatially varying scattering coefficient, absorption, and refractive index. The varying refractive index is implemented by calculating curved photon paths in the medium. The results of the numerical simulations are compared with analytical solutions obtained using the diffusion approximation. The model under investigation is a scattering medium that contains a spherically symmetrical inclusion (inhomogeneity) created by variation in optical properties and having no sharp boundaries. The following steady-state cases are considered: (a) a nonabsorbing medium with a spherically symmetrical varying refractive index, (b) an inclusion with varying absorption and scattering coefficients and constant refractive index, and (c) an inclusion with varying absorption, scattering, and refractive index. In the latter case it is shown that the interplay between the absorption coefficient and the refractive index may create the effect of a hidden inclusion.
Horizon-less Spherically Symmetric Vacuum-Solutions in a Higgs Scalar-Tensor Theory of Gravity
NASA Astrophysics Data System (ADS)
Bezares-Roder, Nils M.; Nandan, Hemwati; Dehnen, Heinz
2007-10-01
The exact static and spherically symmetric solutions of the vacuum field equations for a Higgs Scalar-Tensor theory (HSTT) are derived in Schwarzschild coordinates. It is shown that in general there exists no Schwarzschild horizon and that the fields are only singular (as naked singularity) at the center (i.e. for the case of a point-particle). However, the Schwarzschild solution as in usual general relativity (GR) is obtained for the vanishing limit of Higgs field excitations.
Nonsymmetric trapped surfaces in the Schwarzschild and Vaidya spacetimes
Schnetter, Erik; Krishnan, Badri
2006-01-15
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.
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 Astrophysics Data System (ADS)
Keeton, Charles R.; Petters, A. O.
2005-11-01
We are developing a general, unified, and rigorous analytical framework for using gravitational lensing by compact objects to test different theories of gravity beyond the weak-deflection limit. In this paper we present the formalism for computing corrections to lensing observables for static, spherically symmetric gravity theories in which the corrections to the weak-deflection limit can be expanded as a Taylor series in one parameter, namely, the gravitational radius of the lens object. We take care to derive coordinate-independent expressions and compute quantities that are directly observable. We compute series expansions for the observables that are accurate to second order in the ratio ɛ=ϑ•/ϑE of the angle subtended by the lens’s gravitational radius to the weak-deflection Einstein radius, which scales with mass as ɛ∝M1/2•. The positions, magnifications, and time delays of the individual images have corrections at both first and second order in ɛ, as does the differential time delay between the two images. Interestingly, we find that the first-order corrections to the total magnification and centroid position vanish in all gravity theories that agree with general relativity in the weak-deflection limit, but they can remain nonzero in modified theories that disagree with general relativity in the weak-deflection limit. For the Reissner-Nordström metric and a related metric from heterotic string theory, our formalism reveals an intriguing connection between lensing observables and the condition for having a naked singularity, which could provide an observational method for testing the existence of such objects. We apply our formalism to the galactic black hole and predict that the corrections to the image positions are at the level of 10 μarc s (microarcseconds), while the correction to the time delay is a few hundredths of a second. These corrections would be measurable today if a pulsar were found to be lensed by the galactic black hole, and
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
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)
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)
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)
Qin, Yuming; Zhang, Jianlin; Su, Xing; Cao, Jie
2016-09-01
In this paper, we establish the global existence and exponential stability of spherically symmetric solutions in {H^i× H^i× H^i× H^i (i=1,2,4)} for a multi-dimensional compressible viscous radiative and reactive gas. Our global existence results improve those known results. Moreover, we establish the asymptotic behavior and exponential stability of global solutions on {H^i× H^i× H^i× H^i (i=1,2,4)}. This result is obtained for this problem in the literature for the first time.
NASA Astrophysics Data System (ADS)
Ziad, M.
2003-05-01
General expressions for the components of the Ricci collineation vector are derived and the related constraints are obtained. These constraints are then solved to obtain Ricci collineations and the related constraints on the Ricci tensor components for all spacetime manifolds (degenerate or non-degenerate, diagonal or non-diagonal) admitting symmetries larger than so(3) and already known results are recovered. A complete solution is achieved for the spacetime manifolds admitting so(3) as the maximal symmetry group with non-degenerate and non diagonal Ricci tensor components. It is interesting to point out that there appear cases with finite number of Ricci collineations although the Ricci tensor is degenerate and also the cases with infinitely many Ricci collineations even in the case of non-degenerate Ricci tensor. Interestingly, it is found that the spacetime manifolds with so(3) as maximal symmetry group may admit two extra proper Ricci collineations, although they do not admit a G5 as the maximal symmetry group. Examples are provided which show and clarify some comments made by Camci et al. [Camci, U., and Branes, A. (2002). Class. Quantum Grav. 19, 393-404]. Theorems are proved which correct the earlier claims made in [Carot, J., Nunez, L. A., and Percoco, U. (1997). Gen. Relativ. Gravit. 29, 1223-1237 Contreras, G., Núñez, L. A., and Percolo, U. (2000). Gen. Relativ. Gravit. 32, 285-294].
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.
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)
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).
On Cyclically Symmetrical Spacetimes
NASA Astrophysics Data System (ADS)
Barnes, A.
2001-07-01
In a recent paper Carot et al. considered the definition of cylindrical symmetry as a specialisation of the case of axial symmetry. One of their propositions states that if there is a second Killing vector, which together with the one generating the axial symmetry, forms the basis of a two-dimensional Lie algebra, then the two Killing vectors must commute, thus generating an Abelian group. In this paper a similar result, valid under considerably weaker assumptions, is derived: any two-dimensional Lie transformation group which contains a one-dimensional subgroup whose orbits are circles, must be Abelian. The method used to prove this result is extended to apply to three-dimensional Lie transformation groups. It is shown that the existence of a one-dimensional subgroup with closed orbits restricts the Bianchi type of the associated Lie algebra to be I, II, III, VIIq = 0, VIII or IX. Some results on n-dimensional Lie groups are also derived and applied to show there are severe restrictions on the structure of the allowed four-dimensional Lie transformation groups compatible with cyclic symmetry.
Black holes and global structures of spherical spacetimes in Horava-Lifshitz theory
Greenwald, Jared; Satheeshkumar, V. H.; Lenells, Jonatan; Lu, J. X.; Wang Anzhong
2011-10-15
We systematically study black holes in the Horava-Lifshitz theory by following the kinematic approach, in which a horizon is defined as the surface at which massless test particles are infinitely redshifted. Because of the nonrelativistic dispersion relations, the speed of light is unlimited, and test particles do not follow geodesics. As a result, there are significant differences in causal structures and black holes between general relativity (GR) and the Horava-Lifshitz theory. In particular, the horizon radii generically depend on the energies of test particles. Applying them to the spherical static vacuum solutions found recently in the nonrelativistic general covariant theory of gravity, we find that, for test particles with sufficiently high energy, the radius of the horizon can be made as small as desired, although the singularities can be seen, in principle, only by observers with infinitely high energy. In these studies, we pay particular attention to the global structure of the solutions, and find that, because of the foliation-preserving-diffeomorphism symmetry, Diff(M,F), they are quite different from the corresponding ones given in GR, even though the solutions are the same. In particular, the Diff(M,F) does not allow Penrose diagrams. Among the vacuum solutions, some give rise to the structure of the Einstein-Rosen bridge, in which two asymptotically flat regions are connected by a throat with a finite nonzero radius. We also study slowly rotating solutions in such a setup, and obtain all the solutions characterized by an arbitrary function A{sub 0}(r). The case A{sub 0}=0 reduces to the slowly rotating Kerr solution obtained in GR.
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
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)).
NASA Astrophysics Data System (ADS)
Diakogiannis, Foivos I.; Lewis, Geraint F.; Ibata, Rodrigo A.
2014-09-01
The spherical Jeans equation is widely used to estimate the mass content of stellar systems with apparent spherical symmetry. However, this method suffers from a degeneracy between the assumed mass density and the kinematic anisotropy profile, β(r). In a previous work, we laid the theoretical foundations for an algorithm that combines smoothing B splines with equations from dynamics to remove this degeneracy. Specifically, our method reconstructs a unique kinematic profile of σ _{rr}^2 and σ _{tt}^2 for an assumed free functional form of the potential and mass density (Φ, ρ) and given a set of observed line-of-sight velocity dispersion measurements, σ _los^2. In Paper I, we demonstrated the efficiency of our algorithm with a very simple example and we commented on the need for optimum smoothing of the B-spline representation; this is in order to avoid unphysical variational behaviour when we have large uncertainty in our data. In the current contribution, we present a process of finding the optimum smoothing for a given data set by using information of the behaviour from known ideal theoretical models. Markov Chain Monte Carlo methods are used to explore the degeneracy in the dynamical modelling process. We validate our model through applications to synthetic data for systems with constant or variable mass-to-light ratio Υ. In all cases, we recover excellent fits of theoretical functions to observables and unique solutions. Our algorithm is a robust method for the removal of the mass-anisotropy degeneracy of the spherically symmetric Jeans equation for an assumed functional form of the mass density.
Malec, Edward; Rembiasz, Tomasz
2010-12-15
We compare Newtonian and general relativistic descriptions of the stationary accretion of self-gravitating fluids onto compact bodies. Spherical symmetry and thin gas approximation are assumed. Luminosity depends, among other factors, on the temperature and the contribution of gas to the total mass, in both--general relativistic (L{sub GR}) and Newtonian (L{sub N})--models. We discover a remarkable universal behavior for transonic flows: the ratio of respective luminosities L{sub GR}/L{sub N} is independent of the fractional mass of the gas and depends on asymptotic temperature. It is close to 1 in the regime of low asymptotic temperatures and can grow several times at high temperatures. These conclusions are valid for a wide range of polytropic equations of state.
Hosokawa, Takashi; Omukai, Kazuyuki E-mail: hosokawa@th.nao.ac.j
2009-10-01
The final mass of a newborn star is set at the epoch when the mass accretion onto the star is terminated. We study the evolution of accreting protostars and the limits of accretion in low-metallicity environments under spherical symmetry. Accretion rates onto protostars are estimated via the temperature evolution of prestellar cores with different metallicities. The derived rates increase with decreasing metallicity, from M-dot{approx_equal}10{sup -6} M odot yr{sup -1} at Z = Z {sub sun} to 10{sup -3} M {sub sun} yr{sup -1} at Z = 0. With the derived accretion rates, the protostellar evolution is numerically calculated. We find that, at lower metallicity, the protostar has a larger radius and reaches the zero-age main sequence (ZAMS) at higher stellar mass. Using this protostellar evolution, we evaluate the upper stellar mass limit where the mass accretion is hindered by radiative feedback. We consider the effects of radiation pressure exerted on the accreting envelope, and expansion of an H II region. The mass accretion is finally terminated by radiation pressure on dust grains in the envelope for Z approx> 10{sup -3} Z {sub sun} and by the expanding H II region for lower metallicity. The mass limit from these effects increases with decreasing metallicity from M {sub *} {approx_equal} 10 M {sub sun} at Z = Z {sub sun} to {approx_equal}300 M {sub sun} at Z = 10{sup -6} Z {sub sun}. The termination of accretion occurs after the central star arrives at the ZAMS at all metallicities, which allows us to neglect protostellar evolution effects in discussing the upper mass limit by stellar feedback. The fragmentation induced by line cooling in low-metallicity clouds yields prestellar cores with masses large enough that the final stellar mass is set by the feedback effects. Although relaxing the assumption of spherical symmetry will alter feedback effects, our results will be a benchmark for more realistic evolution to be explored in future studies.
Chang, Yi-Ren; 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. PMID:16724154
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)
Dias, Gonçalo A. S.; Lemos, José P. S.
2006-08-01
A calculation of the entropy of static, electrically charged, black holes with spherical, toroidal, and hyperbolic-compact and oriented horizons, in D spacetime dimensions, is performed. These black holes live in an anti de Sitter spacetime, i.e., a spacetime with negative cosmological constant. To find the entropy, the approach developed by Solodukhin is followed. The method consists in a redefinition of the variables in the metric, by considering the radial coordinate as a scalar field. Then one performs a 2+(D-2) dimensional reduction, where the (D-2) dimensions are in the angular coordinates, obtaining a 2-dimensional effective scalar field theory. This theory is a conformal theory in an infinitesimally small vicinity of the horizon. The corresponding conformal symmetry will then have conserved charges, associated with its infinitesimal conformal generators, which will generate a classical Poisson algebra of the Virasoro type. Shifting the charges and replacing Poisson brackets by commutators, one recovers the usual form of the Virasoro algebra, obtaining thus the level zero conserved charge eigenvalue L0, and a nonzero central charge c. The entropy is then obtained via the Cardy formula.
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.
Short-Period Normal-mode Synthetics and Fr{é}chet kernels for Spherically Symmetric Earth Models
NASA Astrophysics Data System (ADS)
Yang, H.; Zhao, L.; Hung, S.
2007-12-01
Determination of three dimensional multiscale Earth structures requires high-quality seismic data and accurate synthetic waveforms. To extract and interpret the full waveform information from widely available broadband data, we need to be able to calculate complete broadband synthetic seismograms. Normal-mode theory provides the exact solutions to the wave equation in spherically symmetric Earth models, and the efficiency afforded by the usage of precalculated eigenfunction databases makes normal-mode summation the preferred approach for calculating long-period synthetic seismograms in 1-D reference models. In this study, we extend the normal-mode summation to short period by attacking the problems encountered in computing normal-mode eigenfrequencies and eigenfunctions at higher frequencies. Flexible radial sampling scheme based on the WKBJ approximation is adopted to ensure the accuracy of the secular equation when the radial eigenfunctions are highly oscillatory. This allows us to compute accurate normal-mode eigenfunctions up to much higher frequencies (~ 1Hz for Spheroidal and ~ 2Hz for Toroidal modes). Although errors can still be large for certain modes, they are almost all inner-core shear modes, and numerical experiments show that they have no contribution to seismograms on the surface. In contrast, omitting only 0.1% mantle modes at random can lead to noisy synthetics. The capability to compute normal modes up to high frequencies enables us to obtain accurate and complete synthetic seismograms that can be used to both extract waveform information from all seismic phases and to compute their full-wave Fr{é}chet kernels, which opens up possibilities in global and regional high-resolution tomography as well as studies on the seismic structure in the deep mantle and the inner core.
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.
Solitons and hairy black holes in Einstein-non-Abelian-Proca theory in anti-de Sitter spacetime
NASA Astrophysics Data System (ADS)
Ponglertsakul, Supakchai; Winstanley, Elizabeth
2016-08-01
We present new soliton and hairy black hole solutions of Einstein-non-Abelian-Proca theory in asymptotically anti-de Sitter spacetime with gauge group su (2 ) . For static, spherically symmetric configurations, we show that the gauge field must be purely magnetic, and we solve the resulting field equations numerically. The equilibrium gauge field is described by a single function ω (r ) , which must have at least one zero. The solitons and hairy black holes share many properties with the corresponding solutions in asymptotically flat spacetime. In particular, all the solutions we study are unstable under linear, spherically symmetric, perturbations of the metric and gauge field.
Fate of inhomogeneity in Schwarzschild-deSitter space-time
NASA Astrophysics Data System (ADS)
Nambu, Yasusada
1994-03-01
We investigate the global structure of the space-time with a spherically symmetric inhomogeneity using a metric junction, and classify all possible types. We found that a motion with a negative gravitational mass is possible although the energy condition of the matter is not violated. Using the result, formation of black hole and worm hole during the inflationary era is discussed.
Hawking radiation from a spherical loop quantum gravity black hole
NASA Astrophysics Data System (ADS)
Gambini, Rodolfo; Pullin, Jorge
2014-06-01
We introduce quantum field theory on quantum space-times techniques to characterize the quantum vacua as a first step toward studying black hole evaporation in spherical symmetry in loop quantum gravity and compute the Hawking radiation. We use as quantum space-time the recently introduced exact solution of the quantum Einstein equations in vacuum with spherical symmetry and consider a spherically symmetric test scalar field propagating on it. The use of loop quantum gravity techniques in the background space-time naturally regularizes the matter content, solving one of the main obstacles to back-reaction calculations in more traditional treatments. The discreteness of area leads to modifications of the quantum vacua, eliminating the trans-Planckian modes close to the horizon, which in turn eliminates all singularities from physical quantities, like the expectation value of the stress-energy tensor. Apart from this, the Boulware, Hartle-Hawking and Unruh vacua differ little from the treatment on a classical space-time. The asymptotic modes near scri are reproduced very well. We show that the Hawking radiation can be computed, leading to an expression similar to the conventional one but with a high frequency cutoff. Since many of the conclusions concern asymptotic behavior, where the spherical mode of the field behaves in a similar way as higher multipole modes do, the results can be readily generalized to non spherically symmetric fields.
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.
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.
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.
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.
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.
Conformally symmetric traversable wormholes in f( G) gravity
NASA Astrophysics Data System (ADS)
Sharif, M.; Fatima, H. Ismat
2016-11-01
We discuss non-static conformally symmetric traversable wormholes for spherically symmetric spacetime using the model f(G)=α Gn, where n>0 and α is an arbitrary constant. We investigate wormhole solutions by taking two types of shape function and found that physically realistic wormholes exist only for even values of n. We also check the validity of flare-out condition, required for wormhole construction, for the shape functions deduced from two types of equation of state. It is found that this condition is satisfied by these functions in all cases except phantom case with non-static conformal symmetry.
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.
Mezzacappa, A; Liebendörfer, M; Messer, O E; Hix, W R; Thielemann, F K; Bruenn, S W
2001-03-01
With exact three-flavor Boltzmann neutrino transport, we simulate the stellar core collapse, bounce, and postbounce evolution of a 13M star in spherical symmetry, the Newtonian limit, without invoking convection. In the absence of convection, prior spherically symmetric models, which implemented approximations to Boltzmann transport, failed to produce explosions. We consider exact transport to determine if these failures were due to the transport approximations made and to answer remaining fundamental questions in supernova theory. The model presented here is the first in a sequence of models beginning with different progenitors. In this model, a supernova explosion is not obtained.
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.
Spacetime symmetry and mass of a lepton
NASA Astrophysics Data System (ADS)
Dymnikova, Irina
2008-08-01
The Einstein equations admit the class of regular solutions generated by stress-energy tensors representing vacuum with the reduced symmetry as compared with the maximally symmetric de Sitter vacuum. In the spherically symmetric case they describe, in particular, gravitational vacuum solitons with the de Sitter center whose mass is related to the de Sitter vacuum trapped inside and smooth breaking of spacetime symmetry from the de Sitter group in the origin to the Poincaré group at infinity. In nonlinear electrodynamics coupled to gravity and satisfying the weak energy condition, an electrovacuum soliton has an obligatory de Sitter center where the electric field vanishes while the energy density of the electromagnetic vacuum achieves its maximal finite value which gives a natural cutoff on self-energy. By the Gürses-Gürsey algorithm based on the Trautman-Newman technique it is transformed into a spinning electrovacuum soliton asymptotically Kerr-Newman for a distant observer, with the gyromagnetic ratio g = 2. The de Sitter center becomes the de Sitter equatorial disk which has properties of a perfect conductor and ideal diamagnetic. The interior de Sitter vacuum disk displays superconducting behavior within a single spinning particle. This behavior is generic for the class of spinning electrovacuum solitons. The de Sitter vacuum supplies a particle with the finite electromagnetic mass related to breaking of spacetime symmetry.
Paczynski-Wiita-like potential for any static spherical black hole in metric theories of gravity
NASA Astrophysics Data System (ADS)
Faraoni, Valerio; Belknap-Keet, Shawn D.; Lapierre-Léonard, Marianne
2016-02-01
The pseudo-Newtonian potential of Paczynski and Wiita for particles orbiting a Schwarzschild black hole is generalized to arbitrary static and spherically symmetric spacetimes, including black hole solutions of alternative theories of gravity. In addition to being more general, our prescription differs substantially from a previous one in the literature, showing that the association of a pseudo-Newtonian potential even with a simple black hole metric is not unique.
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.
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 Technical Reports Server (NTRS)
Mihalas, D.; Kunasz, P. B.; Hummer, D. G.
1976-01-01
A numerical method is presented of solving the radiative transfer equation in the comoving frame of a spherically symmetric expanding atmosphere in which both the line and the electron-scattering source function can depend on frequency (i.e., when there is partial frequency redistribution in the scattering process). This method is used to assess the adequacy of various assumptions regarding frequency redistribution in the comoving frame and to discuss the effects of electron scattering more accurately than previously possible. The methods developed here can be used in realistic model atmospheres to account for the (major) effects of electron scattering upon emergent flux profiles.
Gravity induced from quantum spacetime
NASA Astrophysics Data System (ADS)
Beggs, Edwin J.; Majid, Shahn
2014-02-01
We show that tensoriality constraints in noncommutative Riemannian geometry in the two-dimensional bicrossproduct model quantum spacetime algebra [x, t] = λx drastically reduce the moduli of possible metrics g up to normalization to a single real parameter, which we interpret as a time in the past from which all timelike geodesics emerge and a corresponding time in the future at which they all converge. Our analysis also implies a reduction of moduli in n-dimensions and we study a suggested spherically symmetric classical geometry in n = 4 in detail, identifying two one-parameter subcases where the Einstein tensor matches that of a perfect fluid for (a) positive pressure, zero density and (b) negative pressure and positive density with ratio w_Q=-{1\\over 2}. The classical geometry is conformally flat and its geodesics motivate new coordinates which we extend to the quantum case as a new description of the quantum spacetime model as a quadratic algebra. The noncommutative Riemannian geometry is fully solved for n = 2 and includes the quantum Levi-Civita connection and a second, nonperturbative, Levi-Civita connection which blows up as λ → 0. We also propose a ‘quantum Einstein tensor’ which is identically zero for the main part of the moduli space of connections (as classically in 2D). However, when the quantum Ricci tensor and metric are viewed as deformations of their classical counterparts there would be an O(λ2) correction to the classical Einstein tensor and an O(λ) correction to the classical metric.
Black-hole-scalar-field interactions in spherical symmetry
NASA Astrophysics Data System (ADS)
Marsa, R. L.; Choptuik, M. W.
1996-10-01
We examine the interactions of a black hole with a massless scalar field using a coordinate system which extends ingoing Eddington-Finkelstein coordinates to dynamic spherically-symmetric spacetimes. We avoid problems with the singularity by excising the region of the black-hole interior to the apparent horizon. We use a second-order finite difference scheme to solve the equations. The resulting program is stable and convergent and will run forever without problems. We are able to observe quasinormal ringing and power-law tails as well as an interesting nonlinear feature.
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.
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.
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.
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.
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.
Spherical gravitational collapse in N dimensions
NASA Astrophysics Data System (ADS)
Goswami, Rituparno; Joshi, Pankaj S.
2007-10-01
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=ti 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.
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.
Acoustic geometry through perturbation of mass accretion rate: radial flow in static spacetimes
NASA Astrophysics Data System (ADS)
Ananda, Deepika B.; Bhattacharya, Sourav; Das, Tapas K.
2015-09-01
In this work we present an alternative derivation of the general relativistic acoustic analogue geometry by perturbing the mass accretion rate or flux of an ideal fluid flowing radially in a general static and spherically symmetric spacetime. To the best of our knowledge, this has so far been done in non-relativistic scenario. The resulting causal structure of the two dimensional acoustic geometry is qualitatively similar to that one derives via the perturbation of the velocity potential. Using this, we then briefly discuss the stability issues by studying the wave configurations generated by the perturbation of the mass accretion rate, and formally demonstrate the stability of the accretion process. This is in qualitative agreement with earlier results on stability, established via study of wave configurations generated by the perturbation of velocity potential, by using the acoustic geometry associated with it. We further discuss explicit examples of the Schwarzschild and Rindler spacetimes.
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.
Past horizons in Robinson-Trautman spacetimes with a cosmological constant
Podolsky, Jiri; Svitek, Otakar
2009-12-15
We study past horizons in the class of type II Robinson-Trautman vacuum spacetimes with a cosmological constant. These exact radiative solutions of Einstein's equations exist in the future of any sufficiently smooth initial data, and they approach the corresponding spherically symmetric Schwarzschild-(anti-)de Sitter metric. By analytic methods we investigate the existence, uniqueness, location, and character of the past horizons in these spacetimes. In particular, we generalize the Penrose-Tod equation for marginally trapped surfaces, which form such white-hole horizons, to the case of a nonvanishing cosmological constant, and we analyze the behavior of its solutions and visualize their evolutions. We also prove that these horizons are explicit examples of an outer trapping horizon and a dynamical horizon, so that they are spacelike past outer horizons.
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.
Unified Bertotti-Robinson and Melvin spacetimes
NASA Astrophysics Data System (ADS)
Mazharimousavi, S. Habib; Halilsoy, M.
2013-09-01
We present a solution for the Einstein-Maxwell equations which unifies both the magnetic Bertotti-Robinson and Melvin solutions as a single metric in the axially symmetric coordinates {t,ρ,z,φ}. Depending on the strength of magnetic field the spacetime manifold, unlike the cases of separate Bertotti-Robinson and Melvin spacetime, develops singularity on the symmetry axis (ρ=0). Our analysis shows, beside other things, that there are regions inaccessible to all null geodesics.
NASA Astrophysics Data System (ADS)
Sun, Yuan; Xu, Hao; Zhao, Liu
2016-09-01
The holographic entanglement entropy is studied numerically in (4+1)-dimensional spherically symmetric Gauss-Bonnet AdS black hole spacetime with compact boundary. On the bulk side the black hole spacetime undergoes a van der Waals-like phase transition in the extended phase space, which is reviewed with emphasis on the behavior on the temperature-entropy plane. On the boundary, we calculated the regularized HEE of a disk region of different sizes. We find strong numerical evidence for the failure of equal area law for isobaric curves on the temperature-HEE plane and for the correctness of first law of entanglement entropy, and briefly give an explanation for why the latter may serve as a reason for the former, i.e. the failure of equal area law on the temperature-HEE plane.
Note on cosmological Levi-Civita spacetimes in higher dimensions
NASA Astrophysics Data System (ADS)
Sarıoǧlu, Özgür; Tekin, Bayram
2009-04-01
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.
Diffraction by spherically symmetric inhomogeneous scatterers
Perel`man, A.Y.
1995-05-01
The problem of diffraction by scatterers optically inhomogeneous in the radial direction illuminated by sources with a fixed azimuthal structure is solved. Standard models are proposed for approximating the exact solution of the problem, in which partial potentials are represented in terms of exponential and exponential and cylindrical functions, and the corresponding algorithms for solving the problem are developed. A formula is deduced for the scattering cross section of a radially inhomogeneous sphere. 8 refs.
Bonnor stars in d spacetime dimensions
Lemos, Jose P. S.; Zanchin, Vilson T.
2008-03-15
Bonnor stars are regular static compact configurations in equilibrium, composed of an extremal dust fluid, i.e., a charged dust fluid where the mass density is equal to the charge density in appropriate units and up to a sign, joined to a suitable exterior vacuum solution, both within Newtonian gravity and general relativity. In four dimensions, these configurations obey the Majumdar-Papapetrou system of equations: in one case, the system is a particular setup of Newtonian gravity coupled to Coulomb electricity and electrically charged matter or fluid, in the other case, the system is a particular setup of general relativity coupled to Maxwell electromagnetism and electrically charged matter or fluid, where the corresponding gravitational potential is a specially simple function of the electric potential field and the fluid, when there is one, is made of extremal dust. Since the Majumdar-Papapetrou system can be generalized to d spacetime dimensions, as has been previously done, and higher-dimensional scenarios can be important in gravitational physics, it is natural to study this type of Bonnor solutions in higher dimensions, d{>=}4. As a preparation, we analyze Newton-Coulomb theory with an electrically charged fluid in a Majumdar-Papapetrou context, in d=n+1 spacetime dimensions, with n being the number of spatial dimensions. We show that within the Newtonian theory, in vacuum, the Majumdar-Papapetrou relation for the gravitational potential in terms of the electric potential, and its related Weyl relation, are equivalent, in contrast to general relativity where they are distinct. We study a class of spherically symmetric Bonnor stars within this theory. Under sufficient compactification they form point mass charged Newtonian singularities. We then study the analogue-type systems in the Einstein-Maxwell theory with an electrically charged fluid. Drawing on our previous work on the d-dimensional Majumdar-Papapetrou system, we restate some properties of this
NASA Astrophysics Data System (ADS)
Su, Daiqin; Ralph, T. C.
2016-02-01
We show that the particle-number distribution of diamond modes, modes that are localized in a finite spacetime region, are thermal for the Minkowski vacuum state of a massless scalar field, an analogue to the Unruh effect. The temperature of the diamond is inversely proportional to its size. An inertial observer can detect this thermal radiation by coupling to the diamond modes using an appropriate energy-scaled detector. We further investigate the correlations between various diamonds and find that entanglement between adjacent diamonds dominates.
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.
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.
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.
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.
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.
Spacetime and Euclidean geometry
NASA Astrophysics Data System (ADS)
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
NASA Astrophysics Data System (ADS)
Visser, Matt
Analogue spacetimes (and more boldly, analogue models both of and for gravity), have attracted significant and increasing attention over the last decade and a half. Perhaps the most straightforward physical example, which serves as a template for most of the others, is Bill Unruh's model for a dumb hole,(mute black hole, acoustic black hole), wherein sound is dragged along by a moving fluid—and can even be trapped behind an acoustic horizon. This and related analogue models for curved spacetimes are useful in many ways: analogue spacetimes provide general relativists with extremely concrete physical models to help focus their thinking, and conversely the techniques of curved spacetime can sometimes help improve our understanding of condensed matter and/or optical systems by providing an unexpected and countervailing viewpoint. In this chapter, I shall provide a few simple examples of analogue spacetimes as general background for the rest of the contributions.
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.
Tendex and Vortex Lines of Black Hole Spacetimes
NASA Astrophysics Data System (ADS)
Zimmerman, Aaron; Nichols, David; Owen, Rob; Zhang, Fan; Brink, Jeandrew; Chen, Yanbei; Kaplan, Jeffrey; Lovelace, Geoffrey; Matthews, Keith; Scheel, Mark; Thorne, Kip
2012-03-01
In a 3+1 split of spacetime, the Riemann curvature tensor is completely characterized by two symmetric, trace-free tensors: the tidal field and the frame-drag field. The eigenvalues and eigenvectors of these tensors characterize them completely, and the streamlines of the eigenvector fields provide a set of six field lines, called the tendex and vortex lines of the spacetime. These lines are directly analogous to the more familiar electric and magnetic field lines, and they provide a visual representation of the preferred directions of stress and frame dragging in a spacetime. I will review the theory of vortex and tendex lines, and discuss their application to the study of black hole spacetimes. In particular, I compare the tendex and vortex lines of a Kerr black hole in several gauges.
Physics on noncommutative spacetimes
NASA Astrophysics Data System (ADS)
Padmanabhan, Pramod
The structure of spacetime at the Planck scale remains a mystery to this date with a lot of insightful attempts to unravel this puzzle. One such attempt is the proposition of a 'pointless' structure for spacetime at this scale. This is done by studying the geometry of the spacetime through a noncommutative algebra of functions defined on it. We call such spacetimes 'noncommutative spacetimes'. This dissertation probes physics on several such spacetimes. These include compact noncommutative spaces called fuzzy spaces and noncompact spacetimes. The compact examples we look at are the fuzzy sphere and the fuzzy Higg's manifold. The noncompact spacetimes we study are the Groenewold-Moyal plane and the Bcn⃗ plane. A broad range of physical effects are studied on these exotic spacetimes. We study spin systems on the fuzzy sphere. The construction of Dirac and chirality operators for an arbitrary spin j is studied on both S2F and S2 in detail. We compute the spectrums of the spin 1 and spin 32 Dirac operators on S2F . These systems have novel thermodynamical properties which have no higher dimensional analogs, making them interesting models. The fuzzy Higg's manifold is found to exhibit topology change, an important property for any theory attempting to quantize gravity. We study how this change occurs in the classical setting and how quantizing this manifold smoothens the classical conical singularity. We also show the construction of the star product on this manifold using coherent states on the noncommutative algebra describing this noncommutative space. On the Moyal plane we develop the LSZ formulation of scalar quantum field theory. We compute scattering amplitudes and remark on renormalization of this theory. We show that the LSZ formalism is equivalent to the interaction representation formalism for computing scattering amplitudes on the Moyal plane. This result is true for on-shell Green's functions and fails to hold for off-shell Green's functions. With the
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)
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.
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.
Covariance in models of loop quantum gravity: Spherical symmetry
NASA Astrophysics Data System (ADS)
Bojowald, Martin; Brahma, Suddhasattwa; Reyes, Juan D.
2015-08-01
Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a linear redefinition of the constraints (with phase-space dependent coefficients) can be used to eliminate structure functions, even Abelianizing the more difficult part of the constraint algebra. The Abelianized constraints can then easily be quantized or modified by putative quantum effects. As pointed out here, however, the method does not automatically provide a covariant quantization, defined as an anomaly-free quantum theory with a classical limit in which the usual (off-shell) gauge structure of hypersurface deformations in space-time appears. The holonomy-modified vacuum theory based on Abelianization is covariant in this sense, but matter theories with local degrees of freedom are not. Detailed demonstrations of these statements show complete agreement with results of canonical effective methods applied earlier to the same systems (including signature change).
Spherical harmonics in texture analysis
NASA Astrophysics Data System (ADS)
Schaeben, Helmut; van den Boogaart, K. Gerald
2003-07-01
The objective of this contribution is to emphasize the fundamental role of spherical harmonics in constructive approximation on the sphere in general and in texture analysis in particular. The specific purpose is to present some methods of texture analysis and pole-to-orientation probability density inversion in a unifying approach, i.e. to show that the classic harmonic method, the pole density component fit method initially introduced as a distinct alternative, and the spherical wavelet method for high-resolution texture analysis share a common mathematical basis provided by spherical harmonics. Since pole probability density functions and orientation probability density functions are probability density functions defined on the sphere Ω3⊂ R3 or hypersphere Ω4⊂ R4, respectively, they belong at least to the space of measurable and integrable functions L1( Ωd), d=3, 4, respectively. Therefore, first a basic and simplified method to derive real symmetrized spherical harmonics with the mathematical property of providing a representation of rotations or orientations, respectively, is presented. Then, standard orientation or pole probability density functions, respectively, are introduced by summation processes of harmonic series expansions of L1( Ωd) functions, thus avoiding resorting to intuition and heuristics. Eventually, it is shown how a rearrangement of the harmonics leads quite canonically to spherical wavelets, which provide a method for high-resolution texture analysis. This unified point of view clarifies how these methods, e.g. standard functions, apply to texture analysis of EBSD orientation measurements.
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.
Chambler, A. F.; Chapman-Sheath, P. J.; Pearse, M. F.; Hollingdale, J.
1997-01-01
Chronic recurrent multifocal osteomyelitis is often confused with symmetrical Brodie's abscess as it has a similar pathogenesis. We report an otherwise healthy 17-year-old boy presenting with a true symmetrical Brodie's abscess. We conclude that a symmetrical Brodie's abscess presenting in an otherwise healthy patient is a separate clinical condition with a different management protocol. Images Figure 1 Figure 2 PMID:9497984
Chambler, A F; Chapman-Sheath, P J; Pearse, M F; Hollingdale, J
1997-10-01
Chronic recurrent multifocal osteomyelitis is often confused with symmetrical Brodie's abscess as it has a similar pathogenesis. We report an otherwise healthy 17-year-old boy presenting with a true symmetrical Brodie's abscess. We conclude that a symmetrical Brodie's abscess presenting in an otherwise healthy patient is a separate clinical condition with a different management protocol.
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.
On the rotating Letelier spacetime
NASA Astrophysics Data System (ADS)
Barbosa, D.; Bezerra, V. B.
2016-11-01
We construct the solution corresponding to a rotating black hole surrounded by a cloud of strings (Rotating Letelier spacetime) from its nonrotating counterpart (Letelier spacetime) by applying a method of coordinate complexification developed by Newman and Janis.
A quantum reduction to spherical symmetry in loop quantum gravity
NASA Astrophysics Data System (ADS)
Bodendorfer, N.; Lewandowski, J.; Świeżewski, J.
2015-07-01
Based on a recent purely geometric construction of observables for the spatial diffeomorphism constraint, we propose two distinct quantum reductions to spherical symmetry within full 3 + 1-dimensional loop quantum gravity. The construction of observables corresponds to using the radial gauge for the spatial metric and allows to identify rotations around a central observer as unitary transformations in the quantum theory. Group averaging over these rotations yields our first proposal for spherical symmetry. Hamiltonians of the full theory with angle-independent lapse preserve this spherically symmetric subsector of the full Hilbert space. A second proposal consists in implementing the vanishing of a certain vector field in spherical symmetry as a constraint on the full Hilbert space, leading to a close analogue of diffeomorphisms invariant states. While this second set of spherically symmetric states does not allow for using the full Hamiltonian, it is naturally suited to implement the spherically symmetric midisuperspace Hamiltonian, as an operator in the full theory, on it. Due to the canonical structure of the reduced variables, the holonomy-flux algebra behaves effectively as a one parameter family of 2 + 1-dimensional algebras along the radial coordinate, leading to a diagonal non-vanishing volume operator on 3-valent vertices. The quantum dynamics thus becomes tractable, including scenarios like spherically symmetric dust collapse.
Solutions on a brane in a bulk spacetime with Kalb-Ramond field
NASA Astrophysics Data System (ADS)
Chakraborty, Sumanta; SenGupta, Soumitra
2016-04-01
Effective gravitational field equations on a brane have been derived, when the bulk spacetime is endowed with the second rank antisymmetric Kalb-Ramond field. Since both the graviton and the Kalb-Ramond field are closed string excitations, they can propagate in the bulk. After deriving the effective gravitational field equations on the brane, we solve them for a static spherically symmetric solution. It turns out that the solution so obtained represents a black hole or naked singularity depending on the parameter space of the model. The stability of this model is also discussed. Cosmological solutions to the gravitational field equations have been obtained, where the Kalb-Ramond field is found to behave as normal pressure free matter. For certain specific choices of the parameters in the cosmological solution, the solution exhibits a transition in the behaviour of the scale factor and hence a transition in the expansion history of the universe. The possibility of accelerated expansion of the universe in this scenario is also discussed.
Pragmatic mode-sum regularization method for semiclassical black-hole spacetimes
NASA Astrophysics Data System (ADS)
Levi, Adam; Ori, Amos
2015-05-01
Computation of the renormalized stress-energy tensor is the most serious obstacle in studying the dynamical, self-consistent, semiclassical evaporation of a black hole in 4D. The difficulty arises from the delicate regularization procedure for the stress-energy tensor, combined with the fact that in practice the modes of the field need to be computed numerically. We have developed a new method for numerical implementation of the point-splitting regularization in 4D, applicable to the renormalized stress-energy tensor as well as to ⟨ϕ2⟩ren , namely the renormalized ⟨ϕ2⟩. So far we have formulated two variants of this method: t -splitting (aimed for stationary backgrounds) and angular splitting (for spherically symmetric backgrounds). In this paper we introduce our basic approach, and then focus on the t -splitting variant, which is the simplest of the two (deferring the angular-splitting variant to a forthcoming paper). We then use this variant, as a first stage, to calculate ⟨ϕ2⟩ren in Schwarzschild spacetime, for a massless scalar field in the Boulware state. We compare our results to previous ones, obtained by a different method, and find full agreement. We discuss how this approach can be applied (using the angular-splitting variant) to analyze the dynamical self-consistent evaporation of black holes.
A new model for spherically symmetric anisotropic compact star
NASA Astrophysics Data System (ADS)
Maurya, S. K.; Gupta, Y. K.; Dayanandan, Baiju; Ray, Saibal
2016-05-01
In this article we obtain a new anisotropic solution for Einstein's field equations of embedding class one metric. The solution represents realistic objects such as Her X-1 and RXJ 1856-37. We perform a detailed investigation of both objects by solving numerically the Einstein field equations with anisotropic pressure. The physical features of the parameters depend on the anisotropic factor i.e. if the anisotropy is zero everywhere inside the star then the density and pressures will become zero and the metric turns out to be flat. We report our results and compare with the above mentioned two compact objects as regards a number of key aspects: the central density, the surface density onset and the critical scaling behaviour, the effective mass and radius ratio, the anisotropization with isotropic initial conditions, adiabatic index and red shift. Along with this we have also made a comparison between the classical limit and theoretical model treatment of the compact objects. Finally we discuss the implications of our findings for the stability condition in a relativistic compact star.
Ladder Operators for Some Spherically Symmetric Potentials in Quantum Mechanics
ERIC Educational Resources Information Center
Newmarch, J. D.; Golding, R. M.
1978-01-01
The energy levels of the free field, Coulomb potential, and the three-dimensional harmonic oscillator are found using the Dirac operator formalism by the construction of suitable ladder operators. The degeneracy of each level is also discussed. (Author/GA)
NASA Astrophysics Data System (ADS)
Lovelady, Benjamin C.; Wheeler, James T.
2016-04-01
According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dimensional Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected S O (n ) connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an S O (n -1 ,1 ) connection on the spacetime. The principal fiber bundle character of the original S O (n ) guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.
NASA Astrophysics Data System (ADS)
Kay, Bernard S.; Lupo, Umberto
2016-11-01
We conjecture that (when the notion of Hadamard state is suitably adapted to spacetimes with timelike boundaries) there is no isometry-invariant Hadamard state for the massive or massless covariant Klein–Gordon equation defined on the region of the Kruskal spacetime to the left of a surface of constant Schwarzschild radius in the right Schwarzschild wedge when Dirichlet boundary conditions are put on that surface. We also prove that, with a suitable definition for ‘boost-invariant Hadamard state’ (which we call ‘strongly boost-invariant globally Hadamard’) which takes into account both the existence of the timelike boundary and the special infra-red pathology of massless fields in 1+1 dimensions, there is no such state for the massless wave equation on the region of 1+1 Minkowski space to the left of an eternally uniformly accelerating mirror—with Dirichlet boundary conditions at the mirror. We argue that this result is significant because, as we point out, such a state does exist if there is also a symmetrically placed decelerating mirror in the left wedge (and the region to the left of this mirror is excluded from the spacetime). We expect a similar existence result to hold for Kruskal when there are symmetrically placed spherical boxes in both right and left Schwarzschild wedges. Our Kruskal no-go conjecture raises basic questions about the nature of the black holes in boxes considered in black hole thermodynamics. If true, it would lend further support to the conclusion of Kay (2015 Gen. Relativ. Gravit. 47 1–27) that the nearest thing to a description of a black hole in equilibrium in a box in terms of a classical spacetime with quantum fields propagating on it has, for the classical spacetime, the exterior Schwarzschild solution, with the classical spacetime picture breaking down near the horizon. Appendix B to the paper points out the existence of, and partially fills, a gap in the proofs of the theorems in Kay and Wald (1991 Phys. Rep. 207 49
A spherical joint piston design for high speed diesel engines
Wiczynski, P.D.; Mielke, S.; Conrow, R.
1996-09-01
A spherical joint piston and connecting rod have been developed through design proof-of-concept. The spherical joint allows piston rotation. The benefits of a rotating, symmetrical piston are: mechanical and thermal load symmetry, improved ring sealing and lubrication, and reduced bearing loads, scuffing, clearances and oil consumption. The assembly includes a squeeze cast, fiber reinforced aluminum spherical joint piston. Reinforcement is located in the piston bowl and skirt. The connecting rod consists of a spherical small end positioned on an elliptical cross-sectioned shank blended into a conventional big end. The assembly has operated at cylinder pressures exceeding of 24 MPa.
Circle of least confusion of a spherical reflector.
Hosken, Robert W
2007-06-01
A simple, tractable equation is provided for determining the size and location of the circle of least confusion of a concave spherical reflector. This method is exact for the object at infinity and with wave effects neglected. Designers of large radius Arecibo-like telescopes, both radio and optical, with symmetrical, spherical primaries should find the method useful. The mathematical results are valid for apertures with an angle of incidence up to 45 degrees. Comparisons of the location of the disk of least confusion with longitudinal spherical aberration and the radius of the disk with transverse spherical aberration are presented. PMID:17514263
NASA Astrophysics Data System (ADS)
Gupta, Aseem
2015-03-01
While Einstein made spacetime relative for observers and an active player in physical phenomena he tacitly assumed that all observers experience spacetimes that are always synchronizableWe propose extension of concept of spacetime by considering possibility of an observer experiencing spacetimes that cannot synchronize with that of a system due to impossibility of transfer of any information between them. This coupled with fundamental premise of quantized action leads to increasing desynchronization between spacetime experienced by observer and that of system leading to only probability distribution functions connecting spacetime coordinates of two. This desynchronization of spacetimes is postulated as the root cause of fundamental probabilistic nature of Quantum Physics. It is shown that Schrodinger's equation models space desynchronization but not that of time inclusion of which leads to Quantum Field Theory. Desynchronization explains fundamental difference in quantum statistics and classical statistics and also existence of dynamic symmetry in addition to geometric symmetry. Nested desynchronized spacetime model of our Universe is proposed. It is shown how desynchronization can allow modeling of elementary particles as extended systems and not point-like explaining why these may be modeled as representations of Lie groups. This is a study to discern one fundamental premise of spacetime conception in classical physics and demonstrating how this premise does not hold in quantum physics. Desynchronization is presented as fundamental aspect of ontology of quantum theory.
Bianchi class B spacetimes with electromagnetic fields
NASA Astrophysics Data System (ADS)
Yamamoto, Kei
2012-02-01
We carry out a thorough analysis on a class of cosmological space-times which admit three spacelike Killing vectors of Bianchi class B and contain electromagnetic fields. Using dynamical system analysis, we show that a family of electro-vacuum plane-wave solutions of the Einstein-Maxwell equations is the stable attractor for expanding universes. Phase dynamics are investigated in detail for particular symmetric models. We integrate the system exactly for some special cases to confirm the qualitative features. Some of the obtained solutions have not been presented previously to the best of our knowledge. Finally, based on those analyses, we discuss the relation between those homogeneous models and perturbations of open Friedmann-Lemaitre-Robertson-Walker universes. We argue that the electro-vacuum plane-wave modes correspond to a certain long-wavelength limit of electromagnetic perturbations.
Crack problems in cylindrical and spherical shells
NASA Technical Reports Server (NTRS)
Erdogan, F.
1976-01-01
Standard plate or shell theories were used as a starting point to study the fracture problems in thin-walled cylindrical and spherical shells, assuming that the plane of the crack is perpendicular to the surface of the sheet. Since recent studies have shown that local shell curvatures may have a rather considerable effect on the stress intensity factor, the crack problem was considered in conjunction with a shell rather than a plate theory. The material was assumed to be isotropic and homogeneous, so that approximate solutions may be obtained by approximating the local shell crack geometry with an ideal shell which has a solution, namely a spherical shell with a meridional crack, a cylindrical shell with a circumferential crack, or a cylindrical shell with an axial crack. A method of solution for the specially orthotropic shells containing a crack was described; symmetric and skew-symmetric problems are considered in cylindrical shells with an axial crack.
Existence of blueshifts in quasispherical Szekeres spacetimes
NASA Astrophysics Data System (ADS)
Krasiński, Andrzej
2016-07-01
In Lemaître-Tolman (L-T) models, light rays emitted radially at the Big Bang (BB) at such radial coordinates r where the bang-time function tB(r ) has d tB /d r ≠0 reach every observer with infinite blueshift, z =-1 . Consequently, there exist rays, emitted soon after the BB, that will reach later observers with finite blueshift (-1
NASA Astrophysics Data System (ADS)
Hervik, S.; Málek, T.; Pravda, V.; Pravdová, A.
2015-12-01
We study type II universal metrics of the Lorentzian signature. These metrics simultaneously solve vacuum field equations of all theories of gravitation with the Lagrangian being a polynomial curvature invariant constructed from the metric, the Riemann tensor and its covariant derivatives of an arbitrary order. We provide examples of type II universal metrics for all composite number dimensions. On the other hand, we have no examples for prime number dimensions and we prove the non-existence of type II universal spacetimes in five dimensions. We also present type II vacuum solutions of selected classes of gravitational theories, such as Lovelock, quadratic and L({{Riemann}}) gravities.
Beal, Jacob; Viroli, Mirko
2015-07-28
Computation increasingly takes place not on an individual device, but distributed throughout a material or environment, whether it be a silicon surface, a network of wireless devices, a collection of biological cells or a programmable material. Emerging programming models embrace this reality and provide abstractions inspired by physics, such as computational fields, that allow such systems to be programmed holistically, rather than in terms of individual devices. This paper aims to provide a unified approach for the investigation and engineering of computations programmed with the aid of space-time abstractions, by bringing together a number of recent results, as well as to identify critical open problems. PMID:26078346
NASA Astrophysics Data System (ADS)
Chapline, George
It has been shown that a nonlinear Schrödinger equation in 2+1 dimensions equipped with an SU(N) Chern-Simons gauge field can provide an exact description of certain self-dual Einstein spaces in the limit N-=∞. Ricci flat Einstein spaces can then be viewed as arising from a quantum pairing of the classical self-dual and anti-self-dual solutions. In this chapter, we will outline how this theory of empty space-time might be generalized to include matter and vacuum energy by transplanting the nonlinear Schrödinger equation used to construct Einstein spaces to the 25+1-dimensional Lorentzian Leech lattice. If the distinguished 2 spatial dimensions underlying the construction of Einstein spaces are identified with a hexagonal lattice section of the Leech lattice, the wave-function becomes an 11 × 11 matrix that can represent fermion and boson degrees of freedom (DOF) associated with 2-form and Yang-Mills gauge symmetries. The resulting theory of gravity and matter in 3+1 dimensions is not supersymmetric, which provides an entry for a vacuum energy. Indeed, in the case of a Lemaitre cosmological model, the emergent space-time will naturally have a vacuum energy on the order of the observed cosmological constant.
NASA Astrophysics Data System (ADS)
Dunajewski, Adam; Dusza, Jacek J.; Rosado Muñoz, Alfredo
2014-11-01
The article presents a proposal for the description of human gait as a periodic and symmetric process. Firstly, the data for researches was obtained in the Laboratory of Group SATI in the School of Engineering of University of Valencia. Then, the periodical model - Mean Double Step (MDS) was made. Finally, on the basis of MDS, the symmetrical models - Left Mean Double Step and Right Mean Double Step (LMDS and RMDS) could be created. The method of various functional extensions was used. Symmetrical gait models can be used to calculate the coefficients of asymmetry at any time or phase of the gait. In this way it is possible to create asymmetry, function which better describes human gait dysfunction. The paper also describes an algorithm for calculating symmetric models, and shows exemplary results based on the experimental data.
Magnetic fields of spherical compact stars in a braneworld
Ahmedov, B. J.; Fattoyev, F. J.
2008-08-15
We study the stellar magnetic field configuration in dependence on brane tension and present solutions of Maxwell equations in the external background space-time of a magnetized spherical star in a Randall-Sundrum II type braneworld. The star is modeled as a sphere consisting of perfect highly magnetized fluid with infinite conductivity and a frozen-in magnetic field. With respect to solutions for magnetic fields found in the Schwarzschild space-time, brane tension introduces enhancing corrections to the exterior magnetic field which could be relevant for the magnetic fields of magnetized compact objects as pulsars and magnetars and may provide observational evidence for the brane tension.
Relativistic spherical plasma waves
NASA Astrophysics Data System (ADS)
Bulanov, S. S.; Maksimchuk, A.; Schroeder, C. B.; Zhidkov, A. G.; Esarey, E.; Leemans, W. P.
2012-02-01
Tightly focused laser pulses that diverge or converge in underdense plasma can generate wake waves, having local structures that are spherical waves. Here we study theoretically and numerically relativistic spherical wake waves and their properties, including wave breaking.
Quantum field theory in the space-time of a cosmic string
Linet, B.
1987-01-15
For a massive scalar field in the static cylindrically symmetric space-time describing a cosmic string, we determine explicitly the Euclidean Green's function. We obtain also an alternative local form which allows us to calculate the vacuum energy-momentum tensor. In the case of a conformal scalar field, we carry out completely the calculations.
Electrostatic mirror objective with eliminated spherical and axial chromatic aberrations.
Bimurzaev, Seitkerim B; Serikbaeva, Gulnur S; Yakushev, Evgeniy M
2003-01-01
Computational formulae for the coefficients of the third-order spherical aberration and the second-order axial chromatic aberration are presented for an axially symmetric electrostatic electron mirror. A technique for eliminating the high-order derivatives of the potential axial distribution in mirror systems from the integrands is described. Conditions for elimination of spherical and axial chromatic aberrations, either separately or simultaneously, are found for a three-electrode axially symmetric mirror composed of coaxial cylinders of the same diameter. A principal scheme of the transmission electron microscope, where an electrostatic electron mirror serves as its objective, is presented. PMID:14599097
Nonadiabatic charged spherical gravitational collapse
Di Prisco, A.; Herrera, L.; Le Denmat, G.; MacCallum, M. A. H.; Santos, N. O.
2007-09-15
We present a complete set of the equations and matching conditions required for the description of physically meaningful charged, dissipative, spherically symmetric gravitational collapse with shear. Dissipation is described with both free-streaming and diffusion approximations. The effects of viscosity are also taken into account. The roles of different terms in the dynamical equation are analyzed in detail. The dynamical equation is coupled to a causal transport equation in the context of Israel-Stewart theory. The decrease of the inertial mass density of the fluid, by a factor which depends on its internal thermodynamic state, is reobtained, with the viscosity terms included. In accordance with the equivalence principle, the same decrease factor is obtained for the gravitational force term. The effect of the electric charge on the relation between the Weyl tensor and the inhomogeneity of the energy density is discussed.
Maia, M.D.
1981-03-01
The concept of contact between manifolds is applied to space--times of general relativity. For a given background space--time a contact approximation of second order is defined and interpreted both from the point of view of a metric pertubation and of a higher order tangent manifold. In the first case, an application to the high frequency gravitational wave hypothesis is suggested. In the second case, a constant curvature tangent bundle is constructed and suggested as a means to define a ten parameter local space--time symmetry.
Braids, shuffles and symmetrizers
NASA Astrophysics Data System (ADS)
Isaev, A. P.; Ogievetsky, O. V.
2009-07-01
Multiplicative analogues of the shuffle elements of the braid group rings are introduced; in local representations they give rise to certain graded associative algebras (b-shuffle algebras). For the Hecke and BMW algebras, the (anti)-symmetrizers have simple expressions in terms of the multiplicative shuffles. The (anti)-symmetrizers can be expressed in terms of the highest multiplicative 1-shuffles (for the Hecke and BMW algebras) and in terms of the highest additive 1-shuffles (for the Hecke algebras). The spectra and multiplicities of eigenvalues of the operators of the multiplication by the multiplicative and additive 1-shuffles are examined. Dedicated to the memory of Aleosha Zamolodchikov.
Central tetrads and quantum spacetimes
NASA Astrophysics Data System (ADS)
Borowiec, Andrzej; Jurić, Tajron; Meljanac, Stjepan; Pachoł, Anna
2016-06-01
In this paper, we perform a parallel analysis to the model proposed in [E. J. Beggs and S. Majid, Gravity induced from quantum spacetime, Class. Quantum Grav. 31 (2014) 035020, arXiv: 1305.2403 [gr-qc
Spacetime metric from linear electrodynamics
NASA Astrophysics Data System (ADS)
Obukhov, Yuri N.; Hehl, Friedrich W.
1999-07-01
The Maxwell equations are formulated on an arbitrary (1+3)-dimensional manifold. Then, imposing a (constrained) linear constitutive relation between electromagnetic field (E,B) and excitation (D,ℌ), we derive the metric of spacetime therefrom.
Space-time compressive imaging.
Treeaporn, Vicha; Ashok, Amit; Neifeld, Mark A
2012-02-01
Compressive imaging systems typically exploit the spatial correlation of the scene to facilitate a lower dimensional measurement relative to a conventional imaging system. In natural time-varying scenes there is a high degree of temporal correlation that may also be exploited to further reduce the number of measurements. In this work we analyze space-time compressive imaging using Karhunen-Loève (KL) projections for the read-noise-limited measurement case. Based on a comprehensive simulation study, we show that a KL-based space-time compressive imager offers higher compression relative to space-only compressive imaging. For a relative noise strength of 10% and reconstruction error of 10%, we find that space-time compressive imaging with 8×8×16 spatiotemporal blocks yields about 292× compression compared to a conventional imager, while space-only compressive imaging provides only 32× compression. Additionally, under high read-noise conditions, a space-time compressive imaging system yields lower reconstruction error than a conventional imaging system due to the multiplexing advantage. We also discuss three electro-optic space-time compressive imaging architecture classes, including charge-domain processing by a smart focal plane array (FPA). Space-time compressive imaging using a smart FPA provides an alternative method to capture the nonredundant portions of time-varying scenes.
Rapidly rotating spacetimes and collisional super-Penrose process
NASA Astrophysics Data System (ADS)
Zaslavskii, O. B.
2016-05-01
We consider generic axially symmetric rotating spacetimes and examine particle collisions in the ergoregion. The results are generic and agree with those obtained in the particular case of the rotating Teo wormhole in Tsukamoto and Bambi, Phys Rev D 91:104040, 2015. It is shown that for sufficiently rapid rotation, the energy of a particle escaping to infinity can become arbitrary large (so-called super-Penrose process). Moreover, this energy is typically much larger than the center-of mass energy of colliding particles. In this sense the situation differs radically from that for collisions near black holes.
Counterrotating perfect fluid discs as sources of electrovacuum static spacetimes
NASA Astrophysics Data System (ADS)
García-Reyes, Gonzalo; González, Guillermo A.
2004-11-01
The interpretation of some electrovacuum spacetimes in terms of counterrotating perfect fluid discs is presented. The interpretation is made by means of an 'inverse problem' approach used to obtain disc sources of known static solutions of the Einstein Maxwell equations. In order to do such an interpretation, a detailed study is presented of the counterrotating model (CRM) for generic electrovacuum static axially symmetric relativistic thin discs with nonzero radial pressure. Four simple families of models of counterrotating charged discs based on Chazy Curzon-type, Zipoy Voorhees-type, Bonnor Sackfield-type and charged and magnetized Darmois electrovacuum metrics are considered, where we obtain some discs with a well-behaved CRM.
Souza Dutra, A. de; Santos, V. G. C. S. dos; Amaro de Faria, A. C. Jr.
2007-06-15
Some kinks for non-Hermitian quantum field theories in 1+1 dimensions are constructed. A class of models where the soliton energies are stable and real are found. Although these kinks are not Hermitian, they are symmetric under PT transformations.
Amore, Paolo; Fernández, Francisco M.; Garcia, Javier; Gutierrez, German
2014-04-15
We study both analytically and numerically the spectrum of inhomogeneous strings with PT-symmetric density. We discuss an exactly solvable model of PT-symmetric string which is isospectral to the uniform string; for more general strings, we calculate exactly the sum rules Z(p)≡∑{sub n=1}{sup ∞}1/E{sub n}{sup p}, with p=1,2,… and find explicit expressions which can be used to obtain bounds on the lowest eigenvalue. A detailed numerical calculation is carried out for two non-solvable models depending on a parameter, obtaining precise estimates of the critical values where pair of real eigenvalues become complex. -- Highlights: •PT-symmetric Hamiltonians exhibit real eigenvalues when PT symmetry is unbroken. •We study PT-symmetric strings with complex density. •They exhibit regions of unbroken PT symmetry. •We calculate the critical parameters at the boundaries of those regions. •There are exact real sum rules for some particular complex densities.
Stability and superluminality of spherical DBI Galileon solutions
Goon, Garrett L.; Hinterbichler, Kurt; Trodden, Mark
2011-04-12
We showed that, when considered as local modifications to gravity, such as in the solar system, there exists a region of parameter space in which spherically symmetric static solutions to a particular class of modified gravity theories exist and are stable.
Emergent space-time and the supersymmetric index
NASA Astrophysics Data System (ADS)
Benjamin, Nathan; Kachru, Shamit; Keller, Christoph A.; Paquette, Natalie M.
2016-05-01
It is of interest to find criteria on a 2d CFT which indicate that it gives rise to emergent gravity in a macroscopic 3d AdS space via holography. Symmetric orbifolds in the large N limit have partition functions which are consistent with an emergent space-time string theory with L string ˜ L AdS. For supersymmetric CFTs, the elliptic genus can serve as a sensitive probe of whether the SCFT admits a large radius gravity description with L string ≪ L AdS after one deforms away from the symmetric orbifold point in moduli space. We discuss several classes of constructions whose elliptic genera strongly hint that gravity with L Planck ≪ L string ≪ L AdS can emerge at suitable points in moduli space.
The solid angle (geometry factor) for a spherical surface source and an arbitrary detector aperture
Favorite, Jeffrey A.
2016-01-13
It is proven that the solid angle (or geometry factor, also called the geometrical efficiency) for a spherically symmetric outward-directed surface source with an arbitrary radius and polar angle distribution and an arbitrary detector aperture is equal to the solid angle for an isotropic point source located at the center of the spherical surface source and the same detector aperture.
Interacting shells in AdS spacetime and chaos
NASA Astrophysics Data System (ADS)
Brito, Richard; Cardoso, Vitor; Rocha, Jorge V.
2016-07-01
We study the simplest two-body problem in asymptotically anti-de Sitter spacetime: two, infinitely thin, concentric spherical shells of matter. We include only gravitational interaction between the two shells, but we show that the dynamics of this system is highly nontrivial. We observe prompt collapse to a black hole, delayed collapse and even perpetual oscillatory motion, depending on the initial location of the shells (or their energy content). The system exhibits critical behavior, and we show strong hints that it is also chaotic.
NASA Astrophysics Data System (ADS)
Müller, Bernhard; Janka, Hans-Thomas; Dimmelmeier, Harald
2010-07-01
We present a new general relativistic code for hydrodynamical supernova simulations with neutrino transport in spherical and azimuthal symmetry (one dimension and two dimensions, respectively). The code is a combination of the COCONUT hydro module, which is a Riemann-solver-based, high-resolution shock-capturing method, and the three-flavor, fully energy-dependent VERTEX scheme for the transport of massless neutrinos. VERTEX integrates the coupled neutrino energy and momentum equations with a variable Eddington factor closure computed from a model Boltzmann equation and uses the "ray-by-ray plus" approximation in two dimensions, assuming the neutrino distribution to be axially symmetric around the radial direction at every point in space, and thus the neutrino flux to be radial. Our spacetime treatment employs the Arnowitt-Deser-Misner 3+1 formalism with the conformal flatness condition for the spatial three metric. This approach is exact for the one-dimensional case and has previously been shown to yield very accurate results for spherical and rotational stellar core collapse. We introduce new formulations of the energy equation to improve total energy conservation in relativistic and Newtonian hydro simulations with grid-based Eulerian finite-volume codes. Moreover, a modified version of the VERTEX scheme is developed that simultaneously conserves energy and lepton number in the neutrino transport with better accuracy and higher numerical stability in the high-energy tail of the spectrum. To verify our code, we conduct a series of tests in spherical symmetry, including a detailed comparison with published results of the collapse, shock formation, shock breakout, and accretion phases. Long-time simulations of proto-neutron star cooling until several seconds after core bounce both demonstrate the robustness of the new COCONUT-VERTEX code and show the approximate treatment of relativistic effects by means of an effective relativistic gravitational potential as in
Mueller, Bernhard; Janka, Hans-Thomas; Dimmelmeier, Harald E-mail: thj@mpa-garching.mpg.d
2010-07-15
We present a new general relativistic code for hydrodynamical supernova simulations with neutrino transport in spherical and azimuthal symmetry (one dimension and two dimensions, respectively). The code is a combination of the COCONUT hydro module, which is a Riemann-solver-based, high-resolution shock-capturing method, and the three-flavor, fully energy-dependent VERTEX scheme for the transport of massless neutrinos. VERTEX integrates the coupled neutrino energy and momentum equations with a variable Eddington factor closure computed from a model Boltzmann equation and uses the 'ray-by-ray plus' approximation in two dimensions, assuming the neutrino distribution to be axially symmetric around the radial direction at every point in space, and thus the neutrino flux to be radial. Our spacetime treatment employs the Arnowitt-Deser-Misner 3+1 formalism with the conformal flatness condition for the spatial three metric. This approach is exact for the one-dimensional case and has previously been shown to yield very accurate results for spherical and rotational stellar core collapse. We introduce new formulations of the energy equation to improve total energy conservation in relativistic and Newtonian hydro simulations with grid-based Eulerian finite-volume codes. Moreover, a modified version of the VERTEX scheme is developed that simultaneously conserves energy and lepton number in the neutrino transport with better accuracy and higher numerical stability in the high-energy tail of the spectrum. To verify our code, we conduct a series of tests in spherical symmetry, including a detailed comparison with published results of the collapse, shock formation, shock breakout, and accretion phases. Long-time simulations of proto-neutron star cooling until several seconds after core bounce both demonstrate the robustness of the new COCONUT-VERTEX code and show the approximate treatment of relativistic effects by means of an effective relativistic gravitational potential as in
Leung, Ka-Ngo
2006-11-21
A spherical neutron generator is formed with a small spherical target and a spherical shell RF-driven plasma ion source surrounding the target. A deuterium (or deuterium and tritium) ion plasma is produced by RF excitation in the plasma ion source using an RF antenna. The plasma generation region is a spherical shell between an outer chamber and an inner extraction electrode. A spherical neutron generating target is at the center of the chamber and is biased negatively with respect to the extraction electrode which contains many holes. Ions passing through the holes in the extraction electrode are focused onto the target which produces neutrons by D-D or D-T reactions.
NASA Astrophysics Data System (ADS)
Chen, Yan; Feng, Huijuan; Ma, Jiayao; Peng, Rui; You, Zhong
2016-06-01
The traditional waterbomb origami, produced from a pattern consisting of a series of vertices where six creases meet, is one of the most widely used origami patterns. From a rigid origami viewpoint, it generally has multiple degrees of freedom, but when the pattern is folded symmetrically, the mobility reduces to one. This paper presents a thorough kinematic investigation on symmetric folding of the waterbomb pattern. It has been found that the pattern can have two folding paths under certain circumstance. Moreover, the pattern can be used to fold thick panels. Not only do the additional constraints imposed to fold the thick panels lead to single degree of freedom folding, but the folding process is also kinematically equivalent to the origami of zero-thickness sheets. The findings pave the way for the pattern being readily used to fold deployable structures ranging from flat roofs to large solar panels.
Rome, J.A.; Harris, J.H.
1984-01-01
A fusion reactor device is provided in which the magnetic fields for plasma confinement in a toroidal configuration is produced by a plurality of symmetrical modular coils arranged to form a symmetric modular torsatron referred to as a symmotron. Each of the identical modular coils is helically deformed and comprise one field period of the torsatron. Helical segments of each coil are connected by means of toroidally directed windbacks which may also provide part of the vertical field required for positioning the plasma. The stray fields of the windback segments may be compensated by toroidal coils. A variety of magnetic confinement flux surface configurations may be produced by proper modulation of the winding pitch of the helical segments of the coils, as in a conventional torsatron, winding the helix on a noncircular cross section and varying the poloidal and radial location of the windbacks and the compensating toroidal ring coils.
Stationary axially symmetric solutions in Brans-Dicke theory
NASA Astrophysics Data System (ADS)
Kirezli, Pınar; Delice, Özgür
2015-11-01
Stationary, axially symmetric Brans-Dicke-Maxwell solutions are reexamined in the framework of the Brans-Dicke (BD) theory. We see that, employing a particular parametrization of the standard axially symmetric metric simplifies the procedure of obtaining the Ernst equations for axially symmetric electrovacuum spacetimes for this theory. This analysis also permits us to construct a two parameter extension in both Jordan and Einstein frames of an old solution generating technique frequently used to construct axially symmetric solutions for BD theory from a seed solution of general relativity. As applications of this technique, several known and new solutions are constructed including a general axially symmetric BD-Maxwell solution of Plebanski-Demianski with vanishing cosmological constant, i.e., the Kinnersley solution and general magnetized Kerr-Newman-type solutions. Some physical properties and the circular motion of test particles for a particular subclass of Kinnersley solution, i.e., a Kerr-Newman-NUT-type solution for BD theory, are also investigated in some detail.
Improvement of stress-energy tensor using space-time symmetries
NASA Astrophysics Data System (ADS)
Bandyopadhyay, Akash
2001-05-01
In 1970 Callan, Coleman, and Jackiw found that it is always possible to improve the symmetric stress-energy tensor of a renormalizable relativistic field theory over (3+1)-dimensional flat space-time manifold. The improved stress-energy tensor defines the same field energy- momentum and angular momentum as the conventional tensor, and it is traceless for a non-interacting field theory when all coupling constants are physically dimensionless. The question for existence of an improved stress-energy tensor for a scale invariant relativistic field theory on a (1+1)-dimensional flat space-time manifold has been a long standing open problem for almost 30 years. In this thesis, I develop the weakest set of necessary and sufficient conditions for existence of a conserved symmetric traceless stress-energy tensor for a scale invariant relativistic field theory over a d-dimensional flat space-time manifold. This improved tensor, which defines the same conserved charges as the canonical tensor, has been explicitly constructed for arbitrary space-time dimensions including d = 2 intrinsically from the flat space-time field theory without coupling it with gravity. As an example, I derive the improved tensor of (1+1)- dimensional Liouville field theory. We discuss two remarkable results: (1)full conformal symmetry over the flat space-time is sufficient but not necessary for the existence of the improved tensor; (2)quite surprisingly, the improved stress-energy tensor exists in all space-time dimensions for a free massless Abelian U(1) gauge theory provided the gauge symmetry has been broken in favor of Lorentz gauge for d ≠ 2, 4.
Wide scanning spherical antenna
NASA Technical Reports Server (NTRS)
Shen, Bing (Inventor); Stutzman, Warren L. (Inventor)
1995-01-01
A novel method for calculating the surface shapes for subreflectors in a suboptic assembly of a tri-reflector spherical antenna system is introduced, modeled from a generalization of Galindo-Israel's method of solving partial differential equations to correct for spherical aberration and provide uniform feed to aperture mapping. In a first embodiment, the suboptic assembly moves as a single unit to achieve scan while the main reflector remains stationary. A feed horn is tilted during scan to maintain the illuminated area on the main spherical reflector fixed throughout the scan thereby eliminating the need to oversize the main spherical reflector. In an alternate embodiment, both the main spherical reflector and the suboptic assembly are fixed. A flat mirror is used to create a virtual image of the suboptic assembly. Scan is achieved by rotating the mirror about the spherical center of the main reflector. The feed horn is tilted during scan to maintain the illuminated area on the main spherical reflector fixed throughout the scan.
Visibility of a spacetime singularity
Joshi, Pankaj S.
2007-02-15
We investigate here the causal structure of spacetime in the vicinity of a spacetime singularity. The particle and energy emission from such ultradense regions forming in gravitational collapse of a massive matter cloud is governed by the nature of nonspacelike paths near the same. These trajectories are examined to show that if a null geodesic comes out from the singularity, then there exist families of future-directed nonspacelike curves which also necessarily escape from the same. The existence of such families is crucial to the physical visibility of the singularity. We do not assume any underlying symmetries for the spacetime, and earlier considerations on the nature of causal trajectories emerging from a naked singularity are generalized and clarified.
Impact of curvature divergences on physical observers in a wormhole space-time with horizons
NASA Astrophysics Data System (ADS)
Olmo, Gonzalo J.; Rubiera-Garcia, D.; Sanchez-Puente, A.
2016-06-01
The impact of curvature divergences on physical observers in a black hole space-time, which, nonetheless, is geodesically complete is investigated. This space-time is an exact solution of certain extensions of general relativity coupled to Maxwell’s electrodynamics and, roughly speaking, consists of two Reissner-Nordström (or Schwarzschild or Minkowski) geometries connected by a spherical wormhole near the center. We find that, despite the existence of infinite tidal forces, causal contact is never lost among the elements making up the observer. This suggests that curvature divergences may not be as pathological as traditionally thought.
A multi-element cosmological model with a complex space-time topology
NASA Astrophysics Data System (ADS)
Kardashev, N. S.; Lipatova, L. N.; Novikov, I. D.; Shatskiy, A. A.
2015-02-01
Wormhole models with a complex topology having one entrance and two exits into the same space-time of another universe are considered, as well as models with two entrances from the same space-time and one exit to another universe. These models are used to build a model of a multi-sheeted universe (a multi-element model of the "Multiverse") with a complex topology. Spherical symmetry is assumed in all the models. A Reissner-Norström black-hole model having no singularity beyond the horizon is constructed. The strength of the central singularity of the black hole is analyzed.
The Historical Origins of Spacetime
NASA Astrophysics Data System (ADS)
Walter, Scott
The idea of spacetime investigated in this chapter, with a view toward understanding its immediate sources and development, is the one formulated and proposed by Hermann Minkowski in 1908. Until recently, the principle source used to form historical narratives of Minkowski's discovery of spacetime has been Minkowski's own discovery account, outlined in the lecture he delivered in Cologne, entitled Space and time [1]. Minkowski's lecture is usually considered as a bona fide first-person narrative of lived events. According to this received view, spacetime was a natural outgrowth of Felix Klein's successful project to promote the study of geometries via their characteristic groups of transformations. Or as Minkowski expressed the same basic thought himself, the theory of relativity discovered by physicists in 1905 could just as well have been proposed by some late-nineteenth-century mathematician, by simply reflecting upon the groups of transformations that left invariant the form of the equation of a propagating light wave. Minkowski's publications and research notes provide a contrasting picture of the discovery of spacetime, in which group theory plays no direct part. In order to relate the steps of Minkowski's discovery, we begin with an account of Poincaré's theory of gravitation, where Minkowski found some of the germs of spacetime. Poincaré's geometric interpretation of the Lorentz transformation is examined, along with his reasons for not pursuing a four-dimensional vector calculus. In the second section, Minkowski's discovery and presentation of the notion of a world line in spacetime is presented. In the third and final section, Poincaré's and Minkowski's diagrammatic interpretations of the Lorentz transformation are compared.
Large displacement spherical joint
Bieg, Lothar F.; Benavides, Gilbert L.
2002-01-01
A new class of spherical joints has a very large accessible full cone angle, a property which is beneficial for a wide range of applications. Despite the large cone angles, these joints move freely without singularities.
NASA Technical Reports Server (NTRS)
Villarreal, James A.; Shelton, Robert O.
1992-01-01
Concept of space-time neural network affords distributed temporal memory enabling such network to model complicated dynamical systems mathematically and to recognize temporally varying spatial patterns. Digital filters replace synaptic-connection weights of conventional back-error-propagation neural network.
Gravitational vacuum polarization around static spherical stars
Hiscock, W.A.
1988-04-15
The gravitational vacuum polarization of conformally coupled quantum fields in the spacetime of a uniform-density, static, spherical star is studied using the approximation developed by Page, Brown, and Ottewill. Approximate vacuum stress-energy tensors are calculated for conformal massless scalar, spinor, and vector fields; in the case of vector fields, both dimensionally regularized and zeta-function results are given. Explicit algebraic forms for the stress-energy tensors are given for the interior of the star and for the exterior Schwarzschild region. If the vacuum stress energy is to be conserved and have the correct trace anomaly at the surface of the star, it is necessary that there be distributional terms in the vacuum stress energy at the surface. The nature and magnitude of these terms are determined. The semiclassical Einstein equations are solved in the exterior region of the star to first order in (h/2..pi..), and the first quantum corrections to Kepler's third law are found.
Symmetrization for redundant channels
NASA Technical Reports Server (NTRS)
Tulplue, Bhalchandra R. (Inventor); Collins, Robert E. (Inventor)
1988-01-01
A plurality of redundant channels in a system each contain a global image of all the configuration data bases in each of the channels in the system. Each global image is updated periodically from each of the other channels via cross channel data links. The global images of the local configuration data bases in each channel are separately symmetrized using a voting process to generate a system signal configuration data base which is not written into by any other routine and is available for indicating the status of the system within each channel. Equalization may be imposed on a suspect signal and a number of chances for that signal to heal itself are provided before excluding it from future votes. Reconfiguration is accomplished upon detecting a channel which is deemed invalid. A reset function is provided which permits an externally generated reset signal to permit a previously excluded channel to be reincluded within the system. The updating of global images and/or the symmetrization process may be accomplished at substantially the same time within a synchronized time frame common to all channels.
Physical constraints on causality-violating spacetimes in general relativity
NASA Astrophysics Data System (ADS)
Janca, Andrew Joseph
The theoretical possibility of global causality violation has long been a problem within general relativity, for there exists a large number of model spacetimes known to admit closed time-like curves, trajectories allowing a timelike observer to return to some point in her own past. However, nearly all such known models have some unphysical feature. These physicality issues rendered causality-violation to the status of an interesting but safely theoretical problem until twenty years ago, when the appearance of a new type of causality-violating model spacetime and the subsequent proliferation of new models admitting closed timelike curves forced the attention of the community to the issue, and made causality violation and its possible physical consequences an active area of research within general relativity. This paper focuses on some of the older causality-violating spacetimes which model matter sources with cylindrical symmetry. By describing how cylindrically-symmetric solutions can be embedded within a spatially bounded and physically realistic body which outwardly has the symmetry of a torus or ring, it is shown that the chief problem of physical plausibility which these older solutions possess can be resolved. The intention is to make these models active candidates for consideration in future experiments to test general relativity's prediction that causality violation is a phenomenon that could be observed in the real world. Attending chapters describe physical systems other than rotating objects that can alter a local observer's experience of time to a substantial extent, including an electrically-charged massive shell slowing time in its interior (though not affecting causality) and a class of trajectories in the Reissner-Nordstrom background that could in principle allow a timelike observer to reverse her personal arrow of time relative to other observers in the spacetime as a whole. The paper concludes with a discussion of one of the plausibility problems
Quantum entanglement in Plebański-Demiański spacetimes
NASA Astrophysics Data System (ADS)
García-Compeán, Hugo; Robledo-Padilla, Felipe
2013-12-01
For an Einstein-Podolsky-Rosen pair of spin-1/2 particles in circular orbits in a general axially symmetric spacetime, the spin precession angle is obtained. Hovering observers are introduced for ensuring fixed reference frames to perform suitable reliable measurements. Frame-dragging of spinning holes is explicitly incorporated relative to hovering observers. The spin-singlet state is found to be mixed with the spin-triplet by acceleration and gravity effects, which deteriorate the perfect anti-correlation of an entangled pair of spins measured by hovering observers. Finally, an algorithm to calculate spin precession for a general axially symmetric spacetime is proposed. This algorithm is applied to study the complete list of expanding and twisting Type-D Plebański-Demiański black holes and their descendent limiting solutions with lower parameters.
Relativistic quantum dynamics of a spinless particle in the Som-Raychaudhuri spacetime
NASA Astrophysics Data System (ADS)
Wang, Zhi; Long, Zheng-wen; Long, Chao-yun; Wu, Ming-li
2015-03-01
The Klein-Gordon equation under the influence of the gravitational field produced by a topology such as the Som-Raychaudhuri spacetime and the Klein-Gordon oscillator in the presence of a uniform magnetic field as well as without magnetic field are investigated. Moreover, the Klein-Gordon equation with a cylindrically symmetric scalar potential in the background spacetime is also studied. By using the quasi-analytical ansatz approach, we obtain the energy eigenvalues and corresponding wave functions of these systems. They show that the energy levels of the considered physical systems depend explicitly on the angular deficit α and the vorticity parameter Ω which characterize the global structure of the metric in the Som-Raychaudhuri spacetime.
Cracked shells under skew-symmetric loading
NASA Technical Reports Server (NTRS)
Lelale, F.
1982-01-01
A shell containing a through crack in one of the principal planes of curvature and under general skew-symmetric loading is considered. By employing a Reissner type shell theory which takes into account the effect of transverse shear strains, all boundary conditions on the crack surfaces are satisfied separately. Consequently, unlike those obtained from the classical shell theory, the angular distributions of the stress components around the crack tips are shown to be identical to the distributions obtained from the plane and antiplane elasticity solutions. Extensive results are given for axially and circumferentially cracked cylindrical shells, spherical shells, and toroidal shells under uniform inplane shearing, out of plane shearing, and torsion. The effect of orthotropy on the results is also studied.
VACUUM calculation in azimuthally symmetric geometry
Chance, M.S.
1996-11-01
A robustly accurate and effective method is presented to solve Laplace`s equation in general azimuthally symmetric geometry for the magnetic scalar potential in the region surrounding a plasma discharge which may or may not contain external conducting shells. These shells can be topologically toroidal or spherical, and may have toroidal gaps in them. The solution is incorporated into the various MHD stability codes either through the volume integrated perturbed magnetic energy in the vacuum region or through the continuity requirements for the normal component of the perturbed magnetic field and the total perturbed pressure across the unperturbed plasma-vacuum boundary. The method is based upon using Green`s second identity and the method of collocation. As useful byproducts, the eddy currents and the simulation of Mirnov loop measurements are calculated.
Affine conformal vectors in space-time
NASA Astrophysics Data System (ADS)
Coley, A. A.; Tupper, B. O. J.
1992-05-01
All space-times admitting a proper affine conformal vector (ACV) are found. By using a theorem of Hall and da Costa, it is shown that such space-times either (i) admit a covariantly constant vector (timelike, spacelike, or null) and the ACV is the sum of a proper affine vector and a conformal Killing vector or (ii) the space-time is 2+2 decomposable, in which case it is shown that no ACV can exist (unless the space-time decomposes further). Furthermore, it is proved that all space-times admitting an ACV and a null covariantly constant vector (which are necessarily generalized pp-wave space-times) must have Ricci tensor of Segré type {2,(1,1)}. It follows that, among space-times admitting proper ACV, the Einstein static universe is the only perfect fluid space-time, there are no non-null Einstein-Maxwell space-times, and only the pp-wave space-times are representative of null Einstein-Maxwell solutions. Otherwise, the space-times can represent anisotropic fluids and viscous heat-conducting fluids, but only with restricted equations of state in each case.
The Wigner-Eckart Theorem for Reducible Symmetric Cartesian Tensor Operators
NASA Astrophysics Data System (ADS)
Bouzas, Antonio O.
2016-08-01
We explicitly establish a unitary correspondence between spherical irreducible tensor operators and Cartesian tensor operators of any rank. That unitary relation is implemented by means of a basis of integer-spin wave functions that constitute simultaneously a basis of the spaces of Cartesian and spherical irreducible tensors. As a consequence, we extend the Wigner-Eckart theorem to Cartesian irreducible tensor operators of any rank, and to totally symmetric reducible ones. We also discuss the tensorial structure of several standard spherical irreducible tensors such as ordinary, bipolar and tensor spherical harmonics, spin-polarization operators and multipole operators. As an application, we obtain an explicit expression for the derivatives of any order of spherical harmonics in terms of tensor spherical harmonics.
Optimal symmetric flight studies
NASA Technical Reports Server (NTRS)
Weston, A. R.; Menon, P. K. A.; Bilimoria, K. D.; Cliff, E. M.; Kelley, H. J.
1985-01-01
Several topics in optimal symmetric flight of airbreathing vehicles are examined. In one study, an approximation scheme designed for onboard real-time energy management of climb-dash is developed and calculations for a high-performance aircraft presented. In another, a vehicle model intermediate in complexity between energy and point-mass models is explored and some quirks in optimal flight characteristics peculiar to the model uncovered. In yet another study, energy-modelling procedures are re-examined with a view to stretching the range of validity of zeroth-order approximation by special choice of state variables. In a final study, time-fuel tradeoffs in cruise-dash are examined for the consequences of nonconvexities appearing in the classical steady cruise-dash model. Two appendices provide retrospective looks at two early publications on energy modelling and related optimal control theory.
Generation of multiple spherical spots with a radially polarized beam in a 4pi focusing system.
Yan, Shaohui; Yao, Baoli; Zhao, Wei; Lei, Ming
2010-09-01
We demonstrate the possibility of creating multiple spherical spots in a 4pi focusing system with a radially polarized beam. Using spherical waves to expand the plane wave factor in the Richards-Wolf integral, it is found that a proper spatial modulation in the amplitude of the input field with radial polarization can form multiple spherical spots with a focusing system satisfying the Herschel condition. These spots are distributed symmetrically about the focus on the optical axis with variable positions and intensities. Although we consider only the case of three spherical spots in this paper, generalization to the multiple-spots case will present no difficulty.
Preserving spherical symmetry in axisymmetric coordinates for diffusion problems
Brunner, T. A.; Kolev, T. V.; Bailey, T. S.; Till, A. T.
2013-07-01
Persevering symmetric solutions, even in the under-converged limit, is important to the robustness of production simulation codes. We explore the symmetry preservation in both a continuous nodal and a mixed finite element method. In their standard formulation, neither method preserves spherical solution symmetry in axisymmetric (RZ) coordinates. We propose two methods, one for each family of finite elements, that recover spherical symmetry for low-order finite elements on linear or curvilinear meshes. This is a first step toward understanding achieving symmetry for higher-order elements. (authors)
Spherical geodesic mesh generation
Fung, Jimmy; Kenamond, Mark Andrew; Burton, Donald E.; Shashkov, Mikhail Jurievich
2015-02-27
In ALE simulations with moving meshes, mesh topology has a direct influence on feature representation and code robustness. In three-dimensional simulations, modeling spherical volumes and features is particularly challenging for a hydrodynamics code. Calculations on traditional spherical meshes (such as spin meshes) often lead to errors and symmetry breaking. Although the underlying differencing scheme may be modified to rectify this, the differencing scheme may not be accessible. This work documents the use of spherical geodesic meshes to mitigate solution-mesh coupling. These meshes are generated notionally by connecting geodesic surface meshes to produce triangular-prismatic volume meshes. This mesh topology is fundamentally different from traditional mesh topologies and displays superior qualities such as topological symmetry. This work describes the geodesic mesh topology as well as motivating demonstrations with the FLAG hydrocode.
Dark Energy from Discrete Spacetime
Trout, Aaron D.
2013-01-01
Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies. PMID:24312502
Dark energy from discrete spacetime.
Trout, Aaron D
2013-01-01
Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, [Formula: see text] in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies.
Quantum walking in curved spacetime
NASA Astrophysics Data System (ADS)
Arrighi, Pablo; Facchini, Stefano; Forets, Marcelo
2016-08-01
A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs admit a continuum limit, leading to familiar PDEs (e.g., the Dirac equation). In this paper, we study the continuum limit of a wide class of QWs and show that it leads to an entire class of PDEs, encompassing the Hamiltonian form of the massive Dirac equation in (1+1) curved spacetime. Therefore, a certain QW, which we make explicit, provides us with a unitary discrete toy model of a test particle in curved spacetime, in spite of the fixed background lattice. Mathematically, we have introduced two novel ingredients for taking the continuum limit of a QW, but which apply to any quantum cellular automata: encoding and grouping.
NASA Astrophysics Data System (ADS)
Meyers, Ronald E.; Deacon, Keith S.; Tunick, Arnold
2013-09-01
We report on an experimental demonstration of quantum imaging where the images are stored in both space and time. Quantum images of remote objects are produced with rotating ground glass induced chaotic laser light and two sensors measuring at different space-time points. Quantum images are observed to move depending on the time delay between the sensor measurements. The experiments provide a new testbed for exploring the time and space scale fundamental physics of quantum imaging and suggest new pathways for quantum information storage and processing. The moved quantum images are in fact new images that are stored in a space-time virtual memory process. The images are stored within the same quantum imaging data sets and thus quantum imaging can produce more information per photon measured than was previously realized.
Spacetimes containing slowly evolving horizons
Kavanagh, William; Booth, Ivan
2006-08-15
Slowly evolving horizons are trapping horizons that are ''almost'' isolated horizons. This paper reviews their definition and discusses several spacetimes containing such structures. These include certain Vaidya and Tolman-Bondi solutions as well as (perturbatively) tidally distorted black holes. Taking into account the mass scales and orders of magnitude that arise in these calculations, we conjecture that slowly evolving horizons are the norm rather than the exception in astrophysical processes that involve stellar-scale black holes.
{PT}-symmetric optical superlattices
NASA Astrophysics Data System (ADS)
Longhi, Stefano
2014-04-01
The spectral and localization properties of {PT}-symmetric optical superlattices, either infinitely extended or truncated at one side, are theoretically investigated, and the criteria that ensure a real energy spectrum are derived. The analysis is applied to the case of superlattices describing a complex ( {PT}-symmetric) extension of the Harper Hamiltonian in the rational case.
NASA Technical Reports Server (NTRS)
Meyer, Jay L. (Inventor); Messick, Glenn C. (Inventor); Nardell, Carl A. (Inventor); Hendlin, Martin J. (Inventor)
2011-01-01
A spherical mounting assembly for mounting an optical element allows for rotational motion of an optical surface of the optical element only. In that regard, an optical surface of the optical element does not translate in any of the three perpendicular translational axes. More importantly, the assembly provides adjustment that may be independently controlled for each of the three mutually perpendicular rotational axes.
Retroreflector spherical satellite
NASA Astrophysics Data System (ADS)
Akentyev, A. S.; Vasiliev, V. P.; Sadovnikov, M. A.; Sokolov, A. L.; Shargorodskiy, V. D.
2015-10-01
Specific features of spherical retroreflector arrays for high-precision laser ranging are considered, and errors in distance measurements are analyzed. A version of a glass retroreflector satellite with a submillimeter "target error" is proposed. Its corner cube reflectors are located in depressions to reduce the working angular aperture, and their faces have a dielectric interference coating.
Spherical colloidal photonic crystals.
Zhao, Yuanjin; Shang, Luoran; Cheng, Yao; Gu, Zhongze
2014-12-16
CONSPECTUS: Colloidal photonic crystals (PhCs), periodically arranged monodisperse nanoparticles, have emerged as one of the most promising materials for light manipulation because of their photonic band gaps (PBGs), which affect photons in a manner similar to the effect of semiconductor energy band gaps on electrons. The PBGs arise due to the periodic modulation of the refractive index between the building nanoparticles and the surrounding medium in space with subwavelength period. This leads to light with certain wavelengths or frequencies located in the PBG being prohibited from propagating. Because of this special property, the fabrication and application of colloidal PhCs have attracted increasing interest from researchers. The most simple and economical method for fabrication of colloidal PhCs is the bottom-up approach of nanoparticle self-assembly. Common colloidal PhCs from this approach in nature are gem opals, which are made from the ordered assembly and deposition of spherical silica nanoparticles after years of siliceous sedimentation and compression. Besides naturally occurring opals, a variety of manmade colloidal PhCs with thin film or bulk morphology have also been developed. In principle, because of the effect of Bragg diffraction, these PhC materials show different structural colors when observed from different angles, resulting in brilliant colors and important applications. However, this angle dependence is disadvantageous for the construction of some optical materials and devices in which wide viewing angles are desired. Recently, a series of colloidal PhC materials with spherical macroscopic morphology have been created. Because of their spherical symmetry, the PBGs of spherical colloidal PhCs are independent of rotation under illumination of the surface at a fixed incident angle of the light, broadening the perspective of their applications. Based on droplet templates containing colloidal nanoparticles, these spherical colloidal PhCs can be
NASA Astrophysics Data System (ADS)
Nichols, David A.; Owen, Robert; Zhang, Fan; Zimmerman, Aaron; Brink, Jeandrew; Chen, Yanbei; Kaplan, Jeffrey D.; Lovelace, Geoffrey; Matthews, Keith D.; Scheel, Mark A.; Thorne, Kip S.
2011-12-01
When one splits spacetime into space plus time, the Weyl curvature tensor (vacuum Riemann tensor) gets split into two spatial, symmetric, and trace-free tensors: (i) the Weyl tensor’s so-called electric part or tidal field Ejk, which raises tides on the Earth’s oceans and drives geodesic deviation (the relative acceleration of two freely falling test particles separated by a spatial vector ξk is Δaj=-Ejkξk), and (ii) the Weyl tensor’s so-called magnetic part or (as we call it) frame-drag field Bjk, which drives differential frame dragging (the precessional angular velocity of a gyroscope at the tip of ξk, as measured using a local inertial frame at the tail of ξk, is ΔΩj=Bjkξk). Being symmetric and trace-free, Ejk and Bjk each have three orthogonal eigenvector fields which can be depicted by their integral curves. We call the integral curves of Ejk’s eigenvectors tidal tendex lines or simply tendex lines, we call each tendex line’s eigenvalue its tendicity, and we give the name tendex to a collection of tendex lines with large tendicity. The analogous quantities for Bjk are frame-drag vortex lines or simply vortex lines, their vorticities, and their vortexes. These concepts are powerful tools for visualizing spacetime curvature. We build up physical intuition into them by applying them to a variety of weak-gravity phenomena: a spinning, gravitating point particle, two such particles side-by-side, a plane gravitational wave, a point particle with a dynamical current-quadrupole moment or dynamical mass-quadrupole moment, and a slow-motion binary system made of nonspinning point particles. We show that a rotating current quadrupole has four rotating vortexes that sweep outward and backward like water streams from a rotating sprinkler. As they sweep, the vortexes acquire accompanying tendexes and thereby become outgoing current-quadrupole gravitational waves. We show similarly that a rotating mass quadrupole has four rotating, outward
NASA Astrophysics Data System (ADS)
Lake, Kayll
2010-12-01
The title immediately brings to mind a standard reference of almost the same title [1]. The authors are quick to point out the relationship between these two works: they are complementary. The purpose of this work is to explain what is known about a selection of exact solutions. As the authors state, it is often much easier to find a new solution of Einstein's equations than it is to understand it. Even at first glance it is very clear that great effort went into the production of this reference. The book is replete with beautifully detailed diagrams that reflect deep geometric intuition. In many parts of the text there are detailed calculations that are not readily available elsewhere. The book begins with a review of basic tools that allows the authors to set the notation. Then follows a discussion of Minkowski space with an emphasis on the conformal structure and applications such as simple cosmic strings. The next two chapters give an in-depth review of de Sitter space and then anti-de Sitter space. Both chapters contain a remarkable collection of useful diagrams. The standard model in cosmology these days is the ICDM model and whereas the chapter on the Friedmann-Lemaître-Robertson-Walker space-times contains much useful information, I found the discussion of the currently popular a representation rather too brief. After a brief but interesting excursion into electrovacuum, the authors consider the Schwarzschild space-time. This chapter does mention the Swiss cheese model but the discussion is too brief and certainly dated. Space-times related to Schwarzschild are covered in some detail and include not only the addition of charge and the cosmological constant but also the addition of radiation (the Vaidya solution). Just prior to a discussion of the Kerr space-time, static axially symmetric space-times are reviewed. Here one can find a very interesting discussion of the Curzon-Chazy space-time. The chapter on rotating black holes is rather brief and, for
Trumpet solution from spherical gravitational collapse with puncture gauges
Thierfelder, Marcus; Bernuzzi, Sebastiano; Hilditch, David; Bruegmann, Bernd; Rezzolla, Luciano
2011-03-15
We investigate the stationary end state obtained by evolving a collapsing spherical star with the gauges routinely adopted to study puncture black holes. We compare the end state of the collapse with the trumpet solution found in the evolution of a single wormhole slice and show that the two solutions closely agree. We demonstrate that the agreement is caused by the use of the Gamma-driver shift condition, which allows the matter to fall inwards into a region of spacetime that is not resolved by the numerical grid, and which simultaneously finds the stationary coordinates of the trumpet outside the matter.
A Model of Classical Space-Times.
ERIC Educational Resources Information Center
Maudlin, Tim
1989-01-01
Discusses some historically important reference systems including those by Newton, Leibniz, and Galileo. Provides models illustrating space-time relationship of the reference systems. Describes building models. (YP)
Quantum singularity of Levi-Civita spacetimes
NASA Astrophysics Data System (ADS)
Konkowski, D. A.; Helliwell, T. M.; Wieland, C.
2004-01-01
Quantum singularities in general relativistic spacetimes are determined by the behaviour of quantum test particles. A static spacetime is quantum mechanically singular if the spatial portion of the wave operator is not essentially self-adjoint. Here Weyl's limit point limit circle criterion is used to determine whether a wave operator is essentially self-adjoint. This test is then applied to scalar wave packets in Levi-Civita spacetimes to help elucidate the physical properties of the spacetimes in terms of their metric parameters.
Geodesics dynamics in the Linet-Tian spacetime with
NASA Astrophysics Data System (ADS)
Brito, Irene; Da Silva, M. F. A.; Mena, Filipe C.; Santos, N. O.
2014-03-01
We investigate the geodesics' kinematics and dynamics in the Linet-Tian metric with and compare with the results for the Levi-Civita metric, when . This is used to derive new stability results about the geodesics' dynamics in static vacuum cylindrically symmetric spacetimes with respect to the introduction of . In particular, we find that increasing always increases the minimum and maximum radial distances to the axis of any spatially confined planar null geodesic. Furthermore, we show that, in some cases, the inclusion of any breaks the geodesics' orbit confinement of the metric, for both planar and non-planar null geodesics, which are therefore unstable. Using the full system of geodesics' equations, we provide numerical examples which illustrate our results.
Hollow spherical shell manufacture
O'Holleran, T.P.
1991-11-26
A process is disclosed for making a hollow spherical shell of silicate glass composition in which an aqueous suspension of silicate glass particles and an immiscible liquid blowing agent is placed within the hollow spherical cavity of a porous mold. The mold is spun to reduce effective gravity to zero and to center the blowing agent, while being heated so as to vaporize the immiscible liquid and urge the water carrier of the aqueous suspension to migrate into the body of the mold, leaving a green shell compact deposited around the mold cavity. The green shell compact is then removed from the cavity, and is sintered for a time and a temperature sufficient to form a silicate glass shell of substantially homogeneous composition and uniform geometry. 3 figures.
Lee, M.C.; Kendall, J.M.,JR.; Bahrami, P.A.; Wang, T.G.
1986-01-01
Fluid-dynamic and capillary forces can be used to form nearly perfect, very small spherical shells when a liquid that can solidify is passed through an annular die to form an annular jet. Gravity and certain properties of even the most ideal materials, however, can cause slight asymmetries. The primary objective of the present work is the control of this shell formation process in earth laboratories rather than space microgravity, through the development of facilities and methods that minimize the deleterious effects of gravity, aerodynamic drag, and uncontrolled cooling. The spherical shells thus produced can be used in insulation, recyclable filter materials, fire retardants, explosives, heat transport slurries, shock-absorbing armor, and solid rocket motors.
Hollow spherical shell manufacture
O'Holleran, Thomas P.
1991-01-01
A process for making a hollow spherical shell of silicate glass composition in which an aqueous suspension of silicate glass particles and an immiscible liquid blowing agent is placed within the hollow spherical cavity of a porous mold. The mold is spun to reduce effective gravity to zero and to center the blowing agent, while being heated so as to vaporize the immiscible liquid and urge the water carrier of the aqueous suspension to migrate into the body of the mold, leaving a green shell compact deposited around the mold cavity. The green shell compact is then removed from the cavity, and is sintered for a time and a temperature sufficient to form a silicate glass shell of substantially homogeneous composition and uniform geometry.
Spherical torus fusion reactor
Peng, Yueng-Kay M.
1989-04-04
A fusion reactor is provided having a near spherical-shaped plasma with a modest central opening through which straight segments of toroidal field coils extend that carry electrical current for generating a toroidal magnet plasma confinement fields. By retaining only the indispensable components inboard of the plasma torus, principally the cooled toroidal field conductors and in some cases a vacuum containment vessel wall, the fusion reactor features an exceptionally small aspect ratio (typically about 1.5), a naturally elongated plasma cross section without extensive field shaping, requires low strength magnetic containment fields, small size and high beta. These features combine to produce a spherical torus plasma in a unique physics regime which permits compact fusion at low field and modest cost.
Spherical torus fusion reactor
Peng, Yueng-Kay M.
1989-01-01
A fusion reactor is provided having a near spherical-shaped plasma with a modest central opening through which straight segments of toroidal field coils extend that carry electrical current for generating a toroidal magnet plasma confinement fields. By retaining only the indispensable components inboard of the plasma torus, principally the cooled toroidal field conductors and in some cases a vacuum containment vessel wall, the fusion reactor features an exceptionally small aspect ratio (typically about 1.5), a naturally elongated plasma cross section without extensive field shaping, requires low strength magnetic containment fields, small size and high beta. These features combine to produce a spherical torus plasma in a unique physics regime which permits compact fusion at low field and modest cost.
Spherical torus experiment (STX)
McManamy, T.J.; Lazarus, E.A.
1985-01-01
The principal engineering features of the proposed Spherical Torus Experiment (STX) are described. Design is dominated by the small bore available for the ohmic heating (OH) solenoid and structural considerations for a situation in which B/sub p/ is approximately equal to B/sub t/. Unique features of a spherical torus plasma include large elongations without shaping fields; an exceptionally high ratio of plasma current to toroidal field, giving the potential for stability at very high beta; strong paramagnetism; and a variety of configurations, ranging from tokamak (q/sub a/) to revised-field pinch (RFP) (q/sub a/ < 1). Access to this regime requires aspect ratios less than 2. A feasibility study has been done for a beam-heated device with A = 1.67, R0 = 0.45, and K = 2. 3 refs., 9 figs.
Is space-time symmetry a suitable generalization of parity-time symmetry?
Amore, Paolo; Fernández, Francisco M.; Garcia, Javier
2014-11-15
We discuss space-time symmetric Hamiltonian operators of the form H=H{sub 0}+igH{sup ′}, where H{sub 0} is Hermitian and g real. H{sub 0} is invariant under the unitary operations of a point group G while H{sup ′} is invariant under transformation by elements of a subgroup G{sup ′} of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0
Quantization of spacetime based on a spacetime interval operator
NASA Astrophysics Data System (ADS)
Chiang, Hsu-Wen; Hu, Yao-Chieh; Chen, Pisin
2016-04-01
Motivated by both concepts of Adler's recent work on utilizing Clifford algebra as the linear line element d s =⟨γμ⟩ d Xμ and the fermionization of the cylindrical worldsheet Polyakov action, we introduce a new type of spacetime quantization that is fully covariant. The theory is based on the reinterpretation of Adler's linear line element as d s =γμ⟨λ γμ⟩ , where λ is the characteristic length of the theory. We name this new operator the "spacetime interval operator" and argue that it can be regarded as a natural extension to the one-forms in the U (s u (2 )) noncommutative geometry. By treating Fourier momentum as the particle momentum, the generalized uncertainty principle of the U (s u (2 )) noncommutative geometry, as an approximation to the generalized uncertainty principle of our theory, is derived and is shown to have a lowest order correction term of the order p2 similar to that of Snyder's. The holography nature of the theory is demonstrated and the predicted fuzziness of the geodesic is shown to be much smaller than conceivable astrophysical bounds.
General Relativity and Spacetime Relationism.
NASA Astrophysics Data System (ADS)
Hoefer, Carl
1992-01-01
This dissertation takes up the project of showing that, in the context of the general theory of relativity (GTR), spacetime relationism is not a refuted or hopeless view, as many in the recent literature have maintained (John Earman, Michael Friedman, and others). Most of the challenges to the relationist view in General Relativity can be satisfactorily answered; in addition, the opposing absolutist and substantivalist views of spacetime can be shown to be problematic. The crucial burden for relationists concerned with GTR is to show that the realistic cosmological models, i.e. those that may be roughly accurate representations of our universe, satisfy Mach's ideas about the origin of inertia. This dissertation clears the way for and begins such a demonstration. After a brief discussion of the problem of the nature of spacetime and its history in the Introduction, chapters 2 and 3 provide conceptual analysis and criticism of contemporary philosophical arguments about relationism, absolutism, and particularly substantivalism. The current best arguments in favor of substantivalism are shown to be flawed, with the exception of the argument from inertial and metrical structure; and on this issue, it is shown that both relationism and substantivalism need to argue for modifications of GTR (restriction of its models to those with certain features) in order to have a non-trivial explanation of inertial and metrical structure. For relationists, a Machian account of the origin of inertia in some models of GTR is required. Chapter 4 demonstrates that such a Machian account is equivalent to the demand for a truly general relativity of motion. Chapter 5 explores the history of Einstein's commitment to Mach's ideas in his work on GTR. Through an examination of the history of Einstein's attempts to impose Machian constraints on the models of General Relativity, further insight into the nature of this problem is obtained, as are reasons to believe that the project is by no means
Spherical nitroguanidine process
Sanchez, John A.; Roemer, Edward L.; Stretz, Lawrence A.
1990-01-01
A process of preparing spherical high bulk density nitroguanidine by dissing low bulk density nitroguanidine in N-methyl pyrrolidone at elevated temperatures and then cooling the solution to lower temperatures as a liquid characterized as a nonsolvent for the nitroguanidine is provided. The process is enhanced by inclusion in the solution of from about 1 ppm up to about 250 ppm of a metal salt such as nickel nitrate, zinc nitrate or chromium nitrate, preferably from about 20 to about 50 ppm.
Wake control with permeable multilayer structures: The spherical symmetry case.
Bowen, Patrick T; Smith, David R; Urzhumov, Yaroslav A
2015-12-01
We explore the possibility of controlling the wake and drag of a spherical object independently of each other, using radial distributions of permeability in the Brinkman-Stokes formalism. By discretizing a graded-permeability shell into discrete, macroscopically homogeneous layers, we are able to sample the entire functional space of spherically-symmetric permeabilities and observe quick convergence to a certain manifold in the wake-drag coordinates. Monte Carlo samplings with 10^{4}-10^{5} points have become possible thanks to our new algorithm, which is based on exact analytical solutions for the Stokes flow through an arbitrary multilayer porous sphere. The algorithm is not restricted to the Brinkman-Stokes equation and can be modified to account for other types of scattering problems for spherically-symmetric systems with arbitrary radial complexity. Our main practical finding for Stokes flow is that it is possible to reduce a certain measure of wake of a spherical object without any energy penalty and without active (power-consuming) force generation. PMID:26764826
Wake control with permeable multilayer structures: The spherical symmetry case.
Bowen, Patrick T; Smith, David R; Urzhumov, Yaroslav A
2015-12-01
We explore the possibility of controlling the wake and drag of a spherical object independently of each other, using radial distributions of permeability in the Brinkman-Stokes formalism. By discretizing a graded-permeability shell into discrete, macroscopically homogeneous layers, we are able to sample the entire functional space of spherically-symmetric permeabilities and observe quick convergence to a certain manifold in the wake-drag coordinates. Monte Carlo samplings with 10^{4}-10^{5} points have become possible thanks to our new algorithm, which is based on exact analytical solutions for the Stokes flow through an arbitrary multilayer porous sphere. The algorithm is not restricted to the Brinkman-Stokes equation and can be modified to account for other types of scattering problems for spherically-symmetric systems with arbitrary radial complexity. Our main practical finding for Stokes flow is that it is possible to reduce a certain measure of wake of a spherical object without any energy penalty and without active (power-consuming) force generation.
Einstein Revisited - Gravity in Curved Spacetime Without Event Horizons
NASA Astrophysics Data System (ADS)
Leiter, Darryl
2000-04-01
In terms of covariant derivatives with respect to flat background spacetimes upon which the physical curved spacetime is imposed (1), covariant conservation of energy momentum requires, via the Bianchi Identity, that the Einstein tensor be equated to the matter energy momentum tensor. However the Einstein tensor covariantly splits (2) into two tensor parts: (a) a term proportional to the gravitational stress energy momentum tensor, and (b) an anti-symmetric tensor which obeys a covariant 4-divergence identity called the Freud Identity. Hence covariant conservation of energy momentum requires, via the Freud Identity, that the Freud tensor be equal to a constant times the matter energy momentum tensor. The resultant field equations (3) agree with the Einstein equations to first order, but differ in higher orders (4) such that black holes are replaced by "red holes" i.e., dense objects collapsed inside of their photon orbits with no event horizons. (1) Rosen, N., (1963), Ann. Phys. v22, 1; (2) Rund, H., (1991), Alg. Grps. & Geom. v8, 267; (3) Yilmaz, Hl, (1992), Nuo. Cim. v107B, 946; (4) Roberstson, S., (1999),Ap.J. v515, 365.
Classical dynamics on Snyder spacetime
NASA Astrophysics Data System (ADS)
Mignemi, S.
2015-04-01
We study the classical dynamics of a particle in Snyder spacetime, adopting the formalism of constrained Hamiltonian systems introduced by Dirac. We show that the motion of a particle in a scalar potential is deformed with respect to special relativity by terms of order βE2. A remarkable result is that in the relativistic Snyder model a consistent choice of the time variable must necessarily depend on the dynamics. This is a consequence of the nontrivial mixing between position and momentum coordinates intrinsic to the Snyder model.
Gravitational collapse of Vaidya spacetime
NASA Astrophysics Data System (ADS)
Vertogradov, Vitalii
2016-03-01
The gravitational collapse of generalized Vaidya spacetime is considered. It is known that the endstate of gravitational collapse, as to whether a black hole or a naked singularity is formed, depends on the mass function M(v,r). Here we give conditions for the mass function which corresponds to the equation of the state P = αρ where α ∈ (0, 1 3] and according to these conditions we obtain either a black hole or a naked singularity at the endstate of gravitational collapse. Also we give conditions for the mass function when the singularity is gravitationally strong.
Trumpet slices in Kerr spacetimes.
Dennison, Kenneth A; Baumgarte, Thomas W; Montero, Pedro J
2014-12-31
We introduce a new time-independent family of analytical coordinate systems for the Kerr spacetime representing rotating black holes. We also propose a (2+1)+1 formalism for the characterization of trumpet geometries. Applying this formalism to our new family of coordinate systems we identify, for the first time, analytical and stationary trumpet slices for general rotating black holes, even for charged black holes in the presence of a cosmological constant. We present results for metric functions in this slicing and analyze the geometry of the rotating trumpet surface.
Analyzing correlation functions with tesseral and Cartesian spherical harmonics
Danielewicz, Pawel; Pratt, Scott
2007-03-15
The dependence of interparticle correlations on the orientation of particle relative momentum can yield unique information on the space-time features of emission in reactions with multiparticle final states. In the present paper, the benefits of a representation and analysis of the three-dimensional correlation information in terms of surface spherical harmonics is presented. The harmonics include the standard complex tesseral harmonics and the real Cartesian harmonics. Mathematical properties of the lesser known Cartesian harmonics are illuminated. The physical content of different angular harmonic components in a correlation is described. The resolving power of different final-state effects with regard to determining angular features of emission regions is investigated. The considered final-state effects include identity interference, strong interactions, and Coulomb interactions. The correlation analysis in terms of spherical harmonics is illustrated with the cases of Gaussian and blast-wave sources for proton-charged meson and baryon-baryon pairs.
Symmetric Composite Laminate Stress Analysis
NASA Technical Reports Server (NTRS)
Wang, T.; Smolinski, K. F.; Gellin, S.
1985-01-01
It is demonstrated that COSMIC/NASTRAN may be used to analyze plate and shell structures made of symmetric composite laminates. Although general composite laminates cannot be analyzed using NASTRAN, the theoretical development presented herein indicates that the integrated constitutive laws of a symmetric composite laminate resemble those of a homogeneous anisotropic plate, which can be analyzed using NASTRAN. A detailed analysis procedure is presented, as well as an illustrative example.
Binary black hole spacetimes with a helical Killing vector
Klein, Christian
2004-12-15
Binary black hole spacetimes with a helical Killing vector, which are discussed as an approximation for the early stage of a binary system, are studied in a projection formalism. In this setting the four-dimensional Einstein equations are equivalent to a three-dimensional gravitational theory with a SL(2,R)/SO(1,1) sigma model as the material source. The sigma model is determined by a complex Ernst equation. 2+1 decompositions of the three-metric are used to establish the field equations on the orbit space of the Killing vector. The two Killing horizons of spherical topology which characterize the black holes, the cylinder of light where the Killing vector changes from timelike to spacelike, and infinity are singular points of the equations. The horizon and the light cylinder are shown to be regular singularities, i.e., the metric functions can be expanded in a formal power series in the vicinity. The behavior of the metric at spatial infinity is studied in terms of formal series solutions to the linearized Einstein equations. It is shown that the spacetime is not asymptotically flat in the strong sense to have a smooth null infinity under the assumption that the metric tends asymptotically to the Minkowski metric. In this case the metric functions have an oscillatory behavior in the radial coordinate in a nonaxisymmetric setting, the asymptotic multipoles are not defined. The asymptotic behavior of the Weyl tensor near infinity shows that there is no smooth null infinity.
Lanczos potential for some non-vacuum spacetimes
NASA Astrophysics Data System (ADS)
Hasmani, A. H.; Panchal, Ravi
2016-09-01
The Lanczos potential is a general relativity analogue of potential in electrodynamics. This potential can be obtained by solving Weyl-Lanczos relations. This computation is easy in the case of vacuum spacetimes and/or spacetimes of particular Petrov type, while obtaining the Lanczos potential for arbitrary spacetime is very difficult. In this paper, we have obtained the Lanczos potential for non-vacuum spacetimes: Vaidya spacetime and Van Stockum spacetime (which is not of any Petrov type).
NASA Technical Reports Server (NTRS)
Braverman, Amy; Nguyen, Hai; Olsen, Edward; Cressie, Noel
2011-01-01
Space-time Data Fusion (STDF) is a methodology for combing heterogeneous remote sensing data to optimally estimate the true values of a geophysical field of interest, and obtain uncertainties for those estimates. The input data sets may have different observing characteristics including different footprints, spatial resolutions and fields of view, orbit cycles, biases, and noise characteristics. Despite these differences all observed data can be linked to the underlying field, and therefore the each other, by a statistical model. Differences in footprints and other geometric characteristics are accounted for by parameterizing pixel-level remote sensing observations as spatial integrals of true field values lying within pixel boundaries, plus measurement error. Both spatial and temporal correlations in the true field and in the observations are estimated and incorporated through the use of a space-time random effects (STRE) model. Once the models parameters are estimated, we use it to derive expressions for optimal (minimum mean squared error and unbiased) estimates of the true field at any arbitrary location of interest, computed from the observations. Standard errors of these estimates are also produced, allowing confidence intervals to be constructed. The procedure is carried out on a fine spatial grid to approximate a continuous field. We demonstrate STDF by applying it to the problem of estimating CO2 concentration in the lower-atmosphere using data from the Atmospheric Infrared Sounder (AIRS) and the Japanese Greenhouse Gasses Observing Satellite (GOSAT) over one year for the continental US.
NASA Astrophysics Data System (ADS)
González-Díaz, Pedro F.
2000-08-01
In this paper the problem of the quantum stability of the two-dimensional warp drive spacetime moving with an apparent faster than light velocity is considered. We regard as a maximum extension beyond the event horizon of that spacetime its embedding in a three-dimensional Minkowskian space with the topology of the corresponding Misner space. It is obtained that the interior of the spaceship bubble becomes then a multiply connected nonchronal region with closed spacelike curves and that the most natural vacuum allows quantum fluctuations which do not induce any divergent behavior of the renormalized stress-energy tensor, even on the event (Cauchy) chronology horizon. In such a case, the horizon encloses closed timelike curves only at scales close to the Planck length, so that the warp drive satisfies Ford's negative energy-time inequality. Also found is a connection between the superluminal two-dimensional warp drive space and two-dimensional gravitational kinks. This connection allows us to generalize the considered Alcubierre metric to a standard, nonstatic metric which is only describable on two different coordinate patches.
Cosmic Censorship for Gowdy Spacetimes
NASA Astrophysics Data System (ADS)
Ringström, Hans
2010-04-01
Due to the complexity of Einstein's equations, it is often natural to study a question of interest in the framework of a restricted class of solutions. One way to impose a restriction is to consider solutions satisfying a given symmetry condition. There are many possible choices, but the present article is concerned with one particular choice, which we shall refer to as Gowdy symmetry. We begin by explaining the origin and meaning of this symmetry type, which has been used as a simplifying assumption in various contexts, some of which we shall mention. Nevertheless, the subject of interest here is strong cosmic censorship. Consequently, after having described what the Gowdy class of spacetimes is, we describe, as seen from the perspective of a mathematician, what is meant by strong cosmic censorship. The existing results on cosmic censorship are based on a detailed analysis of the asymptotic behavior of solutions. This analysis is in part motivated by conjectures, such as the BKL conjecture, which we shall therefore briefly describe. However, the emphasis of the article is on the mathematical analysis of the asymptotics, due to its central importance in the proof and in the hope that it might be of relevance more generally. The article ends with a description of the results that have been obtained concerning strong cosmic censorship in the class of Gowdy spacetimes.
NASA Astrophysics Data System (ADS)
Field, F.; Goodbun, J.; Watson, V.
Architects have a role to play in interplanetary space that has barely yet been explored. The architectural community is largely unaware of this new territory, for which there is still no agreed method of practice. There is moreover a general confusion, in scientific and related fields, over what architects might actually do there today. Current extra-planetary designs generally fail to explore the dynamic and relational nature of space-time, and often reduce human habitation to a purely functional problem. This is compounded by a crisis over the representation (drawing) of space-time. The present work returns to first principles of architecture in order to realign them with current socio-economic and technological trends surrounding the space industry. What emerges is simultaneously the basis for an ecological space architecture, and the representational strategies necessary to draw it. We explore this approach through a work of design-based research that describes the construction of Ocean; a huge body of water formed by the collision of two asteroids at the Translunar Lagrange Point (L2), that would serve as a site for colonisation, and as a resource to fuel future missions. Ocean is an experimental model for extra-planetary space design and its representation, within the autonomous discipline of architecture.
Fully Characterizing Axially Symmetric Szekeres Models with Three Data Sets
NASA Astrophysics Data System (ADS)
Célérier, Marie-Nöelle Mishra, Priti; Singh, Tejinder P.
2015-01-01
Inhomogeneous exact solutions of General Relativity with zero cosmological constant have been used in the literature to challenge the ΛCDM model. From one patch Lemaître-Tolman-Bondi (LTB) models to axially symmetric quasi-spherical Szekeres (QSS) Swiss-cheese models, some of them are able to reproduce to a good accuracy the cosmological data. It has been shown in the literature that a zero Λ LTB model with a central observer can be fully determined by two data sets. We demonstrate that an axially symmetric zero Λ QSS model with an observer located at the origin can be fully reconstructed from three data sets, number counts, luminosity distance and redshift drift. This is a first step towards a future demonstration involving five data sets and the most general Szekeres model.
Heating distribution comparison between asymmetric and symmetric blunt cones
NASA Technical Reports Server (NTRS)
Stewart, D. A.; Kolodziej, P.
1986-01-01
An experiment was performed to compare the heating distribution between symmetric and asymmetric large-angle blunt cones, with cone angles of 100, 120, and 140 deg. These hot-wall data were obtained from models made from typical thermal protection insulation for proposed aeroassisted orbital transfer vehicles. Experimental data are compared with predictions using a boundary-layer integral matrix procedure with kinetics to determine how well the heating distribution over an asymmetric cone could be approximated using axisymmetric solutions for a cone and spherical segment. In addition, a relationship between the stagnation-point heat-transfer rate and the bow-shock standoff distance for these cones is discussed. The heat-distribution data from the symmetric and asymmetric cones were very similar. Numerical results compared well with the measured wall temperatures at the stagnation point but slightly underpredicted them over the conical portion of the models.
Spatial curvature, spacetime curvature, and gravity
NASA Astrophysics Data System (ADS)
Price, Richard H.
2016-08-01
The belief that curved spacetime gravity cannot be simply and correctly presented results in such misleading presentations as elastic two-dimensional sheets deformed as they support heavy objects. This article attempts to show that the conceptual basis of curved spacetime gravity can be simply and correctly presented, and that the spatial curvature of a deformed elastic sheet is very different from the spacetime curvature underlying gravity. This article introduces the idea of a "splittable" spacetime that has spatial curvature, but is missing most of the manifestations of gravity. A section in which no mathematics is used is directed at students who have studied no more than introductory physics. A separate section, for students who have taken only an introductory course in general relativity, gives mathematical arguments centering on splittable spacetimes.
Cosmological power spectrum in a noncommutative spacetime
NASA Astrophysics Data System (ADS)
Kothari, Rahul; Rath, Pranati K.; Jain, Pankaj
2016-09-01
We propose a generalized star product that deviates from the standard one when the fields are considered at different spacetime points by introducing a form factor in the standard star product. We also introduce a recursive definition by which we calculate the explicit form of the generalized star product at any number of spacetime points. We show that our generalized star product is associative and cyclic at linear order. As a special case, we demonstrate that our recursive approach can be used to prove the associativity of standard star products for same or different spacetime points. The introduction of a form factor has no effect on the standard Lagrangian density in a noncommutative spacetime because it reduces to the standard star product when spacetime points become the same. We show that the generalized star product leads to physically consistent results and can fit the observed data on hemispherical anisotropy in the cosmic microwave background radiation.
NASA Astrophysics Data System (ADS)
Georgiev, G. H.; Dinkova, C. L.
2013-10-01
Long spirals in the Euclidean plane have been introduced by A. Kurnosenko five years ago. Using a natural map of the shape sphere into the extended Gaussian plane we study spherical curves that are pre-images of plane long spirals. Loxodromes and spherical spiral antennas are typical examples of such spherical long spirals. The set of all planar spirals leaves invariant under an arbitrary similarity transformation. This set is divided in two disjoint classes by A. Kirnosenko. The first class is consist of the so-called short spirals which are widely used in geometric modeling. The second class of planar long spirals contains well-known logarithmic spiral and Archimedean spirals which have many applications in mathematics, astrophysics and industry. The notion of simplicial shape space is due to D. Kendall. The most popular simplicial shape space of order (2,3) is the set of equivalence classes of similar triangles in the plane. The sphere of radius 1/2 centered at the origin can be considered as a model of this quotient space, so-called the shape sphere. F. Bookstein and J. Lester showed that the one-point extension of the Euclidean plane, so-called the extended Gaussian plane, is another model of the same simplicial shape space. The present paper gives a description of long spirals on the shape sphere by the use a natural conformal mapping between two models. First, we examine long spirals in the extended Gaussian plane. After that, we describe some differential geometric properties of the shape sphere. Finally, we discuss parameterizations of long spirals on the shape sphere.
Compressible inviscid instability of rapidly expanding spherical material interfaces
NASA Astrophysics Data System (ADS)
Mankbadi, Mina R.; Balachandar, S.
2012-03-01
A high-order weighted essentially non-oscillatory scheme is employed to investigate the stability of a rapidly expanding material interface produced by a spherical shock tube. The flow structure is characterized by a forward moving primary shock, a backward moving secondary shock, and a spherical contact interface in-between. We consider herein the linear inviscid regime and focus on the development of the three-dimensional perturbations around the contact interface by solving a one-dimensional system of partial differential equations. Numerical simulations are performed to illustrate the effects of the contact interface's density discontinuity on the growth of the disturbances for various spherical wave numbers. In a spherical shock tube the instability is influenced by various mechanisms which include classical Rayleigh-Taylor (RT) effects, Bell-Plesset or geometry/curvature effects, the effects of impulsively accelerating the interface, and compressibility effects. Henceforth, the present instability will be referred to as non-classical RT instability to distinguish it from classical RT instability. For an extended intermediate time period, it can be shown that the small disturbances grow exponentially as in the classical RT instability. During this stage, the exponential growth rate increases with the spherical wave number, until it saturates for very large wave numbers due to the finite thickness limitation of the numerical representation of the contact interface. The results compare favorably with previous theoretical models; but indicate that in addition to compressibility, the space-time evolution of the contact interface's thickness plays a significant role. A parametric study is performed that varies the pressure and density ratios of the initial spherical container. The characteristics of the contact interface and the applicability of various instability theories is investigated for these regimes. Furthermore, varying the pressure and density ratios aids
Spacetime Metrology with LISA Pathfinder
NASA Astrophysics Data System (ADS)
Congedo, Giuseppe
2012-04-01
LISA is the proposed ESA-NASA gravitational wave detector in the 0.1 mHz - 0.1 Hz band. LISA Pathfinder is the down-scaled version of a single LISA arm. The arm - named Doppler link - can be treated as a differential accelerometer, measuring the relative acceleration between test masses. LISA Pathfinder - the in-flight test of the LISA instrumentation - is currently in the final implementation and planned to be launched in 2014. It will set stringent constraints on the ability to put test masses in geodesic motion to within the required differential acceleration of 3times10^{-14} m s^{-2} Hz^{-1/2} and track their relative motion to within the required differential displacement measurement noise of 9times10^{-12} m Hz^{-1/2}, around 1 mHz. Given the scientific objectives, it will carry out - for the first time with such high accuracy required for gravitational wave detection - the science of spacetime metrology, in which the Doppler link between two free-falling test masses measures the curvature. This thesis contains a novel approach to the calculation of the Doppler response to gravitational waves. It shows that the parallel transport of 4-vectors records the history of gravitational wave signals. In practice, the Doppler link is implemented with 4 bodies in LISA and 3 bodies in LISA Pathfinder. To compensate for noise sources a control logic is implemented during the measurement. The closed-loop dynamics of LISA Pathfinder can be condensed into operators acting on the motion coordinates, handling the couplings, as well as the cross-talks. The scope of system identification is the optimal calibration of the instrument. This thesis describes some data analysis procedures applied to synthetic experiments and shows the relevance of system identification for the success of LISA Pathfinder in demonstrating the principles of spacetime metrology for all future space-based missions.
Rocha, Roldao da; Rodrigues, Waldyr A. Jr.
2010-12-22
In a previous paper we investigate a Lagrangian field theory for the gravitational field, which is there represented by a section {l_brace}g{sup {alpha}}{r_brace} of the coframe bundle over Minkowski spacetime (M{approx_equal}R{sup 4},g ring, D ring,{tau}{sub g{sup ring}},{up_arrow}). Such theory, under appropriate conditions, has been proved to be equivalent to a Lorentzian spacetime structure (M{approx_equal}R{sup 4},g,D,{tau}{sub g},{up_arrow}) where the metric tensor g satisfies the Einstein field equation. Here, we first recall that according to quantum field theory ideas gravitation is described by a Lagrangian theory of a possible massive graviton field (generated by matter fields and coupling also to itself) living in Minkowski spacetime. The massive graviton field is moreover supposed to be represented by a symmetric tensor field h carrying the representations of spin two and zero of the Lorentz group. Such a field, then (as it is well known) must necessarily satisfy the gauge condition given by Eq.(10) below. Next, we introduce an ansatz relating h with the 1-form fields {l_brace}g{sup {alpha}}{r_brace}. Then, using the Clifford bundle formalism we derive from our Lagrangian theory the exact wave equation for the graviton and investigate the role of the gauge condition given by Eq.(10) by asking the question: does Eq.(10) fix any gauge condition for the field g of the effective Lorentzian spacetime structure (M{approx_equal}R{sup 4},g,D,{tau}{sub g},{up_arrow}) that represents the field h in our theory? We show that no gauge condition is fixed a priory, as it is the case in General Relativity. Moreover we prove that if we use Logunov gauge condition, i.e., D ring{sub {gamma}}({radical}-detgg{sup {gamma}{kappa}} = 0) then only a restricted class of coordinate systems (including harmonic ones) are allowed by the theory.
Quasi-Schwarzchild R/sup 4/ as a spherical wave embedding in flat M/sup 4/ x D/sup 2/ x D/sup 2/
Rosen, G.
1986-11-01
It is shown that an R/sup 4/ which closely approximates exterior Schwarzschild space-time for a gravitating mass at rest can be viewed as a four-dimensional subspace of the eight-dimensional flat manifold M/sup 4/ x D/sup 2/ x D/sup 2/, where M/sup 4/ is Minkowski space-time and each D/sup 2/ is the Euclidean space interior to a circle of small radius. This representation for quasi-Schwarzschild space-time exterior to the Schwarzschild singularity involves spherical-wave embedding constraints on the D/sup 2/ x D/sup 2/ Kaehlerian coordinates.
Self-organization of laterally asymmetrical movements as a consequence of space-time optimization.
Mangalam, Madhur; Desai, Nisarg; Singh, Mewa
2016-02-01
Laterally asymmetrical movements are ubiquitous among organisms. A bilaterally symmetrical organism cannot maneuver through a two- or three-dimensional space unless and until one side of its body leads, because the forces that cause the movements of the body are generated within the body. One question follows: are there any costs or benefits of laterally asymmetrical movements? We test whether directionally consistent laterally asymmetrical movements at different levels of organization of movements (at the individual, and not the population level) can work synergistically. We show-by means of a hypothetical system resembling a humanoid robot-that a laterally asymmetrical movement at a lower level of organization of movements can stimulate laterally asymmetrical movements that are directionally consistent at consecutive higher levels. We show-by comparing two hypothetical systems, incorporating laterally symmetrical and asymmetrical movements, respectively-that the asymmetrical system outperforms the symmetrical system by optimizing space and time and that this space-time advantage increases with the increasing complexity of the task. Together, these results suggest that laterally asymmetrical movements can self-organize as a consequence of space-time optimization.
Geodesic motion in equal angular momenta Myers-Perry-AdS spacetimes
NASA Astrophysics Data System (ADS)
Delsate, Térence; Rocha, Jorge V.; Santarelli, Raphael
2015-10-01
We study the geodesic motion of massive and massless test particles in the background of equally spinning Myers-Perry-anti-de Sitter (AdS) black holes in five dimensions. By adopting a coordinate system that makes manifest the cohomogeneity-1 property of these spacetimes, the equations of motion simplify considerably. This allows us to easily separate the radial motion from the angular part and to obtain solutions for angular trajectories in a compact closed form. For the radial motion, we focus our attention on spherical orbits. In particular, we determine the timelike innermost stable circular orbits (ISCOs) for these asymptotically AdS spacetimes, as well as the location of null circular orbits. We find that the ISCO dives below the ergosurface for black holes rotating close to extremality and merges with the event horizon exactly at extremality, in analogy with the four-dimensional Kerr case. For sufficiently massive black holes in AdS, there exists a spin parameter range in which the background spacetime is stable against super-radiance and the ISCO lies inside the ergoregion. Our results for massless geodesics show that there are no stable circular null orbits outside the horizon, but there exist such orbits inside the horizon, as well as around overextremal spacetimes, i.e., naked singularities. We also discuss how these orbits deform from the static to the rotating case.
Equivalence of the Path Integral for Fermions in Cartesian and Spherical Coordinates
NASA Astrophysics Data System (ADS)
Briggs, Andrew; Camblong, Horacio E.; Ordóñez, Carlos R.
2013-06-01
The path integral calculation for the free energy of a spin-1/2 Dirac-fermion gas is performed in spherical polar coordinates for a flat space-time geometry. Its equivalence with the Cartesian-coordinate representation is explicitly established. This evaluation involves a relevant limiting case of the fermionic path integral in a Schwarzschild background, whose near-horizon limit has been shown to be related to black hole thermodynamics.
Decay of Dirac massive hair in the background of a spherical black hole
Moderski, Rafal; Rogatko, Marek
2008-06-15
The intermediate and late-time behavior of massive Dirac hair in the static spherically general black hole spacetime is studied. It is revealed that the intermediate asymptotic pattern of decay of massive Dirac spinor hair is dependent on the mass of the field under consideration as well as the multiple number of the wave mode. The long-lived oscillatory tail observed at timelike infinity in the considered background decays slowly as t{sup -5/6}.
Interpolation via symmetric exponential functions
NASA Astrophysics Data System (ADS)
Bezubik, Agata; Pošta, Severin
2013-11-01
Complex valued functions on the Euclidean space Bbb Rn, symmetric or antisymmetric with respect to the permutation group Sn, are often dealt with in various branches of physics, such as quantum theory or theory of integrable systems. One often needs to approximate such functions with series consisting of various special functions which satisfy nice properties. Questions of uniform convergence of such approximations are crucial for applications. In this article a family of special functions called the symmetric exponential functions are used for such approximation and the uniform convergence of their sums is considered.
Local spacetime effects on gyroscope systems
NASA Astrophysics Data System (ADS)
Wohlfarth, Mattias N. R.; Pfeifer, Christian
2013-01-01
We give a precise theoretical description of initially aligned sets of orthogonal gyroscopes which are transported along different paths from some initial point to the same final point in spacetime. These gyroscope systems can be used to synchronize separated observers’ spatial frames by free fall along timelike geodesics. We find that initially aligned gyroscope systems, or spatial frames, lose their synchronization due to the curvature of spacetime and their relative motion. On the basis of our results we propose a simple experiment that enables observers to determine locally whether their spacetime is described by a rotating Kerr or a nonrotating Schwarzschild metric.
Lorenz gauge quantization in conformally flat spacetimes
NASA Astrophysics Data System (ADS)
Cresswell, Jesse C.; Vollick, Dan N.
2015-04-01
Recently it was shown that Dirac's method of quantizing constrained dynamical systems can be used to impose the Lorenz gauge condition in a four-dimensional cosmological spacetime. In this paper we use Dirac's method to impose the Lorenz gauge condition in a general four-dimensional conformally flat spacetime and find that there is no particle production. We show that in cosmological spacetimes with dimension D ≠4 there will be particle production when the scale factor changes, and we calculate the particle production due to a sudden change.
The Dirac point electron in zero-gravity Kerr–Newman spacetime
Kiessling, M. K.-H.; Tahvildar-Zadeh, A. S.
2015-04-15
Dirac’s wave equation for a point electron in the topologically nontrivial maximal analytically extended electromagnetic Kerr–Newman spacetime is studied in a limit G → 0, where G is Newton’s constant of universal gravitation. The following results are obtained: the formal Dirac Hamiltonian on the static spacelike slices is essentially self-adjoint and the spectrum of the self-adjoint extension is symmetric about zero, featuring a continuum with a gap about zero that, under two smallness conditions, contains a point spectrum. The symmetry result extends to the Dirac operator on a generalization of the zero-G Kerr–Newman spacetime with different electric-monopole/magnetic-dipole-moment ratios.
Spherical grating spectrometers
NASA Astrophysics Data System (ADS)
O'Donoghue, Darragh; Clemens, J. Christopher
2014-07-01
We describe designs for spectrometers employing convex dispersers. The Offner spectrometer was the first such instrument; it has almost exclusively been employed on satellite platforms, and has had little impact on ground-based instruments. We have learned how to fabricate curved Volume Phase Holographic (VPH) gratings and, in contrast to the planar gratings of traditional spectrometers, describe how such devices can be used in optical/infrared spectrometers designed specifically for curved diffraction gratings. Volume Phase Holographic gratings are highly efficient compared to conventional surface relief gratings; they have become the disperser of choice in optical / NIR spectrometers. The advantage of spectrometers with curved VPH dispersers is the very small number of optical elements used (the simplest comprising a grating and a spherical mirror), as well as illumination of mirrors off axis, resulting in greater efficiency and reduction in size. We describe a "Half Offner" spectrometer, an even simpler version of the Offner spectrometer. We present an entirely novel design, the Spherical Transmission Grating Spectrometer (STGS), and discuss exemplary applications, including a design for a double-beam spectrometer without any requirement for a dichroic. This paradigm change in spectrometer design offers an alternative to all-refractive astronomical spectrometer designs, using expensive, fragile lens elements fabricated from CaF2 or even more exotic materials. The unobscured mirror layout avoids a major drawback of the previous generation of catadioptric spectrometer designs. We describe laboratory measurements of the efficiency and image quality of a curved VPH grating in a STGS design, demonstrating, simultaneously, efficiency comparable to planar VPH gratings along with good image quality. The stage is now set for construction of a prototype instrument with impressive performance.
NASA Astrophysics Data System (ADS)
Beyer, F.; Escobar, L.; Frauendiener, J.
2016-02-01
In this paper we consider the single patch pseudospectral scheme for tensorial and spinorial evolution problems on the 2-sphere presented by Beyer et al. [Classical Quantum Gravity 32, 175013 (2015); Classical Quantum Gravity31, 075019 (2014)], which is based on the spin-weighted spherical harmonics transform. We apply and extend this method to Einstein's equations and certain classes of spherical cosmological spacetimes. More specifically, we use the hyperbolic reductions of Einstein's equations obtained in the generalized wave map gauge formalism combined with Geroch's symmetry reduction, and focus on cosmological spacetimes with spatial S3 -topologies and symmetry groups U(1) or U (1 )×U (1 ) . We discuss analytical and numerical issues related to our implementation. We test our code by reproducing the exact inhomogeneous cosmological solutions of the vacuum Einstein field equations obtained by Beyer and Hennig [Classical Quantum Gravity 31, 095010 (2014)].
Prior Distributions on Symmetric Groups
ERIC Educational Resources Information Center
Gupta, Jayanti; Damien, Paul
2005-01-01
Fully and partially ranked data arise in a variety of contexts. From a Bayesian perspective, attention has focused on distance-based models; in particular, the Mallows model and extensions thereof. In this paper, a class of prior distributions, the "Binary Tree," is developed on the symmetric group. The attractive features of the class are: it…
The bizarre anti-de Sitter spacetime
NASA Astrophysics Data System (ADS)
Sokołowski, Leszek M.
2016-08-01
Anti-de Sitter spacetime is important in general relativity and modern field theory. We review its geometrical features and properties of light signals and free particles moving in it. By applying only the elementary tools of tensor calculus, we derive ab initio of all these properties and show that they are really weird. One finds superluminal velocities of light and particles, infinite particle energy necessary to escape at infinite distance and spacetime regions inaccessible by a free fall, though reachable by an accelerated spaceship. Radial timelike geodesics are identical to the circular ones and actually all timelike geodesics are identical to one circle in a fictitious five-dimensional space. Employing the latter space, one is able to explain these bizarre features of anti-de Sitter spacetime; in this sense the spacetime is not self-contained. This is not a physical world.
Space-time singularities in Weyl manifolds
NASA Astrophysics Data System (ADS)
Lobo, I. P.; Barreto, A. B.; Romero, C.
2015-09-01
We extend one of the Hawking-Penrose singularity theorems in general relativity to the case of some scalar-tensor gravity theories in which the scalar field has a geometrical character and space-time has the mathematical structure of a Weyl integrable space-time. We adopt an invariant formalism, so that the extended version of the theorem does not depend on a particular frame.
Space--Time from Topos Quantum Theory
NASA Astrophysics Data System (ADS)
Flori, Cecilia
One of the main challenges in theoretical physics in the past 50 years has been to define a theory of quantum gravity, i.e. a theory which consistently combines general relativity and quantum theory in order to define a theory of space-time itself seen as a fluctuating field. As such, a definition of space-time is of paramount importance, but it is precisely the attainment of such a definition which is one of the main stumbling blocks in quantum gravity. One of the striking features of quantum gravity is that although both general relativity and quantum theory treat space-time as a four-dimensional (4D) manifold equipped with a metric, quantum gravity would suggest that, at the microscopic scale, space-time is somewhat discrete. Therefore the continuum structure of space-time suggested by the two main ingredients of quantum gravity seems to be thrown into discussion by quantum gravity itself. This seems quite an odd predicament, but it might suggest that perhaps a different mathematical structure other than a smooth manifold should model space-time. These considerations seem to shed doubts on the use of the continuum in general in a possible theory of quantum gravity. An alternative would be to develop a mathematical formalism for quantum gravity in which no fundamental role is played by the continuum and where a new concept of space-time, not modeled on a differentiable manifold, will emerge. This is precisely one of the aims of the topos theory approach to quantum theory and quantum gravity put forward by Isham, Butterfield, and Doering and subsequently developed by other authors. The aim of this article is to precisely elucidate how such an approach gives rise to a new definition of space-time which might be more appropriate for quantum gravity.
Casimir effect in spacetimes with cosmological constant
NASA Astrophysics Data System (ADS)
Bessa, C. H. G.; Bezerra, V. B.; Silva, J. C. J.
2016-06-01
In this work, we study the influence of the gravitational field induced by the presence of a cosmological constant Λ on the Casimir energy density. We consider two metrics with the presence of the Λ-term, namely de Sitter and Schwarzschild-de Sitter (SdS). In the former case, we consider a conformal de Sitter spacetime and in the last one, a weak gravitational SdS spacetime.
Double slotted socket spherical joint
Bieg, Lothar F.; Benavides, Gilbert L.
2001-05-22
A new class of spherical joints is disclosed. These spherical joints are capable of extremely large angular displacements (full cone angles in excess of 270.degree.), while exhibiting no singularities or dead spots in their range of motion. These joints can improve or simplify a wide range of mechanical devices.
Spherical Torus Center Stack Design
C. Neumeyer; P. Heitzenroeder; C. Kessel; M. Ono; M. Peng; J. Schmidt; R. Woolley; I. Zatz
2002-01-18
The low aspect ratio spherical torus (ST) configuration requires that the center stack design be optimized within a limited available space, using materials within their established allowables. This paper presents center stack design methods developed by the National Spherical Torus Experiment (NSTX) Project Team during the initial design of NSTX, and more recently for studies of a possible next-step ST (NSST) device.
Features of spherical torus plasmas
Peng, Y.K.M.; Strickler, D.J.
1985-12-01
The spherical torus is a very small aspect ratio (A < 2) confinement concept obtained by retaining only the indispensable components inboard to the plasma torus. MHD equilibrium calculations show that spherical torus plasmas with safety factor q > 2 are characterized by high toroidal beta (..beta../sub t/ > 0.2), low poloidal beta (..beta../sub p/ < 0.3), naturally large elongation (kappa greater than or equal to 2), large plasma current with I/sub p//(aB/sub t0/) up to about 7 MA/mT, strong paramagnetism (B/sub t//B/sub t0/ > 1.5), and strong plasma helicity (F comparable to THETA). A large near-omnigeneous region is seen at the large-major-radius, bad-curvature region of the plasma in comparison with the conventional tokamaks. These features combine to engender the spherical torus plasma in a unique physics regime which permits compact fusion at low field and modest cost. Because of its strong paramagnetism and helicity, the spherical torus plasma shares some of the desirable features of spheromak and reversed-field pinch (RFP) plasmas, but with tokamak-like confinement and safety factor q. The general class of spherical tori, which includes the spherical tokamak (q > 1), the spherical pinch (1 > q > O), and the spherical RFP (q < O), have magnetic field configurations unique in comparison with conventional tokamaks and RFPs. 22 refs., 12 figs.
Self-action of a point charge in a wormhole space-time
Khusnutdinov, Nail R.; Bakhmatov, Ilya V.
2007-12-15
We consider the self-energy and the self-force for an electrically charged particle at rest in the wormhole space-time. We develop a general approach to finding the self-force and apply it to the two specific profiles of the wormhole throat with singular and with smooth curvature. The self-force for these two profiles is found in manifest form; it turns out to be an attractive force. We also find an expression for the self-force in the case of arbitrary symmetric throat profile. Far from the throat the self-force is always attractive.
Information content of nonautonomous free fields in curved space-time
Parreira, J. E.; Nemes, M. C.; Fonseca-Romero, K. M.
2011-03-15
We show that it is possible to quantify the information content of a nonautonomous free field state in curved space-time. A covariance matrix is defined and it is shown that, for symmetric Gaussian field states, the matrix is connected to the entropy of the state. This connection is maintained throughout a quadratic nonautonomous (including possible phase transitions) evolution. Although particle-antiparticle correlations are dynamically generated, the evolution is isoentropic. If the current standard cosmological model for the inflationary period is correct, in absence of decoherence such correlations will be preserved, and could potentially lead to observable effects, allowing for a test of the model.
NASA Astrophysics Data System (ADS)
Shen, Yanxia; Ji, Zhicheng; Su, Zhouping
2013-01-01
A numerical optimization method (genetic algorithm) is employed to design the spherical light-emitting diode (LED) array for highly uniform illumination distribution. An evaluation function related to the nonuniformity is constructed for the numerical optimization. With the minimum of evaluation function, the LED array produces the best uniformity. The genetic algorithm is used to seek the minimum of evaluation function. By this method, we design two LED arrays. In one case, LEDs are positioned symmetrically on the sphere and the illuminated target surface is a plane. However, in the other case, LEDs are positioned nonsymmetrically with a spherical target surface. Both the symmetrical and nonsymmetrical spherical LED arrays generate good uniform illumination distribution with calculated nonuniformities of 6 and 8%, respectively.
NASA Astrophysics Data System (ADS)
Laubenstein, John; Cockream, Kandi
2009-05-01
3D spacetime was developed by the IWPD Scale Metrics (SM) team using a coordinate system that translates n dimensions to n-1. 4-vectors are expressed in 3D along with a scaling factor representing time. Time is not orthogonal to the three spatial dimensions, but rather in alignment with an object's axis-of-motion. We have defined this effect as the object's ``orientation'' (X). The SM orientation (X) is equivalent to the orientation of the 4-velocity vector positioned tangent to its worldline, where X-1=θ+1 and θ is the angle of the 4-vector relative to the axis-of -motion. Both 4-vectors and SM appear to represent valid conceptualizations of the relationship between space and time. Why entertain SM? Scale Metrics gravity is quantized and may suggest a path for the full unification of gravitation with quantum theory. SM has been tested against current observation and is in agreement with the age of the universe, suggests a physical relationship between dark energy and dark matter, is in agreement with the accelerating expansion rate of the universe, contributes to the understanding of the fine-structure constant and provides a physical explanation of relativistic effects.
Bondi-type accretion in the Reissner-Nordström-(anti-)de Sitter spacetime
NASA Astrophysics Data System (ADS)
Ficek, F.
2015-12-01
In this paper I study the stationary, spherically symmetric accretion of fluids onto a charged black hole in the presence of a cosmological constant. For some isothermal equations of state it is possible to obtain analytic solutions. For the case of a radiation fluid I derive the relation between the locations of horizons and sonic (critical) points. In specific cases the solutions form closed, binocular-like trajectories in a phase diagram of the velocity versus radius.
Immunomodulatory spherical nucleic acids.
Radovic-Moreno, Aleksandar F; Chernyak, Natalia; Mader, Christopher C; Nallagatla, Subbarao; Kang, Richard S; Hao, Liangliang; Walker, David A; Halo, Tiffany L; Merkel, Timothy J; Rische, Clayton H; Anantatmula, Sagar; Burkhart, Merideth; Mirkin, Chad A; Gryaznov, Sergei M
2015-03-31
Immunomodulatory nucleic acids have extraordinary promise for treating disease, yet clinical progress has been limited by a lack of tools to safely increase activity in patients. Immunomodulatory nucleic acids act by agonizing or antagonizing endosomal toll-like receptors (TLR3, TLR7/8, and TLR9), proteins involved in innate immune signaling. Immunomodulatory spherical nucleic acids (SNAs) that stimulate (immunostimulatory, IS-SNA) or regulate (immunoregulatory, IR-SNA) immunity by engaging TLRs have been designed, synthesized, and characterized. Compared with free oligonucleotides, IS-SNAs exhibit up to 80-fold increases in potency, 700-fold higher antibody titers, 400-fold higher cellular responses to a model antigen, and improved treatment of mice with lymphomas. IR-SNAs exhibit up to eightfold increases in potency and 30% greater reduction in fibrosis score in mice with nonalcoholic steatohepatitis (NASH). Given the clinical potential of SNAs due to their potency, defined chemical nature, and good tolerability, SNAs are attractive new modalities for developing immunotherapies.
Buckling of spherical capsules.
Knoche, Sebastian; Kierfeld, Jan
2011-10-01
We investigate buckling of soft elastic capsules under negative pressure or for reduced capsule volume. Based on nonlinear shell theory and the assumption of a hyperelastic capsule membrane, shape equations for axisymmetric and initially spherical capsules are derived and solved numerically. A rich bifurcation behavior is found, which is presented in terms of bifurcation diagrams. The energetically preferred stable configuration is deduced from a least-energy principle both for prescribed volume and prescribed pressure. We find that buckled shapes are energetically favorable already at smaller negative pressures and larger critical volumes than predicted by the classical buckling instability. By preventing self-intersection for strongly reduced volume, we obtain a complete picture of the buckling process and can follow the shape from the initial undeformed state through the buckling instability into the fully collapsed state. Interestingly, the sequences of bifurcations and stable capsule shapes differ for prescribed volume and prescribed pressure. In the buckled state, we find a relation between curvatures at the indentation rim and the bending modulus, which can be used to determine elastic moduli from experimental shape analysis. PMID:22181297
Immunomodulatory spherical nucleic acids
Radovic-Moreno, Aleksandar F.; Chernyak, Natalia; Mader, Christopher C.; Nallagatla, Subbarao; Kang, Richard S.; Hao, Liangliang; Walker, David A.; Halo, Tiffany L.; Merkel, Timothy J.; Rische, Clayton H.; Anantatmula, Sagar; Burkhart, Merideth; Mirkin, Chad A.; Gryaznov, Sergei M.
2015-01-01
Immunomodulatory nucleic acids have extraordinary promise for treating disease, yet clinical progress has been limited by a lack of tools to safely increase activity in patients. Immunomodulatory nucleic acids act by agonizing or antagonizing endosomal toll-like receptors (TLR3, TLR7/8, and TLR9), proteins involved in innate immune signaling. Immunomodulatory spherical nucleic acids (SNAs) that stimulate (immunostimulatory, IS-SNA) or regulate (immunoregulatory, IR-SNA) immunity by engaging TLRs have been designed, synthesized, and characterized. Compared with free oligonucleotides, IS-SNAs exhibit up to 80-fold increases in potency, 700-fold higher antibody titers, 400-fold higher cellular responses to a model antigen, and improved treatment of mice with lymphomas. IR-SNAs exhibit up to eightfold increases in potency and 30% greater reduction in fibrosis score in mice with nonalcoholic steatohepatitis (NASH). Given the clinical potential of SNAs due to their potency, defined chemical nature, and good tolerability, SNAs are attractive new modalities for developing immunotherapies. PMID:25775582
An, Yu; Lu, Tao; Yang, Bing
2005-02-01
The perturbation of nonspherical symmetrical acoustic pressure is added to the equation governing the spherical stability of sonoluminescing bubbles. The numerical calculations of the shape instability of sonoluminescing bubbles with the modified equation are conducted and the results are illustrated accordingly in the p(a) - R0 phase diagrams. The calculated results indicate that the stability region vanishes as the amplitude of the driving acoustic pressure p(a) arrives at the upper threshold ( approximately 1.6 atm) due to the perturbation of a small nonspherical symmetrical acoustic pressure (about a few Pa), which is in consistence with the experimental observations.
Dynamics of intense particle beam in axial-symmetric magnetic field
NASA Astrophysics Data System (ADS)
Batygin, Yuri K.
2015-02-01
Axial-symmetric magnetic field is often used in focusing of particle beams. Most existing ion Low Energy Beam Transport lines are based on solenoid focusing. Modern accelerator projects utilize superconducting solenoids in combination with superconducting accelerating cavities for acceleration of high-intensity particle beams. Present article discusses conditions for matched beam in axial-symmetric magnetic field. Analysis allows us to minimize power consumption of solenoids and beam emittance growth due to nonlinear space charge, lens aberrations, and maximize acceptance of the channel. Expressions for maximum beam current in focusing structure, beam emittance growth due to spherical aberrations and non-linear space charge forces are derived.
FAST TRACK COMMUNICATION: Late-time tails in the Kerr spacetime
NASA Astrophysics Data System (ADS)
Gleiser, Reinaldo J.; Price, Richard H.; Pullin, Jorge
2008-04-01
Outside a black hole, perturbation fields die off in time as 1/tn. For spherical holes n = 2ell + 3 where ell is the multipole index. In the nonspherical Kerr spacetime there is no coordinate-independent meaning of 'multipole', and a common sense viewpoint is to set ell to the lowest radiatiable index, although theoretical studies have led to very different claims. Numerical results, to date, have been controversial. Here we show that expansion for small Kerr spin parameter a leads to very definite numerical results confirming previous theoretical predictions.
Motion of the charged test particles in Kerr-Newman-Taub-NUT spacetime and analytical solutions
NASA Astrophysics Data System (ADS)
Cebeci, Hakan; Özdemir, Nülifer; Şentorun, Seçil
2016-05-01
In this work, we study the motion of charged test particles in Kerr-Newman-Taub-NUT spacetime. We analyze the angular and the radial parts of the orbit equations and examine the possible orbit types. We also investigate the spherical orbits and their stabilities. Furthermore, we obtain the analytical solutions of the equations of motion and express them in terms of Jacobian and Weierstrass elliptic functions. Finally, we discuss the observables of the bound motion and calculate the perihelion shift and Lense-Thirring effect for the bound orbits.
Kinematic relative velocity with respect to stationary observers in Schwarzschild spacetime
NASA Astrophysics Data System (ADS)
Bolós, Vicente J.
2013-04-01
We study the kinematic relative velocity of general test particles with respect to stationary observers (using spherical coordinates) in Schwarzschild spacetime, obtaining that its modulus does not depend on the observer, unlike Fermi, spectroscopic, and astrometric relative velocities. We study some fundamental particular cases, generalizing some results given in other work about stationary and radial free-falling test particles. Moreover, we give a new result about test particles with circular geodesic orbits: the modulus of their kinematic relative velocity with respect to any stationary observer depends only on the radius of the circular orbit, and so it remains constant.
Hund's First and Second Rules in Spherical Artificial Atoms
NASA Astrophysics Data System (ADS)
Asari, Yusuke; Tamura, Hiroyuki; Takeda, Kyozaburo
2002-03-01
Hund's first and second rules are investigated in a semiconductor GaAs spherical artificial atom (quantum dot). We extend an unrestricted Hartree-Fock (exUHF) method by restricting the total orbital angular momentum and obtain the eigenstates having correct angular momenta for the targeting quantum dot. The exUHF calculation reveals that the ground state in the spherically symmetrical quantum dot has the largest total orbital angular momentum obeying Hund's second rule. When external magnetic fields are applied, we find that the circular symmetry of the quantum dot can produce a new shell structure where four levels are degenerate in the fifth shell. The noticeable point is that spin filling up to the fifth shell can be well understood by the generalized Hund's first rule.
A robust method for rotation estimation using spherical harmonics representation.
Althloothi, Salah; Mahoor, Mohammad H; Voyles, Richard M
2013-06-01
This paper presents a robust method for 3D object rotation estimation using spherical harmonics representation and the unit quaternion vector. The proposed method provides a closed-form solution for rotation estimation without recurrence relations or searching for point correspondences between two objects. The rotation estimation problem is casted as a minimization problem, which finds the optimum rotation angles between two objects of interest in the frequency domain. The optimum rotation angles are obtained by calculating the unit quaternion vector from a symmetric matrix, which is constructed from the two sets of spherical harmonics coefficients using eigendecomposition technique. Our experimental results on hundreds of 3D objects show that our proposed method is very accurate in rotation estimation, robust to noisy data, missing surface points, and can handle intra-class variability between 3D objects. PMID:23475364
Near spherical illumination of ion-beam and laser targets
Mark, J.W.K.
1985-12-12
A procedure is developed for reducing energy-deposition asymmetry in spherical targets driven directly by ion or laser beams. This work is part of a strategy for achieving illumination symmetry in such targets, which is proposed as an alternative to those in the literature. This strategy allows an axially symmetric placement of beamlets, which would be convenient for some driven or reactor scenarios. It also allows the use of beam currents or energy fluxes and beam transverse profiles to help reduce deposition asymmetry with fewer beamlets. In the ideal limit of thin deposition layers and controlled beam profiles, at most six beamlets are needed for target symmetry.
Shearing expansion-free spherical anisotropic fluid evolution
Herrera, L.; Santos, N. O.; Wang Anzhong
2008-10-15
Spherically symmetric expansion-free distributions are systematically studied. The entire set of field equations and junction conditions are presented for a general distribution of dissipative anisotropic fluid (principal stresses unequal), and the expansion-free condition is integrated. In order to understand the physical meaning of expansion-free motion, two different definitions for the radial velocity of a fluid element are discussed. It is shown that the appearance of a cavity is inevitable in the expansion-free evolution. The nondissipative case is considered in detail, and the Skripkin model is recovered.
Symmetric States Requiring System Asymmetry.
Nishikawa, Takashi; Motter, Adilson E
2016-09-01
Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the complete synchronization of the entire network is the state inheriting the system symmetry. As in other systems subject to symmetry breaking, such symmetric states are not always stable. Here, we report on the discovery of the converse of symmetry breaking-the scenario in which complete synchronization is not stable for identically coupled identical oscillators but becomes stable when, and only when, the oscillator parameters are judiciously tuned to nonidentical values, thereby breaking the system symmetry to preserve the state symmetry. Aside from demonstrating that diversity can facilitate and even be required for uniformity and consensus, this suggests a mechanism for convergent forms of pattern formation in which initially asymmetric patterns evolve into symmetric ones. PMID:27661690
Symmetric States Requiring System Asymmetry
NASA Astrophysics Data System (ADS)
Nishikawa, Takashi; Motter, Adilson E.
2016-09-01
Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the complete synchronization of the entire network is the state inheriting the system symmetry. As in other systems subject to symmetry breaking, such symmetric states are not always stable. Here, we report on the discovery of the converse of symmetry breaking—the scenario in which complete synchronization is not stable for identically coupled identical oscillators but becomes stable when, and only when, the oscillator parameters are judiciously tuned to nonidentical values, thereby breaking the system symmetry to preserve the state symmetry. Aside from demonstrating that diversity can facilitate and even be required for uniformity and consensus, this suggests a mechanism for convergent forms of pattern formation in which initially asymmetric patterns evolve into symmetric ones.
Plethystic algebras and vector symmetric functions.
Rota, G C; Stein, J A
1994-01-01
An isomorphism is established between the plethystic Hopf algebra Pleth(Super[L]) and the algebra of vector symmetric functions. The Hall inner product of symmetric function theory is extended to the Hopf algebra Pleth(Super[L]). PMID:11607504
Plastic instabilities in statically and dynamically loaded spherical vessels
Duffey, Thomas A; Rodriguez, Edward A
2010-01-01
Significant changes were made in design limits for pressurized vessels in the 2007 version of the ASME Code (Section VIII, Div. 3) and 2008 and 2009 Addenda. There is now a local damage-mechanics based strain-exhaustion limit as well as the well-known global plastic collapse limit. Moreover, Code Case 2564 (Section VIII, Div. 3) has recently been approved to address impulsively loaded vessels. It is the purpose of this paper to investigate the plastic collapse limit as it applies to dynamically loaded spherical vessels. Plastic instabilities that could potentially develop in spherical shells under symmetric loading conditions are examined for a variety of plastic constitutive relations. First, a literature survey of both static and dynamic instabilities associated with spherical shells is presented. Then, a general plastic instability condition for spherical shells subjected to displacement controlled and impulsive loading is given. This instability condition is evaluated for six plastic and visco-plastic constitutive relations. The role of strain-rate sensitivity on the instability point is investigated. Calculations for statically and dynamically loaded spherical shells are presented, illustrating the formation of instabilities as well as the role of imperfections. Conclusions of this work are that there are two fundamental types of instabilities associated with failure of spherical shells. In the case of impulsively loaded vessels, where the pulse duration is short compared to the fundamental period of the structure, one instability type is found not to occur in the absence of static internal pressure. Moreover, it is found that the specific role of strain-rate sensitivity on the instability strain depends on the form of the constitutive relation assumed.
Is classical flat Kasner spacetime flat in quantum gravity?
NASA Astrophysics Data System (ADS)
Singh, Parampreet
2016-05-01
Quantum nature of classical flat Kasner spacetime is studied using effective spacetime description in loop quantum cosmology (LQC). We find that even though the spacetime curvature vanishes at the classical level, nontrivial quantum gravitational effects can arise. For the standard loop quantization of Bianchi-I spacetime, which uniquely yields universal bounds on expansion and shear scalars and results in a generic resolution of strong singularities, we find that a flat Kasner metric is not a physical solution of the effective spacetime description, except in a limit. The lack of a flat Kasner metric at the quantum level results from a novel feature of the loop quantum Bianchi-I spacetime: quantum geometry induces nonvanishing spacetime curvature components, making it not Ricci flat even when no matter is present. The noncurvature singularity of the classical flat Kasner spacetime is avoided, and the effective spacetime transits from a flat Kasner spacetime in asymptotic future, to a Minkowski spacetime in asymptotic past. Interestingly, for an alternate loop quantization which does not share some of the fine features of the standard quantization, flat Kasner spacetime with expected classical features exists. In this case, even with nontrivial quantum geometric effects, the spacetime curvature vanishes. These examples show that the character of even a flat classical vacuum spacetime can alter in a fundamental way in quantum gravity and is sensitive to the quantization procedure.
NASA Astrophysics Data System (ADS)
Bender, Carl M.
2015-07-01
The average quantum physicist on the street would say that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy eigenvalues are real and that time evolution is unitary. However, the Hamiltonian H = p2 + ix3, which is obviously not Dirac Hermitian, has a positive real discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory. Evidently, the axiom of Dirac Hermiticity is too restrictive. While H = p2 + ix3 is not Dirac Hermitian, it is PT symmetric; that is, invariant under combined parity P (space reflection) and time reversal T. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics is extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past few years, some of these properties have been verified in laboratory experiments. A particularly interesting PT-symmetric Hamiltonian is H = p2 - x4, which contains an upside-down potential. This potential is discussed in detail, and it is explained in intuitive as well as in rigorous terms why the energy levels of this potential are real, positive, and discrete. Applications of PT-symmetry in quantum field theory are also discussed.
Photoelectric sheath formation around small spherical objects in space
Misra, Shikha Sodha, M. S.; Mishra, S. K.
2015-04-15
The formation of a photoelectron sheath around positively charged small (∼cm) spherical objects roaming in near earth space due to the solar radiation (with continuous spectrum) and the solar wind plasma has been investigated. The sheath structure has been derived, taking into account anisotropic photoelectron flux with the Poisson equation, spherical geometry of the object, and half Fermi Dirac distribution of photoelectron velocities. Two cases, viz., when the object is illuminated by (i) isotropic or (ii) unidirectional (parallel beam) radiation, have been analyzed. The analysis predicts a spherically symmetric sheath in case of isotropic illumination, while a symmetry in sheath about a θ=π/4 is seen in case of parallel beam illumination; θ is the angle of incidence which is the angle made by the normal to a surface element with the direction of incidence of solar radiation. The radial and angular profiles of the electric potential and electron density in the photoelectron sheath have been evaluated and illustrated graphically; the dependence of the sheath structure on the solar wind plasma parameters, material properties of the spherical object, and its size have been discussed.
Spherical tensor Slepian functions for satellite gravity gradiometry
NASA Astrophysics Data System (ADS)
Seibert, Katrin; Plattner, Alain; Simons, Frederik J.; Michel, Volker
2016-04-01
For data on the sphere in scalar and vectorial form spatially concentrated and spectrally limited, or spatially limited and spectrally concentrated functions have proven to be a viable and versatile tool. These so-called Slepian functions have been applied in a variety of fields including geodesy, planetary magnetism, cosmology, and biomedical imaging. Their focus on a chosen region on the planet allows for local inversions, when only regional data are available or are of desired quality, or they enable us to extract regional information. For tensorial data, as for example provided by the gravity satellite mission GOCE, no such Slepian functions are available. We present a method for an efficient construction of tensor Slepian functions for symmetric regions such as spherical caps. These functions arise from the solution of an optimization problem involving tensor spherical harmonics (by Freeden and Schreiner) and primarily, spin-weighted spherical harmonics (by Newman and Penrose). Our work also implies the improvement of the theory of the spin-weighted spherical harmonics as a main aspect.
Spherical Model for Turbulence
NASA Astrophysics Data System (ADS)
Mou, Chung-Yu.
A new set of models for homogeneous, isotropic turbulence is considered in which the Navier-Stokes equations for incompressible fluid flow are generalized to a set of N coupled equations in N velocity fields. It is argued that in order to be useful these models must embody a new group of symmetries, and a general formalism is laid out for their construction. The work is motivated by similar techniques that have had extraordinary success in improving the theoretical understanding of equilibrium phase transitions in condensed matter systems. The key result is that these models simplify when N is large. The so-called spherical limit, N to infty, can be solved exactly, yielding a closed pair of nonlinear integral equations for the response and correlation functions. These equations, known as Kraichnan's Direct Interaction Approximation (DIA) equations, are, for the first time, solved fully in the scale-invariant turbulent regime, and the implications of these solutions for real turbulence (N = 1) are discussed. In particular, it is argued that previously applied renormalization group techniques, based on an expansion in the exponent, y, that characterizes the driving spectrum, are incorrect, and that the Kolmogorov exponent zeta has a nontrivial dependence on N, with zeta(N toinfty) = {3over2}. This value is remarkably close to the experimental result, zeta~{5over3}, which must therefore result from higher order corrections in powers of {1over N}. Prospects for calculating these corrections are briefly discussed: though daunting, such a calculations would, for the first time, provide a controlled perturbation expansion for the Kolmogorov, and other, exponents. Our techniques may also be applied to other nonequilibrium dynamical problems, such as the KPZ equation for interface growth, and perhaps to turbulence in nonlinear wave systems.
Spherical model for turbulence
NASA Astrophysics Data System (ADS)
Mou, Chung-Yu
A new set of models for homogeneous, isotropic turbulence is considered in which the Navier-Stokes equations for incompressible fluid flow are generalized to a set of N coupled equations in N velocity fields. It is argued that in order to be useful these models must embody a new group of symmetries, and a general formalism is laid out for their construction. The work is motivated by similar techniques that have had extraordinary success in improving the theoretical understanding of equilibrium phase transitions in condensed matter systems. The key result is that these models simplify when N is large. The so-called spherical limit, N approaches infinity, can be solved exactly, yielding a closed pair of nonlinear integral equations for the response and correlation functions. These equations, known as Kraichnan's Direct Interaction Approximation (DIA) equations, are, for the first time, solved fully in the scale-invariant turbulent regime, and the implications of these solutions for real turbulence (N = 1) are discussed. In particular, it is argued that previously applied renormalization group techniques, based on an expansion in the exponent, y, that characterizes the driving spectrum, are incorrect, and that the Kolmogorov exponent zeta has a nontrivial dependence on N, with zeta(N approaches infinity) = 3/2. This value is remarkably close to the experimental result, zeta approximately equals 5/3, which must therefore result from higher order corrections in powers of 1/N. Prospects for calculating these corrections are briefly discussed: though daunting, such a calculation would, for the first time, provide a controlled perturbation expansion for the Kolmogorov, and other exponents. Our techniques may also be applied to other nonequilibrium dynamical problems, such as the KPZ equation for interface growth, and perhaps to turbulence in nonlinear wave systems.
Casimir interaction between spheres in ( D + 1)-dimensional Minkowski spacetime
NASA Astrophysics Data System (ADS)
Teo, L. P.
2014-05-01
We consider the Casimir interaction between two spheres in ( D + 1)-dimensional Minkowski spacetime due to the vacuum fluctuations of scalar fields. We consider combinations of Dirichlet and Neumann boundary conditions. The TGTG formula of the Casimir interaction energy is derived. The computations of the T matrices of the two spheres are straightforward. To compute the two G matrices, known as translation matrices, which relate the hyper-spherical waves in two spherical coordinate frames differ by a translation, we generalize the operator approach employed in [39]. The result is expressed in terms of an integral over Gegenbauer polynomials. In contrast to the D=3 case, we do not re-express the integral in terms of 3 j-symbols and hyper-spherical waves, which in principle, can be done but does not simplify the formula. Using our expression for the Casimir interaction energy, we derive the large separation and small separation asymptotic expansions of the Casimir interaction energy. In the large separation regime, we find that the Casimir interaction energy is of order L -2 D+3, L -2 D+1 and L -2 D-1 respectively for Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions, where L is the center-to-center distance of the two spheres. In the small separation regime, we confirm that the leading term of the Casimir interaction agrees with the proximity force approximation, which is of order , where d is the distance between the two spheres. Another main result of this work is the analytic computations of the next-to-leading order term in the small separation asymptotic expansion. This term is computed using careful order analysis as well as perturbation method. In the case the radius of one of the sphere goes to infinity, we find that the results agree with the one we derive for sphere-plate configuration. When D=3, we also recover previously known results. We find that when D is large, the ratio of the next-to-leading order term to the leading
Stationary axisymmetric and slowly rotating spacetimes in Hořava-Lifshitz gravity.
Wang, Anzhong
2013-03-01
Stationary, axisymmetric, and slowly rotating vacuum spacetimes in the Hořava-Lifshitz (HL) gravity are studied, and it is shown that, for any given spherical static vacuum solution of the HL theory (of any model, including the ones with an additional U(1) symmetry), there always exists a corresponding slowly rotating, stationary, and axisymmetric vacuum solution, which reduces to the former, when the rotation is switched off. The rotation is universal and only implicitly depends on the models of the HL theory and their coupling constants through the spherical seed solution. As a result, all asymptotically flat slowly rotating vacuum solutions are asymptotically identical to the slowly rotating Kerr solution. This is in contrast to the claim of Barausse and Sotiriou [Phys. Rev. Lett. 109, 181101 (2012)], in which slowly rotating black holes were reported (incorrectly) not to exist in the infrared limit of the nonprojectable HL theory.
Spacetime encodings. III. Second order Killing tensors
Brink, Jeandrew
2010-01-15
This paper explores the Petrov type D, stationary axisymmetric vacuum (SAV) spacetimes that were found by Carter to have separable Hamilton-Jacobi equations, and thus admit a second-order Killing tensor. The derivation of the spacetimes presented in this paper borrows from ideas about dynamical systems, and illustrates concepts that can be generalized to higher-order Killing tensors. The relationship between the components of the Killing equations and metric functions are given explicitly. The origin of the four separable coordinate systems found by Carter is explained and classified in terms of the analytic structure associated with the Killing equations. A geometric picture of what the orbital invariants may represent is built. Requiring that a SAV spacetime admits a second-order Killing tensor is very restrictive, selecting very few candidates from the group of all possible SAV spacetimes. This restriction arises due to the fact that the consistency conditions associated with the Killing equations require that the field variables obey a second-order differential equation, as opposed to a fourth-order differential equation that imposes the weaker condition that the spacetime be SAV. This paper introduces ideas that could lead to the explicit computation of more general orbital invariants in the form of higher-order Killing tensors.
Scalar Green function of the Kerr spacetime
NASA Astrophysics Data System (ADS)
Yang, Huan; Zhang, Fan; Zimmerman, Aaron; Chen, Yanbei
2014-03-01
In this paper we study the scalar Green function in the Kerr spacetime using Wentzel-Kramers-Brillouin (WKB) methods. The Green function can be expressed by Fourier-transforming to its frequency-domain counterpart, and with the help of complex analysis it can be divided into parts: 1) the "direct part," which propagates on the light cone and dominates at very early times; 2) the "quasinormal-mode part," which represents the waves traveling around the photon sphere and is important at early and intermediate times; and 3) the "tail part," which is due to scattering by the Coulomb-type potential and becomes more important at later times. We focus on the "quasinormal-mode part" of the Green function and derive an approximate analytical formula for it using WKB techniques. This approximate Green function diverges at points that are connected by null geodesics, and it recovers the fourfold singular structure of Green functions that are seen in Schwarzschild and other spacetimes. It also carries unique signatures of the Kerr spacetime such as frame dragging. Along the way, we also derive approximate quasinormal-mode wave functions and expressions for the black hole excitation factors in the Kerr spacetime. We expect this work to benefit the understanding of both wave propagation and the problem of self-force in the Kerr spacetime.
Spherical stellarator with plasma current
NASA Astrophysics Data System (ADS)
Moroz, Paul E.
1996-08-01
Recently proposed novel concept of a spherical stellarator (P. E. Moroz, ``Spherical stellarator configuration,'' to appear in Phys. Rev. Lett) is enhanced by adding the plasma current to the otherwise pure stellarator system. The coil configuration of this ultra low aspect ratio system differs from that of a spherical tokamak by inclination of external parts of the toroidal field coils. It is shown that the configuration considered possesses many attractive properties, including: wide flexibility of operating regimes, compact design and coil simplicity, good access to the plasma, closed vacuum flux surfaces with large enclosed volume, significant external rotational transform, strong magnetic well, and a high plasma β [β(0) in excess of 30%] equilibrium. It is shown that the bootstrap effect in a spherical stellarator, in principle, can supply the full plasma current required for the high-β equilibrium.
Toroidal equilibria in spherical coordinates
Tsui, K. H.
2008-11-15
The standard Grad-Shafranov equation for axisymmetric toroidal plasma equilibrium is customary expressed in cylindrical coordinates with toroidal contours, and through which benchmark equilibria are solved. An alternative approach to cast the Grad-Shafranov equation in spherical coordinates is presented. This equation, in spherical coordinates, is examined for toroidal solutions to describe low {beta} Solovev and high {beta} plasma equilibria in terms of elementary functions.
Maximal hypersurfaces in asymptotically stationary spacetimes
NASA Astrophysics Data System (ADS)
Chrusciel, Piotr T.; Wald, Robert M.
1992-12-01
The purpose of the work is to extend the results on the existence of maximal hypersurfaces to encompass some situations considered by other authors. The existence of maximal hypersurface in asymptotically stationary spacetimes is proven. Existence of maximal surface and of foliations by maximal hypersurfaces is proven in two classes of asymptotically flat spacetimes which possess a one parameter group of isometries whose orbits are timelike 'near infinity'. The first class consists of strongly causal asymptotically flat spacetimes which contain no 'blackhole or white hole' (but may contain 'ergoregions' where the Killing orbits fail to be timelike). The second class of space times possess a black hole and a white hole, with the black and white hole horizon intersecting in a compact 2-surface S.
Spacetime and Quantum Propagation From Digital Clocks
NASA Astrophysics Data System (ADS)
Ord, Garnet. N.
2013-09-01
Minkowski spacetime predates quantum mechanics and is frequently regarded as an extension of the classical paradigm of Newtonian physics, rather than a harbinger of quantum mechanics. By inspecting how discrete clocks operate in a relativistic world we show that this view is misleading. Discrete relativistic clocks implicate classical spacetime provided a continuum limit is taken in such a way that successive ticks of the clock yield a smooth worldline. The classical picture emerges but does so by confining unitary propagation into spacetime regions between ticks that have zero area in the continuum limit. Clocks allowed a continuum limit that does not force inter-event intervals to zero, satisfy the Dirac equation. This strongly suggests that the origin of quantum propagation is to be found in the shift from Newton's absolute time to Minkowski's frame dependent time and is ultimately relativistic in origin.
Causal structure and electrodynamics on Finsler spacetimes
NASA Astrophysics Data System (ADS)
Pfeifer, Christian; Wohlfarth, Mattias N. R.
2011-08-01
We present a concise new definition of Finsler spacetimes that generalizes Lorentzian metric manifolds and provides consistent backgrounds for physics. Extending standard mathematical constructions known from Finsler spaces, we show that geometric objects like the Cartan nonlinear connection and its curvature are well defined almost everywhere on Finsler spacetimes, including their null structure. This allows us to describe the complete causal structure in terms of timelike and null curves; these are essential to model physical observers and the propagation of light. We prove that the timelike directions form an open convex cone with a null boundary, as is the case in Lorentzian geometry. Moreover, we develop action integrals for physical field theories on Finsler spacetimes, and tools to deduce the corresponding equations of motion. These are applied to construct a theory of electrodynamics that confirms the claimed propagation of light along Finsler null geodesics.
Quantum Larmor radiation in de Sitter spacetime
NASA Astrophysics Data System (ADS)
Blaga, Robert; Busuioc, Sergiu
2016-09-01
We study the radiation emitted by inertial charge evolving on the expanding de Sitter spacetime. Performing a perturbative calculation, within scalar quantum electrodynamics (sQED), we obtain the transition amplitude for the process and using this we define the energy radiated by the source. In the non-relativistic limit we find that the leading term is compatible with the classical result (Larmor formula). The first quantum correction is found to be negative, a result which is in line with a number of similar quantum field theory results. For the ultra-relativistic case we find a logarithmic divergence of the emitted energy for large frequencies, which we link to the nature of the spacetime. We compare our results with that of Nomura et al. (JCAP 11:013, 2006), where the authors make a similar calculation for a general conformally flat spacetime.
Noncommutative effects of spacetime on holographic superconductors
NASA Astrophysics Data System (ADS)
Ghorai, Debabrata; Gangopadhyay, Sunandan
2016-07-01
The Sturm-Liouville eigenvalue method is employed to analytically investigate the properties of holographic superconductors in higher dimensions in the framework of Born-Infeld electrodynamics incorporating the effects of noncommutative spacetime. In the background of pure Einstein gravity in noncommutative spacetime, we obtain the relation between the critical temperature and the charge density. We also obtain the value of the condensation operator and the critical exponent. Our findings suggest that the higher value of noncommutative parameter and Born-Infeld parameter make the condensate harder to form. We also observe that the noncommutative structure of spacetime makes the critical temperature depend on the mass of the black hole and higher value of black hole mass is favourable for the formation of the condensate.
Tautology of quantum mechanics and spacetime
NASA Astrophysics Data System (ADS)
Keller, Jaime
Multivector Clifford algebra allows a series of factorizations of the Laplacian (the spacetime d'Alembert operator), similar to the well known Dirac factorization, generating sets of Diraclike equations. It is shown that a basic set has the symmetry corresponding to the standard electroweak-color model. But in contrast to the usual approach to the standard model the properties for the different fields of the model are consequences of the relative properties of the equations, among themselves and in relation to spacetime, and therefore, they do not need to be postulates of the theory. Spinors are the basis of geometric algebra and in fact, they can be considered the basis of all algebras representable by matrices. Here a unified mathematical approach to spinors and multivectors or superalgebra is constructed in a form, to be useful to study the mathematical description of matter and its interaction fields. Matter fields in turn generate the spacetime geometric superalgebra.
Alice and Bob in an expanding spacetime
NASA Astrophysics Data System (ADS)
Alexander, Helder; de Souza, Gustavo; Mansfield, Paul; Sampaio, Marcos
2015-09-01
We investigate the teleportation of a qubit between two observers Alice and Bob in an asymptotically flat Robertson-Walker expanding spacetime. We use scalar or fermionic field modes inside Alice's and Bob's ideal cavities and show the degradation of the teleportation quality, as measured by the fidelity, through a mechanism governed by spacetime expansion. This reduction is demonstrated to increase with the rapidity of the expansion and to be highly sensitive to the coupling of the field to spacetime curvature, becoming considerably stronger as it reduces from conformal to minimal. We explore a perturbative approach in the cosmological parameters to compute the Bogoliubov coefficients in order to evaluate and compare the fidelity degradation of fermionic and scalar fields.
Spacetime Average Density (SAD) cosmological measures
Page, Don N.
2014-11-01
The measure problem of cosmology is how to obtain normalized probabilities of observations from the quantum state of the universe. This is particularly a problem when eternal inflation leads to a universe of unbounded size so that there are apparently infinitely many realizations or occurrences of observations of each of many different kinds or types, making the ratios ambiguous. There is also the danger of domination by Boltzmann Brains. Here two new Spacetime Average Density (SAD) measures are proposed, Maximal Average Density (MAD) and Biased Average Density (BAD), for getting a finite number of observation occurrences by using properties of the Spacetime Average Density (SAD) of observation occurrences to restrict to finite regions of spacetimes that have a preferred beginning or bounce hypersurface. These measures avoid Boltzmann brain domination and appear to give results consistent with other observations that are problematic for other widely used measures, such as the observation of a positive cosmological constant.
NASA Astrophysics Data System (ADS)
Géré, Antoine; Hack, Thomas-Paul; Pinamonti, Nicola
2016-05-01
We develop a renormalisation scheme for time-ordered products in interacting field theories on curved space-times that consists of an analytic regularisation of Feynman amplitudes and a minimal subtraction of the resulting pole parts. This scheme is directly applicable to space-times with Lorentzian signature, manifestly generally covariant, invariant under any space-time isometries present, and constructed to all orders in perturbation theory. Moreover, the scheme correctly captures the nongeometric state-dependent contribution of Feynman amplitudes, and it is well suited for practical computations. To illustrate this last point, we compute explicit examples on a generic curved space-time and demonstrate how momentum space computations in cosmological space-times can be performed in our scheme. In this work, we discuss only scalar fields in four space-time dimensions, but we argue that the renormalisation scheme can be directly generalised to other space-time dimensions and field theories with higher spin as well as to theories with local gauge invariance.
Dynamics of non-spherical colloidal particles near and at oil-water interfaces
NASA Astrophysics Data System (ADS)
Wang, Anna; Dimiduk, Thomas G.; Fung, Jerome; Chaudhary, Kundan; Lewis, Jennifer A.; Razavi, Sepideh; Kretzschmar, Ilona; Manoharan, Vinothan N.
2014-03-01
Whereas much is known about how spherical colloidal particles interact with and at oil-water interfaces, not much is known about their non-spherical counterparts. The rotation of non-spherically symmetric particles adds extra degrees of freedom to how such particles interact with each other and the interface, so to study their three-dimensional dynamics we must first be able to image the rotation which has so far only been possible in viscous fluids or for particles with large aspect ratios. Here we track both the three-dimensional translation and the rotation of non-spherical colloidal particles at high speeds using the discrete dipole approximation in conjunction with digital holographic microscopy. We study the dynamics of such particles at an oil-water interface to determine interactions and dynamics prior to or after attachment. We aim to connect these measurements to the formation and stability of Pickering emulsions.
A Novel View of Space-Time Permitting Faster-Than-Light Travel
NASA Astrophysics Data System (ADS)
Meholic, Gregory
2000-04-01
The mathematically symmetrical nature of general relativity suggests that for a given absolute energy state, a particle of real mass must be moving either slower or faster than the speed of light. Relativistic symmetry implies that the sub and superluminal realms can therefore be construed as separate space-times with a common, unattainable boundary condition (the luminal plane), and both can contain particles with real and quantifiable properties. Although mass energy can only exist in one space-time and distort the luminal plane to create gravity, the disturbance can be observed in the other space as an equal gravitational distortion with no associated mass. The postulated characteristics of superluminal space, its resident particles, and their similarity to entities in subluminal space reveal a possible connection between the space-times which lies deep within the quantum-mechanical events observed thus far. Quarks may hold the key to these events and seem capable of existing and jumping between sub and superluminal spaces. If a subluminal mass were converted at the quark-level of matter to exist in superluminal space, traveling faster than light would be possible without violating causality and relativity.
NASA Astrophysics Data System (ADS)
Gundlach, Carsten; Martín-García, José M.; Garfinkle, David
2013-07-01
We investigate numerical methods for wave equations in n + 2 spacetime dimensions, written in spherical coordinates, decomposed in spherical harmonics on Sn, and finite-differenced in the remaining coordinates r and t. Such an approach is useful when the full physical problem has spherical symmetry, for perturbation theory about a spherical background, or in the presence of boundaries with spherical topology. The key numerical difficulty arises from lower order 1/r terms at the origin r = 0. As a toy model for this, we consider the flat space linear wave equation in the form \\dot{\\pi }=\\psi ^{\\prime }+p\\psi /r, \\dot{\\psi }=\\pi ^{\\prime }, where p = 2l + n and l is the leading spherical harmonic index. We propose a class of summation by parts (SBP) finite-differencing methods that conserve a discrete energy up to boundary terms, thus guaranteeing stability and convergence in the energy norm. We explicitly construct SBP schemes that are second- and fourth-order accurate at interior points and the symmetry boundary r = 0, and first- and second-order accurate at the outer boundary r = R.
Space-time framework of internal measurement
NASA Astrophysics Data System (ADS)
Matsuno, Koichiro
1998-07-01
Measurement internal to material bodies is ubiquitous. The internal observer has its own local space-time framework that enables the observer to distinguish, even to a slightest degree, those material bodies fallen into that framework. Internal measurement proceeding among the internal observers come to negotiate a construction of more encompassing local framework of space and time. The construction takes place through friction among the internal observers. Emergent phenomena are related to an occurrence of enlarging the local space-time framework through the frictional negotiation among the material participants serving as the internal observers. Unless such a negotiation is obtained, the internal observers would have to move around in the local space-time frameworks of their own that are mutually incommensurable. Enhancement of material organization as demonstrated in biological evolutionary processes manifests an inexhaustible negotiation for enlarging the local space-time framework available to the internal observers. In contrast, Newtonian space-time framework, that remains absolute and all encompassing, is an asymptote at which no further emergent phenomena could be expected. It is thus ironical to expect something to emerge within the framework of Newtonian absolute space and time. Instead of being a complex and organized configuration of interaction to appear within the global space-time framework, emergent phenomena are a consequence of negotiation among the local space-time frameworks available to internal measurement. Most indicative of the negotiation of local space-time frameworks is emergence of a conscious self grounding upon the reflexive nature of perceptions, that is, a self-consciousness in short, that certainly goes beyond the Kantian transcendental subject. Accordingly, a synthetic discourse on securing consciousness upon the ground of self-consciousness can be developed, though linguistic exposition of consciousness upon self
Inflationary spacetimes are incomplete in past directions.
Borde, Arvind; Guth, Alan H; Vilenkin, Alexander
2003-04-18
Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating--or just expanding sufficiently fast--must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.
Special Relativity Derived from Spacetime Magma
Greensite, Fred
2014-01-01
We present a derivation of relativistic spacetime largely untethered from specific physical considerations, in constrast to the many physically-based derivations that have appeared in the last few decades. The argument proceeds from the inherent magma (groupoid) existing on the union of spacetime frame components and Euclidean which is consistent with an “inversion symmetry” constraint from which the Minkowski norm results. In this context, the latter is also characterized as one member of a class of “inverse norms” which play major roles with respect to various unital -algebras more generally. PMID:24959889
Special relativity derived from spacetime magma.
Greensite, Fred
2014-01-01
We present a derivation of relativistic spacetime largely untethered from specific physical considerations, in constrast to the many physically-based derivations that have appeared in the last few decades. The argument proceeds from the inherent magma (groupoid) existing on the union of spacetime frame components [Formula: see text] and Euclidean [Formula: see text] which is consistent with an "inversion symmetry" constraint from which the Minkowski norm results. In this context, the latter is also characterized as one member of a class of "inverse norms" which play major roles with respect to various unital [Formula: see text]-algebras more generally.
Special relativity derived from spacetime magma.
Greensite, Fred
2014-01-01
We present a derivation of relativistic spacetime largely untethered from specific physical considerations, in constrast to the many physically-based derivations that have appeared in the last few decades. The argument proceeds from the inherent magma (groupoid) existing on the union of spacetime frame components [Formula: see text] and Euclidean [Formula: see text] which is consistent with an "inversion symmetry" constraint from which the Minkowski norm results. In this context, the latter is also characterized as one member of a class of "inverse norms" which play major roles with respect to various unital [Formula: see text]-algebras more generally. PMID:24959889
Pair creation in noncommutative space-time
NASA Astrophysics Data System (ADS)
Hamil, B.; Chetouani, L.
2016-09-01
By taking two interactions, the Volkov plane wave and a constant electromagnetic field, the probability related to the process of pair creation from the vacuum is exactly and analytically determined via the Schwinger method in noncommutative space-time. For the plane wave, it is shown that the probability is simply null and for the electromagnetic wave it is found that the expression of the probability has a similar form to that obtained by Schwinger in a commutative space-time. For a certain critical value of H, the probability is simply equal to 1.
On the architecture of spacetime geometry
NASA Astrophysics Data System (ADS)
Bianchi, Eugenio; Myers, Robert C.
2014-11-01
We propose entanglement entropy as a probe of the architecture of spacetime in quantum gravity. We argue that the leading contribution to this entropy satisfies an area law for any sufficiently large region in a smooth spacetime, which, in fact, is given by the Bekenstein-Hawking formula. This conjecture is supported by various lines of evidence from perturbative quantum gravity, simplified models of induced gravity, the AdS/CFT correspondence and loop quantum gravity, as well as Jacobson's ‘thermodynamic’ perspective of gravity.
Generalised space-time and gauge transformations
NASA Astrophysics Data System (ADS)
West, Peter
2014-08-01
We consider the generalised space-time introduced by the author in 2003 in the context of the non-linear realisation of the semi-direct product of E 11 and its first fundamental representation. For all the fields we propose gauge transformations which are compatible with the underlying E 11 structure. A crucial role is played by the generalised vielbein that the generalised space-time possess. We work out the explicit form of the gauge transformations, at low levels, in four, five and eleven dimensions.
An exact smooth Gowdy-symmetric generalized Taub-NUT solution
NASA Astrophysics Data System (ADS)
Beyer, Florian; Hennig, Jörg
2014-05-01
In a recent paper (Beyer and Hennig 2012 Class. Quantum Grav. 29 245017), we have introduced a class of inhomogeneous cosmological models: the smooth Gowdy-symmetric generalized Taub-NUT solutions. Here we derive a three-parametric family of exact solutions within this class, which contains the two-parametric Taub solution as a special case. We also study properties of this solution. In particular, we show that for a special choice of the parameters, the spacetime contains a curvature singularity with directional behaviour that can be interpreted as a ‘true spike’ in analogy to previously known Gowdy-symmetric solutions with spatial {T}^3-topology. For other parameter choices, the maximal globally hyperbolic region is singularity-free, but may contain ‘false spikes’.
Maxwell-Higgs equation on higher dimensional static curved spacetimes
NASA Astrophysics Data System (ADS)
Mulyanto, Akbar, Fiki Taufik; Gunara, Bobby Eka
2015-09-01
In this paper we consider a class of solutions of Maxwell-Higgs equation in higher dimensional static curved spacetimes called Schwarzchild de-Sitter spacetimes. We obtain the general form of the electric fields and magnetic fields in background Schwarzchild de-Sitter spacetimes. However, determining the interaction between photons with the Higgs scalar fields is needed further studies.
Maxwell-Higgs equation on higher dimensional static curved spacetimes
Mulyanto; Akbar, Fiki Taufik Gunara, Bobby Eka
2015-09-30
In this paper we consider a class of solutions of Maxwell-Higgs equation in higher dimensional static curved spacetimes called Schwarzchild de-Sitter spacetimes. We obtain the general form of the electric fields and magnetic fields in background Schwarzchild de-Sitter spacetimes. However, determining the interaction between photons with the Higgs scalar fields is needed further studies.
Cracked shells under skew-symmetric loading. [Reissner theory
NASA Technical Reports Server (NTRS)
Delale, F.
1981-01-01
The general problem of a shell containing a through crack in one of the principal planes of curvature and under general skew-symmetric loading is considered. By employing a Reissner type shell theory which takes into account the effect of transverse shear strains, all boundary conditions on the crack surfaces are satisfied separately. Consequently, unlike those obtained from the classical shell theory, the angular distributions of the stress components around the crack tips are shown to be identical to the distributions obtained from the plane and anti-plane elasticity solutions. Results are given for axially and circumferentially cracked cylindrical shells, spherical shells, and toroidal shells under uniform in-plane shearing, out of plane shearing, and torsion. The problem is formulated for specially orthostropic materials, therefore, the effect of orthotropy on the results is also studied.
Spacetime encodings. II. Pictures of integrability
Brink, Jeandrew
2008-11-15
I visually explore the features of geodesic orbits in arbitrary stationary axisymmetric vacuum (SAV) spacetimes that are constructed from a complex Ernst potential. Some of the geometric features of integrable and chaotic orbits are highlighted. The geodesic problem for these SAV spacetimes is rewritten as a 2 degree of freedom problem and the connection between current ideas in dynamical systems and the study of two manifolds sought. The relationship between the Hamilton-Jacobi equations, canonical transformations, constants of motion, and Killing tensors are commented on. Wherever possible I illustrate the concepts by means of examples from general relativity. This investigation is designed to build the readers' intuition about how integrability arises, and to summarize some of the known facts about 2 degree of freedom systems. Evidence is given, in the form of an orbit-crossing structure, that geodesics in SAV spacetimes might admit a fourth constant of motion that is quartic in momentum (by contrast with Kerr spacetime, where Carter's fourth constant is quadratic)
Twin Paradox in de Sitter Spacetime
ERIC Educational Resources Information Center
Boblest, Sebastian; Muller, Thomas; Wunner, Gunter
2011-01-01
The "twin paradox" of special relativity offers the possibility of making interstellar flights within a lifetime. For very long journeys with velocities close to the speed of light, however, we have to take into account the expansion of the universe. Inspired by the work of Rindler on hyperbolic motion in curved spacetime, we study the worldline…
Communicating with Accelerated Observers in Minkowski Spacetime
ERIC Educational Resources Information Center
FLores, F. J.
2008-01-01
Our goal here is to determine the spatial and temporal constraints on communication between two observers at least one of which moves with constant proper acceleration in two-dimensional Minkowski spacetime. We take as a simplified model of communication one observer bouncing a light signal off another observer. Our derivations use only elementary…
Riemann curvature of a boosted spacetime geometry
NASA Astrophysics Data System (ADS)
Battista, Emmanuele; Esposito, Giampiero; Scudellaro, Paolo; Tramontano, Francesco
2016-10-01
The ultrarelativistic boosting procedure had been applied in the literature to map the metric of Schwarzschild-de Sitter spacetime into a metric describing de Sitter spacetime plus a shock-wave singularity located on a null hypersurface. This paper evaluates the Riemann curvature tensor of the boosted Schwarzschild-de Sitter metric by means of numerical calculations, which make it possible to reach the ultrarelativistic regime gradually by letting the boost velocity approach the speed of light. Thus, for the first time in the literature, the singular limit of curvature, through Dirac’s δ distribution and its derivatives, is numerically evaluated for this class of spacetimes. Moreover, the analysis of the Kretschmann invariant and the geodesic equation shows that the spacetime possesses a “scalar curvature singularity” within a 3-sphere and it is possible to define what we here call “boosted horizon”, a sort of elastic wall where all particles are surprisingly pushed away, as numerical analysis demonstrates. This seems to suggest that such “boosted geometries” are ruled by a sort of “antigravity effect” since all geodesics seem to refuse to enter the “boosted horizon” and are “reflected” by it, even though their initial conditions are aimed at driving the particles toward the “boosted horizon” itself. Eventually, the equivalence with the coordinate shift method is invoked in order to demonstrate that all δ2 terms appearing in the Riemann curvature tensor give vanishing contribution in distributional sense.
Scalar field theory on noncommutative Snyder spacetime
Battisti, Marco Valerio; Meljanac, Stjepan
2010-07-15
We construct a scalar field theory on the Snyder noncommutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincare algebra is undeformed. The Lorentz sector is undeformed at both the algebraic and co-algebraic level, but the coproduct for momenta (defining the star product) is non-coassociative. The Snyder-deformed Poincare group is described by a non-coassociative Hopf algebra. The definition of the interacting theory in terms of a nonassociative star product is thus questionable. We avoid the nonassociativity by the use of a space-time picture based on the concept of the realization of a noncommutative geometry. The two main results we obtain are (i) the generic (namely, for any realization) construction of the co-algebraic sector underlying the Snyder geometry and (ii) the definition of a nonambiguous self-interacting scalar field theory on this space-time. The first-order correction terms of the corresponding Lagrangian are explicitly computed. The possibility to derive Noether charges for the Snyder space-time is also discussed.
Spacetime encodings. II. Pictures of integrability
NASA Astrophysics Data System (ADS)
Brink, Jeandrew
2008-11-01
I visually explore the features of geodesic orbits in arbitrary stationary axisymmetric vacuum (SAV) spacetimes that are constructed from a complex Ernst potential. Some of the geometric features of integrable and chaotic orbits are highlighted. The geodesic problem for these SAV spacetimes is rewritten as a 2 degree of freedom problem and the connection between current ideas in dynamical systems and the study of two manifolds sought. The relationship between the Hamilton-Jacobi equations, canonical transformations, constants of motion, and Killing tensors are commented on. Wherever possible I illustrate the concepts by means of examples from general relativity. This investigation is designed to build the readers’ intuition about how integrability arises, and to summarize some of the known facts about 2 degree of freedom systems. Evidence is given, in the form of an orbit-crossing structure, that geodesics in SAV spacetimes might admit a fourth constant of motion that is quartic in momentum (by contrast with Kerr spacetime, where Carter’s fourth constant is quadratic).
Thermodynamic Phase Transition and Critical Behavior of a Spherical Symmetric Black Hole
NASA Astrophysics Data System (ADS)
Jiang, Ji-Jian; Li, Chuan-An; Cheng, Xie-Feng
2016-04-01
In this paper, we builded the thermodynamics model of black hole based on the method of York. We obtained the reduced temperature reciprocal function using the action of the system. We studied the phase structure of black holes and Hawking-Page phase transition. We obtained the first order phase transition and critical values of black hole in Rerssner-NordstrÖm space time. The results showed that only when two-phase coexistence appeared only when | q| < | q c |.
Spherically symmetric collapse of a perfect fluid in f(R) gravity
NASA Astrophysics Data System (ADS)
Chakrabarti, Soumya; Banerjee, Narayan
2016-05-01
The present work investigates the gravitational collapse of a perfect fluid in f ( R) gravity models. For a general f ( R) theory, it is shown analytically that a collapse is quite possible. The singularity formed as a result of the collapse is found to be a curvature singularity of shell focusing type. The possibility of the formation of an apparent horizon hiding the central singularity depends on the initial conditions.
NASA Technical Reports Server (NTRS)
Han, S. M.; Wu, S. T.; Nakagawa, Y.
1982-01-01
Radial propagation of one-dimensional magnetohydrodynamic (MHD) waves are analyzed numerically on the basis of the Implicit-Continuous-Fluid-Eulerian (ICE) scheme. Accuracy of the numerical method and other properties are tested through the study of MHD wave propagation. The three different modes of MHD waves (i.e., fast-, slow- and Alfven (transverse) mode) are generated by applying physically consistent boundary perturbations derived from MHD compatibility relations. It is shown that the resulting flow following these waves depend upon the relative configurations of the initial magnetic field and boundary perturbations.
Lake, Kayll
2009-09-15
I use the Newtonian equation of hydrostatic equilibrium for an isotropic fluid sphere to generate exact anisotropic solutions of Einstein's equations. The input function is simply the density. An infinite number of regular solutions are constructed, some of which satisfy all the standard energy conditions. Two classes of these solutions generalize the Newtonian polytropes of index 0 and 1.
Mass bounds for compact spherically symmetric objects in generalized gravity theories
NASA Astrophysics Data System (ADS)
Burikham, Piyabut; Harko, Tiberiu; Lake, Matthew J.
2016-09-01
We derive upper and lower bounds on the mass-radius ratio of stable compact objects in extended gravity theories, in which modifications of the gravitational dynamics via-á-vis standard general relativity are described by an effective contribution to the matter energy-momentum tensor. Our results include the possibility of a variable coupling between the matter sector and the gravitational field and are valid for a large class of generalized gravity models. The generalized continuity and Tolman-Oppenheimer-Volkoff equations are expressed in terms of the effective mass, density, and pressure, given by the bare values plus additional contributions from the total energy-momentum tensor, and general theoretical limits for the maximum and minimum mass-radius ratios are explicitly obtained. As applications of the formalism developed herein, we consider compact bosonic objects, described by scalar-tensor gravitational theories with self-interacting scalar field potentials, and charged compact objects, respectively. For Higgs-type models, we find that these bounds can be expressed in terms of the value of the potential at the surface of the compact object. Minimizing the energy with respect to the radius, we obtain explicit upper and lower bounds on the mass, which admits a Chandrasekhar-type representation. For charged compact objects, we consider the effects of the Poincaré stresses on the equilibrium structure and obtain bounds on the radial and tangential stresses. As a possible astrophysical test of our results, we obtain the general bound on the gravitational redshift for compact objects in extended gravity theories and explicitly compute the redshift restrictions for objects with nonzero effective surface pressure. General implications of minimum mass bounds for the gravitational stability of fundamental particles and for the existence of holographic duality between bulk and boundary degrees of freedom are also considered.
NASA Astrophysics Data System (ADS)
Schwartz, Benjamin L.; Yin, Ziying; Magin, Richard L.
2016-09-01
Cylindrical homogenous phantoms for magnetic resonance (MR) elastography in biomedical research provide one way to validate an imaging systems performance, but the simplified geometry and boundary conditions can cloak complexity arising at tissue interfaces. In an effort to develop a more realistic gel tissue phantom for MRE, we have constructed a heterogenous gel phantom (a sphere centrally embedded in a cylinder). The actuation comes from the phantom container, with the mechanical waves propagating toward the center, focusing the energy and thus allowing for the visualization of high-frequency waves that would otherwise be damped. The phantom was imaged and its stiffness determined using a 9.4 T horizontal MRI with a custom build piezo-elastic MRE actuator. The phantom was vibrated at three frequencies, 250, 500, and 750 Hz. The resulting shear wave images were first used to reconstruct material stiffness maps for thin (1 mm) axial slices at each frequency, from which the complex shear moduli μ were estimated, and then compared with forward modeling using a recently developed theoretical model which took μ as inputs. The overall accuracy of the measurement process was assessed by comparing theory with experiment for selected values of the shear modulus (real and imaginary parts). Close agreement is shown between the experimentally obtained and theoretically predicted wave fields.
Probabilistic cloning of three symmetric states
Jimenez, O.; Bergou, J.; Delgado, A.
2010-12-15
We study the probabilistic cloning of three symmetric states. These states are defined by a single complex quantity, the inner product among them. We show that three different probabilistic cloning machines are necessary to optimally clone all possible families of three symmetric states. We also show that the optimal cloning probability of generating M copies out of one original can be cast as the quotient between the success probability of unambiguously discriminating one and M copies of symmetric states.
Basketballs as spherical acoustic cavities
NASA Astrophysics Data System (ADS)
Russell, Daniel A.
2010-06-01
The sound field resulting from striking a basketball is found to be rich in frequency content, with over 50 partials in the frequency range of 0-12 kHz. The frequencies are found to closely match theoretical expectations for standing wave patterns inside a spherical cavity. Because of the degenerate nature of the mode shapes, explicit identification of the modes is not possible without internal investigation with a microphone probe. A basketball proves to be an interesting application of a boundary value problem involving spherical coordinates.
Walking dynamics are symmetric (enough)
Ankaralı, M. Mert; Sefati, Shahin; Madhav, Manu S.; Long, Andrew; Bastian, Amy J.; Cowan, Noah J.
2015-01-01
Many biological phenomena such as locomotion, circadian cycles and breathing are rhythmic in nature and can be modelled as rhythmic dynamical systems. Dynamical systems modelling often involves neglecting certain characteristics of a physical system as a modelling convenience. For example, human locomotion is frequently treated as symmetric about the sagittal plane. In this work, we test this assumption by examining human walking dynamics around the steady state (limit-cycle). Here, we adapt statistical cross-validation in order to examine whether there are statistically significant asymmetries and, even if so, test the consequences of assuming bilateral symmetry anyway. Indeed, we identify significant asymmetries in the dynamics of human walking, but nevertheless show that ignoring these asymmetries results in a more consistent and predictive model. In general, neglecting evident characteristics of a system can be more than a modelling convenience—it can produce a better model.
Symmetric blanket nuclear fuel assembly
Penkrot, J.A.
1986-08-19
This patent describes a fuel assembly having spaced-apart fuel rods, the combination comprising: (a) a first group of the fuel rods containing natural uranium only; and (b) a second group of the fuel rods constituting the remainder therof containing enriched uranium only; (c) the fuel rods of the first group being surrounded by the fuel rods of the second group in a predetermined symmetrical relationship; (d) the first group of the fuel rods forming an inner, centrally-located, generally squared pattern wherein the only fuel rods present in the inner squared pattern are the fuel rods of the first group; (e) the second group of the fuel rods forming an outer, peripherally-located, generally squared annular pattern which surrounds the first group wherein the only fuel rods present in the outer squared pattern are the fuel rods of the second group.
Computing symmetric colorings of the dihedral group
NASA Astrophysics Data System (ADS)
Zelenyuk, Yuliya
2016-06-01
A symmetry on a group G is a mapping G ∋ x ↦ gx-1 g ∈ G, where g ∈ G. A subset A ⊆ G is symmetric if it is invariant under some symmetry, that is, A = gA-1g. The notion of symmetry has interesting relations to enumerative combinatorics. A coloring is symmetric if χ(gx-1g) = χ(x) for some g ∈ G. We discuss an approach how to compute the number of symmetric r-colorings for any finite group. Using this approach we derive the formula for the number of symmetric r-colorings of the dihedral group D3.
NASA Astrophysics Data System (ADS)
Mach, Patryk; Malec, Edward; Karkowski, Janusz
2013-10-01
We investigate spherical, isothermal and polytropic steady accretion models in the presence of the cosmological constant. Exact solutions are found for three classes of isothermal fluids, assuming the test gas approximation. The cosmological constant damps the mass accretion rate and—above a certain limit—completely stops the steady accretion onto black holes. A “homoclinic-type” accretion flow of polytropic gas has been discovered in anti-de Sitter spacetimes in the test-gas limit. These results can have cosmological connotation, through the Einstein-Straus vacuole model of embedding local structures into Friedman-Lemaitre-Robertson-Walker spacetimes. In particular, one infers that steady accretion would not exist in the late phases of Penrose’s scenario of the evolution of the Universe, known as the Weyl curvature hypothesis.
Redshift drift in axially symmetric quasispherical Szekeres models
NASA Astrophysics Data System (ADS)
Mishra, Priti; Célérier, Marie-Noëlle; Singh, Tejinder P.
2012-10-01
Models of inhomogeneous universes constructed with exact solutions of Einstein’s general relativity have been proposed in the literature with the aim of reproducing the cosmological data without any need for a dark energy component. Besides large scale inhomogeneity models spherically symmetric around the observer, Swiss-cheese models have also been studied. Among them, Swiss cheeses where the inhomogeneous patches are modeled by different particular Szekeres solutions have been used for reproducing the apparent dimming of the type Ia supernovae. However, the problem of fitting such models to the type Ia supernovae data is completely degenerate and we need other constraints to fully characterize them. One of the tests which is known to be able to discriminate between different cosmological models is the redshift drift. This drift has already been calculated by different authors for Lemaître-Tolman-Bondi models. We compute it here for one particular axially symmetric quasispherical Szekeres Swiss cheese which has previously been shown to reproduce to a good accuracy the type Ia supernovae data, and we compare the results to the drift in the ΛCDM model and in some Lemaître-Tolman-Bondi models that can be found in the literature. We show that it is a good discriminator between them. Then, we discuss our model’s remaining degrees of freedom and propose a recipe to fully constrain them.
NASA Astrophysics Data System (ADS)
Whale, B. E.
2014-01-01
I demonstrate that the chart based approach to the study of the global structure of Lorentzian manifolds induces a homeomorphism of the manifold into a topological space as an open dense set. The topological boundary of this homeomorphism is a chart independent boundary of ideal points equipped with a topological structure and a physically motivated classification. I show that this new boundary contains all other boundaries that can be presented as the topological boundary of an envelopment. Hence, in particular, it is a generalisation of Penrose's conformal boundary. I provide three detailed examples: the conformal compactification of Minkowski spacetime, Scott and Szekeres' analysis of the Curzon singularity and Beyer and Hennig's analysis of smooth Gowdy symmetric generalised Taub-NUT spacetimes.
Static and symmetric wormholes respecting energy conditions in Einstein-Gauss-Bonnet gravity
Maeda, Hideki; Nozawa, Masato
2008-07-15
Properties of n({>=}5)-dimensional static wormhole solutions are investigated in Einstein-Gauss-Bonnet gravity with or without a cosmological constant {lambda}. We assume that the spacetime has symmetries corresponding to the isometries of an (n-2)-dimensional maximally symmetric space with the sectional curvature k={+-}1, 0. It is also assumed that the metric is at least C{sup 2} and the (n-2)-dimensional maximally symmetric subspace is compact. Depending on the existence or absence of the general relativistic limit {alpha}{yields}0, solutions are classified into general relativistic (GR) and non-GR branches, respectively, where {alpha} is the Gauss-Bonnet coupling constant. We show that a wormhole throat respecting the dominant energy condition coincides with a branch surface in the GR branch, otherwise the null energy condition is violated there. In the non-GR branch, it is shown that there is no wormhole solution for k{alpha}{>=}0. For the matter field with zero tangential pressure, it is also shown in the non-GR branch with k{alpha}<0 and {lambda}{<=}0 that the dominant energy condition holds at the wormhole throat if the radius of the throat satisfies some inequality. In the vacuum case, a fine-tuning of the coupling constants is shown to be necessary and the radius of a wormhole throat is fixed. Explicit wormhole solutions respecting the energy conditions in the whole spacetime are obtained in the vacuum and dust cases with k=-1 and {alpha}>0.
Geometry of a Quantized Spacetime: The Quantum Potential Approach
NASA Astrophysics Data System (ADS)
Mirza, Babur M.
2014-03-01
Quantum dynamics in a curved spacetime can be studied using a modified Lagrangian approach directly in terms of the spacetime variables [Mirza, B.M., Quantum Dynamics in Black Hole Spacetimes, IC-MSQUARE 2012]. Here we investigate the converse problem of determining the nature of the background spacetime when quantum dynamics of a test particle is known. We employ the quantum potential formalism here to obtain the modifications introduced by the quantum effects to the background spacetime. This leads to a novel geometry for the spacetime in which a test particle modifies the spacetime via interaction through the quantum potential. We present here the case of a Gaussian wave packet, and a localized quantum soliton, representing the test particle, and determine the corresponding geometries that emerge.
Quantum statistical entropy of Schwarzchild-de Sitter spacetime
NASA Astrophysics Data System (ADS)
Zhao, Ren; Zhang, Li-Chun; Zhao, Hui-Hua
2012-10-01
Using the quantum statistical method, we calculate quantum statistical entropy between the black hole horizon and the cosmological horizon in Schwarzchild spacetime and derive the expression of quantum statistical entropy in de Sitter spacetime. Under the Unruh-Verlinde temperature of Schwarzchild-de Sitter spacetime in the entropic force views, we obtain the expression of quantum statistical entropy in de Sitter spacetime. It is shown that in de Sitter spacetime quantum statistical entropy is the sum of thermodynamic entropy corresponding black hole horizon and the one corresponding cosmological horizon. And the correction term of de Sitter spacetime entropy is obtained. Therefore, it is confirmed that the black hole entropy is the entropy of quantum field outside the black hole horizon. The entropy of de Sitter spacetime is the entropy of quantum field between the black hole horizon and the cosmological horizon.
Euclidean, Spherical, and Hyperbolic Shadows
ERIC Educational Resources Information Center
Hoban, Ryan
2013-01-01
Many classical problems in elementary calculus use Euclidean geometry. This article takes such a problem and solves it in hyperbolic and in spherical geometry instead. The solution requires only the ability to compute distances and intersections of points in these geometries. The dramatically different results we obtain illustrate the effect…
Effect of baffles on inflow patterns in spherical containers during weightlessness
NASA Technical Reports Server (NTRS)
Labus, T. L.; Aydelott, J. C.; Andracchio, C. R.
1972-01-01
An experimental investigation of isothermal liquid inflow patterns in a spherical container during weightlessness was conducted in a 2.2-Second Zero-Gravity Facility. The test liquids employed exhibited an essentially zero-degree static contact angle on the surface of the container. Qualitative results are presented for both baffled and unbaffled containers describing the uniformity of tank wall wetting and the liquid loss through two symmetrically located vents.
Understanding singularities — Classical and quantum
NASA Astrophysics Data System (ADS)
Konkowski, Deborah A.; Helliwell, Thomas M.
2016-01-01
The definitions of classical and quantum singularities are reviewed. Examples are given of both as well as their utility in general relativity. In particular, the classical and quantum singularity structure of certain interesting conformally static spherically symmetric spacetimes modeling scalar field collapse are reviewed. The spacetimes include the Roberts spacetime, the Husain-Martinez-Nuñez spacetime and the Fonarev spacetime. The importance of understanding spacetime singularity structure is discussed.
Continuity and Separation in Symmetric Topologies
ERIC Educational Resources Information Center
Harris, J.; Lynch, M.
2007-01-01
In this note, it is shown that in a symmetric topological space, the pairs of sets separated by the topology determine the topology itself. It is then shown that when the codomain is symmetric, functions which separate only those pairs of sets that are already separated are continuous, generalizing a result found by M. Lynch.
Varying electric charge in multiscale spacetimes
NASA Astrophysics Data System (ADS)
Calcagni, Gianluca; Magueijo, João; Fernández, David Rodríguez
2014-01-01
We derive the covariant equations of motion for Maxwell field theory and electrodynamics in multiscale spacetimes with weighted Laplacian. An effective spacetime-dependent electric charge of geometric origin naturally emerges from the theory, thus giving rise to a varying fine-structure constant. The theory is compared with other varying-coupling models, such as those with a varying electric charge or varying speed of light. The theory is also confronted with cosmological observations, which can place constraints on the characteristic scales in the multifractional measure. We note that the model considered here is fundamentally different from those previously proposed in the literature, either of the varying-e or varying-c persuasion.
Swimming versus swinging effects in spacetime
Gueron, Eduardo; Maia, Clovis A. S.; Matsas, George E. A.
2006-01-15
Wisdom has recently unveiled a new relativistic effect, called 'spacetime swimming', where quasirigid free bodies in curved spacetimes can 'speed up', 'slow down' or 'deviate' their falls by performing local cyclic shape deformations. We show here that for fast enough cycles this effect dominates over a nonrelativistic related one, named here 'space swinging', where the fall is altered through nonlocal cyclic deformations in Newtonian gravitational fields. We expect, therefore, to clarify the distinction between both effects leaving no room to controversy. Moreover, the leading contribution to the swimming effect predicted by Wisdom is enriched with a higher order term and the whole result is generalized to be applicable in cases where the tripod is in large redshift regions.
Quantum singularities in the BTZ spacetime
Pitelli, Joao Paulo M.; Letelier, Patricio S.
2008-06-15
The spinless Banados-Teiltelboim-Zanelli spacetime is considered in the quantum theory context. Specifically, we study the case of a negative mass parameter using quantum test particles obeying the Klein-Gordon and Dirac equations. We study if this classical singular spacetime, with a naked singularity at the origin, remains singular when tested with quantum particles. The need for additional information near the origin is confirmed for massive scalar particles and all of the possible boundary conditions necessary to turn the spatial portion of the wave operator self-adjoint are found. When tested by massless scalar particles or fermions, the singularity is ''healed'' and no extra boundary condition is needed. Near infinity, no boundary conditions are necessary.
Black hole evaporation rates without spacetime.
Braunstein, Samuel L; Patra, Manas K
2011-08-12
Verlinde recently suggested that gravity, inertia, and even spacetime may be emergent properties of an underlying thermodynamic theory. This vision was motivated in part by Jacobson's 1995 surprise result that the Einstein equations of gravity follow from the thermodynamic properties of event horizons. Taking a first tentative step in such a program, we derive the evaporation rate (or radiation spectrum) from black hole event horizons in a spacetime-free manner. Our result relies on a Hilbert space description of black hole evaporation, symmetries therein which follow from the inherent high dimensionality of black holes, global conservation of the no-hair quantities, and the existence of Penrose processes. Our analysis is not wedded to standard general relativity and so should apply to extended gravity theories where we find that the black hole area must be replaced by some other property in any generalized area theorem. PMID:21902381
A spacetime cloak, or a history editor
NASA Astrophysics Data System (ADS)
McCall, Martin W.; Favaro, Alberto; Kinsler, Paul; Boardman, Allan
2011-02-01
We introduce a new type of electromagnetic cloak, the spacetime cloak (STC), which conceals events rather than objects. Non-emitting events occurring during a restricted period are never suspected by a distant observer. The cloak works by locally manipulating the speed of light of an initially uniform light distribution, whilst the light rays themselves always follow straight paths. Any 'perfect' spacetime cloak would necessarily rely upon the technology of electromagnetic metamaterials, which has already been shown to be capable of deforming light in ways hitherto unforeseen—to produce, for example, an electromagnetic object cloak. Nevertheless, we show how it is possible to use intensity-dependent refractive indices to construct an approximate STC, an implementation that would enable the distinct signature of successful event cloaking to be observed. Potential demonstrations include systems that apparently violate quantum statistics, 'interrupt-without-interrupt' computation on convergent data channels and the illusion of a Star Trek transporter.
Black hole evaporation rates without spacetime.
Braunstein, Samuel L; Patra, Manas K
2011-08-12
Verlinde recently suggested that gravity, inertia, and even spacetime may be emergent properties of an underlying thermodynamic theory. This vision was motivated in part by Jacobson's 1995 surprise result that the Einstein equations of gravity follow from the thermodynamic properties of event horizons. Taking a first tentative step in such a program, we derive the evaporation rate (or radiation spectrum) from black hole event horizons in a spacetime-free manner. Our result relies on a Hilbert space description of black hole evaporation, symmetries therein which follow from the inherent high dimensionality of black holes, global conservation of the no-hair quantities, and the existence of Penrose processes. Our analysis is not wedded to standard general relativity and so should apply to extended gravity theories where we find that the black hole area must be replaced by some other property in any generalized area theorem.
Gravitational collapse of generalized Vaidya spacetime
NASA Astrophysics Data System (ADS)
Mkenyeleye, Maombi D.; Goswami, Rituparno; Maharaj, Sunil D.
2014-09-01
We study the gravitational collapse of a generalized Vaidya spacetime in the context of the cosmic censorship hypothesis. We develop a general mathematical framework to study the conditions on the mass function so that future directed nonspacelike geodesics can terminate at the singularity in the past. Thus our result generalizes earlier works on gravitational collapse of the combinations of Type-I and Type-II matter fields. Our analysis shows transparently that there exist classes of generalized Vaidya mass functions for which the collapse terminates with a locally naked central singularity. We calculate the strength of these singularities to show that they are strong curvature singularities and there can be no extension of spacetime through them.
On the initial value problem for the wave equation in Friedmann-Robertson-Walker space-times.
Abbasi, Bilal; Craig, Walter
2014-09-01
The propagator W(t0,t1)(g,h) for the wave equation in a given space-time takes initial data (g(x),h(x)) on a Cauchy surface {(t,x) : t=t0} and evaluates the solution (u(t1,x),∂ tu(t1,x)) at other times t1. The Friedmann-Robertson-Walker space-times are defined for t0,t1>0, whereas for t0→0, there is a metric singularity. There is a spherical means representation for the general solution of the wave equation with the Friedmann-Robertson-Walker background metric in the three spatial dimensional cases of curvature K=0 and K=-1 given by S. Klainerman and P. Sarnak. We derive from the expression of their representation three results about the wave propagator for the Cauchy problem in these space-times. First, we give an elementary proof of the sharp rate of time decay of solutions with compactly supported data. Second, we observe that the sharp Huygens principle is not satisfied by solutions, unlike in the case of three-dimensional Minkowski space-time (the usual Huygens principle of finite propagation speed is satisfied, of course). Third, we show that for 0
On the initial value problem for the wave equation in Friedmann-Robertson-Walker space-times.
Abbasi, Bilal; Craig, Walter
2014-09-01
The propagator W(t 0,t 1)(g,h) for the wave equation in a given space-time takes initial data (g(x),h(x)) on a Cauchy surface {(t,x) : t=t 0} and evaluates the solution (u(t 1,x),∂ t u(t 1,x)) at other times t 1. The Friedmann-Robertson-Walker space-times are defined for t 0,t 1>0, whereas for t 0→0, there is a metric singularity. There is a spherical means representation for the general solution of the wave equation with the Friedmann-Robertson-Walker background metric in the three spatial dimensional cases of curvature K=0 and K=-1 given by S. Klainerman and P. Sarnak. We derive from the expression of their representation three results about the wave propagator for the Cauchy problem in these space-times. First, we give an elementary proof of the sharp rate of time decay of solutions with compactly supported data. Second, we observe that the sharp Huygens principle is not satisfied by solutions, unlike in the case of three-dimensional Minkowski space-time (the usual Huygens principle of finite propagation speed is satisfied, of course). Third, we show that for 0
Principle of Spacetime and Black Hole Equivalence
NASA Astrophysics Data System (ADS)
Zhang, Tianxi
2016-06-01
Modelling the universe without relying on a set of hypothetical entities (HEs) to explain observations and overcome problems and difficulties is essential to developing a physical cosmology. The well-known big bang cosmology, widely accepted as the standard model, stands on two fundamentals, which are Einstein’s general relativity (GR) that describes the effect of matter on spacetime and the cosmological principle (CP) of spacetime isotropy and homogeneity. The field equation of GR along with the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric of spacetime derived from CP generates the Friedmann equation (FE) that governs the development and dynamics of the universe. The big bang theory has made impressive successes in explaining the universe, but still has problems and solutions of them rely on an increasing number of HEs such as inflation, dark matter, dark energy, and so on. Recently, the author has developed a new cosmological model called black hole universe, which, instead of making many those hypotheses, only includes a new single postulate (or a new principle) to the cosmology - Principle of Spacetime and Black Hole Equivalence (SBHEP) - to explain all the existing observations of the universe and overcome all the existing problems in conventional cosmologies. This study thoroughly demonstrates how this newly developed black hole universe model, which therefore stands on the three fundamentals (GR, CP, and SBHEP), can fully explain the universe as well as easily conquer the difficulties according to the well-developed physics, thus, neither needing any other hypotheses nor existing any unsolved difficulties. This work was supported by NSF/REU (Grant #: PHY-1263253) at Alabama A & M University.
Snyder dynamics in a Schwarzschild spacetime
NASA Astrophysics Data System (ADS)
Mignemi, S.; Štrajn, R.
2014-08-01
We calculate the orbits of a particle in Schwarzschild spacetime, assuming that the dynamics is governed by a Snyder symplectic structure. With this assumption, the perihelion shift of the planets acquires an additional contribution with respect to the one predicted by general relativity. Moreover, the equivalence principle is violated. If one assumes that Snyder mechanics is valid also for macroscopic systems, these results impose strong constraints on the value of the coupling parameter of the Snyder model.
Spacetime and orbits of bumpy black holes
Vigeland, Sarah J.; Hughes, Scott A.
2010-01-15
Our Universe contains a great number of extremely compact and massive objects which are generally accepted to be black holes. Precise observations of orbital motion near candidate black holes have the potential to determine if they have the spacetime structure that general relativity demands. As a means of formulating measurements to test the black hole nature of these objects, Collins and Hughes introduced ''bumpy black holes'': objects that are almost, but not quite, general relativity's black holes. The spacetimes of these objects have multipoles that deviate slightly from the black hole solution, reducing to black holes when the deviation is zero. In this paper, we extend this work in two ways. First, we show how to introduce bumps which are smoother and lead to better behaved orbits than those in the original presentation. Second, we show how to make bumpy Kerr black holes--objects which reduce to the Kerr solution when the deviation goes to zero. This greatly extends the astrophysical applicability of bumpy black holes. Using Hamilton-Jacobi techniques, we show how a spacetime's bumps are imprinted on orbital frequencies, and thus can be determined by measurements which coherently track the orbital phase of a small orbiting body. We find that in the weak field, orbits of bumpy black holes are modified exactly as expected from a Newtonian analysis of a body with a prescribed multipolar structure, reproducing well-known results from the celestial mechanics literature. The impact of bumps on strong-field orbits is many times greater than would be predicted from a Newtonian analysis, suggesting that this framework will allow observations to set robust limits on the extent to which a spacetime's multipoles deviate from the black hole expectation.
Hypermotion due to space-time deformation
NASA Astrophysics Data System (ADS)
Fil'Chenkov, Michael; Laptev, Yuri
2016-03-01
A superluminal motion (hypermotion) via M. Alcubierre’s warp drive is considered. Parameters of the warp drive have been estimated. The equations of starship geodesics have been solved. The starship velocity have been shown to exceed the speed of light, with the local velocity relative to the deformed space-time being below it. Hawking’s radiation does not prove to affect the ship interior considerably. Difficulties related to a practical realization of the hypermotion are indicated.
Vaidya spacetime for Galileon gravity's rainbow
NASA Astrophysics Data System (ADS)
Rudra, Prabir; Faizal, Mir; Ali, Ahmed Farag
2016-08-01
In this paper, we analyze Vaidya spacetime with an energy dependent metric in Galileon gravity's rainbow. This will be done using the rainbow functions which are motivated from the results obtained in loop quantum gravity approach and noncommutative geometry. We will investigate the Gravitational collapse in this Galileon gravity's rainbow. We will discuss the behavior of singularities formed from the gravitational collapse in this rainbow deformed Galileon gravity.
Anomalies in curved spacetime at finite temperature
Boschi-Filho, H. Departamento de Fisica e Quimica, Universidade Estadual Paulista, Campus de Guaratingueta, 12500 Guaratingueta, Caixa Postal 205 Sao Paulo ); Natividade, C.P. )
1992-12-15
We discuss the problem of the breakdown of conformal and gauge symmetries at finite temperature in curved-spacetime background, when the changes in the background are gradual, in order to have a well-defined quantum field theory at finite temperature. We obtain the expressions for Seeley's coefficients and the heat-kernel expansion in this regime. As applications, we consider the self-interacting [lambda][phi][sup 4] and chiral Schwinger models in curved backgrounds at finite temperature.
A statistical mechanical problem in Schwarzschild spacetime
NASA Astrophysics Data System (ADS)
Collas, Peter; Klein, David
2007-06-01
We use Fermi coordinates to calculate the canonical partition function for an ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the validity of the results we prove theorems for limiting cases. We recover the Newtonian gas law subject only to tidal forces in the Newtonian limit. Additionally we recover the special relativistic gas law as the radius of the orbit increases to infinity. We also discuss how the method can be extended to the non ideal gas case.
Symmetrical thalamic lesions in infants.
Eicke, M; Briner, J; Willi, U; Uehlinger, J; Boltshauser, E
1992-01-01
Clinical observations and findings on imaging are reported in six newborns with symmetrical thalamic lesions (STL). In three cases the diagnosis was confirmed by postmortem examination. Characteristic observations in this series and 17 previously reported cases include no evidence of perinatal asphyxia, high incidence of polyhydramnios, absent suck and swallow, absent primitive reflexes, appreciable spasticity at or within days of birth, lack of psychomotor development, and death within days or months. Characteristic pathological findings include loss of neurons, astrogliosis, and 'incrusted' neurons particularly in the thalamus. In two thirds of cases the basal ganglia and brain stem are involved as well. A hypoxic-ischaemic event occurring two to four weeks before birth is most likely responsible for STL. Bilateral thalamic calcification can often, but not always, be demonstrated in the newborn period by computed tomography and/or cranial ultrasound. The presence of these calcifications and the observation of spasticity at birth imply that the responsible insult occurred at least two to four weeks earlier. The small number of published cases with STL suggest that it may be easily missed. Images Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 PMID:1536580
Baryon symmetric big bang cosmology
NASA Technical Reports Server (NTRS)
Stecker, F. W.
1978-01-01
Both the quantum theory and Einsteins theory of special relativity lead to the supposition that matter and antimatter were produced in equal quantities during the big bang. It is noted that local matter/antimatter asymmetries may be reconciled with universal symmetry by assuming (1) a slight imbalance of matter over antimatter in the early universe, annihilation, and a subsequent remainder of matter; (2) localized regions of excess for one or the other type of matter as an initial condition; and (3) an extremely dense, high temperature state with zero net baryon number; i.e., matter/antimatter symmetry. Attention is given to the third assumption, which is the simplest and the most in keeping with current knowledge of the cosmos, especially as pertains the universality of 3 K background radiation. Mechanisms of galaxy formation are discussed, whereby matter and antimatter might have collided and annihilated each other, or have coexisted (and continue to coexist) at vast distances. It is pointed out that baryon symmetric big bang cosmology could probably be proved if an antinucleus could be detected in cosmic radiation.
Parity-time-symmetric teleportation
NASA Astrophysics Data System (ADS)
Ra'di, Y.; Sounas, D. L.; Alù, A.; Tretyakov, S. A.
2016-06-01
We show that electromagnetic plane waves can be fully "teleported" through thin, nearly fully reflective sheets, assisted by a pair of parity-time-symmetric lossy and active sheets in front and behind the screen. The proposed structure is able to almost perfectly absorb incident waves over a wide range of frequency and incidence angles, while waves having a specific frequency and incidence angle are replicated behind the structure in synchronization with the input signal. It is shown that the proposed structure can be designed to teleport waves at any desired frequency and incidence angle. Furthermore, we generalize the proposed concept to the case of teleportation of electromagnetic waves over electrically long distances, enabling full absorption at one surface and the synthesis of the same signal at another point located electrically far away from the first surface. The physical principle behind this selective teleportation is discussed, and similarities and differences with tunneling and cloaking concepts based on PT symmetry are investigated. From the application point of view, the proposed structure works as an extremely selective filter, both in frequency and spatial domains.
Spacetime approach to force-free magnetospheres
NASA Astrophysics Data System (ADS)
Gralla, Samuel E.; Jacobson, Ted
2014-12-01
Force-free electrodynamics (FFE) describes magnetically dominated relativistic plasma via non-linear equations for the electromagnetic field alone. Such plasma is thought to play a key role in the physics of pulsars and active black holes. Despite its simple covariant formulation, FFE has primarily been studied in 3+1 frameworks, where spacetime is split into space and time. In this paper, we systematically develop the theory of force-free magnetospheres taking a spacetime perspective. Using a suite of spacetime tools and techniques (notably exterior calculus), we cover (1) the basics of the theory, (2) exact solutions that demonstrate the extraction and transport of the rotational energy of a compact object (in the case of a black hole, the Blandford-Znajek mechanism), (3) the behaviour of current sheets, (4) the general theory of stationary, axisymmetric magnetospheres, and (5) general properties of pulsar and black hole magnetospheres. We thereby synthesize, clarify, and generalize known aspects of the physics of force-free magnetospheres, while also introducing several new results.
Relativistic Positioning System in perturbed spacetime
NASA Astrophysics Data System (ADS)
Kostić, Uroš; Horvat, Martin; Gomboc, Andreja
2015-11-01
We present a variant of a Global Navigation Satellite System called a Relativistic Positioning System (RPS), which is based on emission coordinates. We modelled the RPS dynamics in a spacetime around Earth, described by a perturbed Schwarzschild metric, where we included the perturbations due to Earth multipoles (up to the 6th), the Moon, the Sun, Venus, Jupiter, solid tide, ocean tide, and Kerr rotation effect. The exchange of signals between the satellites and a user was calculated using a ray-tracing method in the Schwarzschild spacetime. We find that positioning in a perturbed spacetime is feasible and is highly accurate already with standard numerical procedures: the positioning algorithms used to transform between the emission and the Schwarzschild coordinates of the user are very accurate and time efficient—on a laptop it takes 0.04 s to determine the user’s spatial and time coordinates with a relative accuracy of {10}-28-{10}-26 and {10}-32-{10}-30, respectively.
Asymptotically flat space-times: an enigma
NASA Astrophysics Data System (ADS)
Newman, Ezra T.
2016-07-01
We begin by emphasizing that we are dealing with standard Einstein or Einstein-Maxwell theory—absolutely no new physics has been inserted. The fresh item is that the well-known asymptotically flat solutions of the Einstein-Maxwell theory are transformed to a new coordinate system with surprising and (seemingly) inexplicable results. We begin with the standard description of (Null) asymptotically flat space-times described in conventional Bondi-coordinates. After transforming the variables (mainly the asymptotic Weyl tensor components) to a very special set of Newman-Unti (NU) coordinates, we find a series of relations totally mimicking standard Newtonian classical mechanics and Maxwell theory. The surprising and troubling aspect of these relations is that the associated motion and radiation does not take place in physical space-time. Instead these relations takes place in an unusual inherited complex four-dimensional manifold referred to as H-space that has no immediate relationship with space-time. In fact these relations appear in two such spaces, H-space and its dual space \\bar{H}.
Perturbative Critical Behavior from Spacetime Dependent Couplings
Dong, Xi; Horn, Bart; Silverstein, Eva; Torroba, Gonzalo
2012-08-03
We find novel perturbative fixed points by introducing mildly spacetime-dependent couplings into otherwise marginal terms. In four-dimensional QFT, these are physical analogues of the small-{epsilon} Wilson-Fisher fixed point. Rather than considering 4-{epsilon} dimensions, we stay in four dimensions but introduce couplings whose leading spacetime dependence is of the form {lambda}x{sup {kappa}}{mu}{sup {kappa}}, with a small parameter {kappa} playing a role analogous to {epsilon}. We show, in {phi}{sup 4} theory and in QED and QCD with massless flavors, that this leads to a critical theory under perturbative control over an exponentially wide window of spacetime positions x. The exact fixed point coupling {lambda}{sub *}(x) in our theory is identical to the running coupling of the translationally invariant theory, with the scale replaced by 1/x. Similar statements hold for three-dimensional {phi}{sup 6} theories and two-dimensional sigma models with curved target spaces. We also describe strongly coupled examples using conformal perturbation theory.
Bidirectional slapper detonators in spherical explosion systems
NASA Astrophysics Data System (ADS)
Martinez, Ernest C.
1990-11-01
A bidirectional slapper detonator has been proven effective for producing a spherically expanding shock wave. Two bridge foils are used to propel flyers in opposite directions, thereby initiating two explosive pellets, each embedded in one hemisphere of a spherical system. This detonation system produces a nearly perfect spherically expanding detonation front.
Symmetric Monotone Venn Diagrams with Seven Curves
NASA Astrophysics Data System (ADS)
Cao, Tao; Mamakani, Khalegh; Ruskey, Frank
An n-Venn diagram consists of n curves drawn in the plane in such a way that each of the 2 n possible intersections of the interiors and exteriors of the curves forms a connected non-empty region. A k-region in a diagram is a region that is in the interior of precisely k curves. A n-Venn diagram is symmetric if it has a point of rotation about which rotations of the plane by 2π/n radians leaves the diagram fixed; it is polar symmetric if it is symmetric and its stereographic projection about the infinite outer face is isomorphic to the projection about the innermost face. A Venn diagram is monotone if every k-region is adjacent to both some (k - 1)-region (if k > 0) and also to some k + 1 region (if k < n). A Venn diagram is simple if at most two curves intersect at any point. We prove that the "Grünbaum" encoding uniquely identifies monotone simple symmetric n-Venn diagrams and describe an algorithm that produces an exhaustive list of all of the monotone simple symmetric n-Venn diagrams. There are exactly 23 simple monotone symmetric 7-Venn diagrams, of which 6 are polar symmetric.
The symmetric extendibility of quantum states
NASA Astrophysics Data System (ADS)
Nowakowski, Marcin L.
2016-09-01
Studies on the symmetric extendibility of quantum states have become particularly important in the context of the analysis of one-way quantum measures of entanglement, and the distillability and security of quantum protocols. In this paper we analyze composite systems containing a symmetric extendible part, with particular attention devoted to the one-way security of such systems. Further, we introduce a new one-way entanglement monotone based on the best symmetric approximation of a quantum state and the extendible number of a quantum state. We underpin these results with geometric observations about the structures of multi-party settings which posses substantial symmetric extendible components in their subspaces. The impossibility of reducing the maximal symmetric extendibility by means of the one-way local operations and classical communication method is pointed out on multiple copies. Finally, we state a conjecture linking symmetric extendibility with the one-way distillability and security of all quantum states, analyzing the behavior of a private key in the neighborhood of symmetric extendible states.
Domain structure of black hole space-times
Harmark, Troels
2009-07-15
We introduce the domain structure for stationary black hole space-times. The domain structure lives on the submanifold of fixed points of the Killing vector fields. Depending on which Killing vector field has fixed points the submanifold is naturally divided into domains. The domain structure provides invariants of the space-time, both topological and continuous. It is defined for any space-time dimension and any number of Killing vector fields. We examine the domain structure for asymptotically flat space-times and find a canonical form for the metric of such space-times. The domain structure generalizes the rod structure introduced for space-times with D-2 commuting Killing vector fields. We analyze in detail the domain structure for Minkowski space, the Schwarzschild-Tangherlini black hole and the Myers-Perry black hole in six and seven dimensions. Finally, we consider the possible domain structures for asymptotically flat black holes in six and seven dimensio0008.
Sphere-plate Casimir interaction in (D + 1)-dimensional spacetime
NASA Astrophysics Data System (ADS)
Teo, L. P.
2014-04-01
In this paper, we derive the formula for the Casimir interaction energy between a sphere and a plate in (D + 1)-dimensional Minkowski spacetime. It is assumed that the scalar field satisfies the Dirichlet or Neumann boundary conditions on the sphere and the plate. As in the D = 3 case, the formula is of TGTG type. One of our main contributions is deriving the translation matrices which express the change of bases between plane waves and spherical waves for general D. Using orthogonality of Gegenbauer polynomials, it turns out that the final TGTG formula for the Casimir interaction energy can be simplified to one that is similar to the D = 3 case. To illustrate the application of the formula, both large separation and small separation asymptotic behaviors of the Casimir interaction energy are computed. The large separation leading term is proportional to L-D+1 if the sphere is imposed with Dirichlet boundary condition, and to L-D-1 if the sphere is imposed with Neumann boundary condition, where L is distance from the center of the sphere to the plane. For the small separation asymptotic behavior, it is shown that the leading term is equal to the one obtained using proximity force approximation. The next-to-leading order term is also computed using perturbation method. It is shown that when the space dimension D is larger than 5, the next-to-leading order has sign opposite to the leading order term. Moreover, the ratio of the next-to-leading order term to the leading order term is linear in D, indicating a larger correction at higher dimensions.
Spacetime geodesy and the LAGEOS-3 satellite experiment
Miller, W.A.; Chen, Kaiyou; Habib, S.; Kheyfets, A.; Holz, D.E.
1996-04-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). LAGEOS-1 is a dense spherical satellite whose tracking accuracy is such as to yield a medium-term inertial reference frame and that is used as an adjunct to more difficult and more data-intensive absolute frame measurements. LAGEOS-3, an identical satellite to be launched into an orbit complementary to that of LAGEOS-1, would experience an equal and opposite classical precession to that of LAGEOS- 1. Besides providing a more accurate real-time measurement of the earth`s length of day and polar wobble, this paired-satellite system would provide the first direct measurement of the general relativistic frame-dragging effect. Of the five dominant error sources in this experiment, the largest one involves surface forces on the satellite and their consequent impact on the orbital nodal precession. The surface forces are a function of the spin dynamics of the satellite. We have modeled the spin dynamics of a LAGEOS-type satellite and used this spin model to estimate the impact of the thermal rocketing effect on the LAGEOS-3 experiment. We have also performed an analytic tensor expansion of Synge`s world function to better reveal the nature of the predicted frame-dragging effect. We showed that this effect is not due to the Riemann curvature tensor, but rather is a ``potential effect`` arising from the acceleration of the world lines in the Kerr spacetime geometry.
Sphere-plate Casimir interaction in (D + 1)-dimensional spacetime
Teo, L. P.
2014-04-15
In this paper, we derive the formula for the Casimir interaction energy between a sphere and a plate in (D + 1)-dimensional Minkowski spacetime. It is assumed that the scalar field satisfies the Dirichlet or Neumann boundary conditions on the sphere and the plate. As in the D = 3 case, the formula is of TGTG type. One of our main contributions is deriving the translation matrices which express the change of bases between plane waves and spherical waves for general D. Using orthogonality of Gegenbauer polynomials, it turns out that the final TGTG formula for the Casimir interaction energy can be simplified to one that is similar to the D = 3 case. To illustrate the application of the formula, both large separation and small separation asymptotic behaviors of the Casimir interaction energy are computed. The large separation leading term is proportional to L{sup −D+1} if the sphere is imposed with Dirichlet boundary condition, and to L{sup −D−1} if the sphere is imposed with Neumann boundary condition, where L is distance from the center of the sphere to the plane. For the small separation asymptotic behavior, it is shown that the leading term is equal to the one obtained using proximity force approximation. The next-to-leading order term is also computed using perturbation method. It is shown that when the space dimension D is larger than 5, the next-to-leading order has sign opposite to the leading order term. Moreover, the ratio of the next-to-leading order term to the leading order term is linear in D, indicating a larger correction at higher dimensions.
Symmetric Kullback-Leibler Metric Based Tracking Behaviors for Bioinspired Robotic Eyes
Liu, Hengli; Luo, Jun; Wu, Peng; Xie, Shaorong; Li, Hengyu
2015-01-01
A symmetric Kullback-Leibler metric based tracking system, capable of tracking moving targets, is presented for a bionic spherical parallel mechanism to minimize a tracking error function to simulate smooth pursuit of human eyes. More specifically, we propose a real-time moving target tracking algorithm which utilizes spatial histograms taking into account symmetric Kullback-Leibler metric. In the proposed algorithm, the key spatial histograms are extracted and taken into particle filtering framework. Once the target is identified, an image-based control scheme is implemented to drive bionic spherical parallel mechanism such that the identified target is to be tracked at the center of the captured images. Meanwhile, the robot motion information is fed forward to develop an adaptive smooth tracking controller inspired by the Vestibuloocular Reflex mechanism. The proposed tracking system is designed to make the robot track dynamic objects when the robot travels through transmittable terrains, especially bumpy environment. To perform bumpy-resist capability under the condition of violent attitude variation when the robot works in the bumpy environment mentioned, experimental results demonstrate the effectiveness and robustness of our bioinspired tracking system using bionic spherical parallel mechanism inspired by head-eye coordination. PMID:27019592
Symmetric Kullback-Leibler Metric Based Tracking Behaviors for Bioinspired Robotic Eyes.
Liu, Hengli; Luo, Jun; Wu, Peng; Xie, Shaorong; Li, Hengyu
2015-01-01
A symmetric Kullback-Leibler metric based tracking system, capable of tracking moving targets, is presented for a bionic spherical parallel mechanism to minimize a tracking error function to simulate smooth pursuit of human eyes. More specifically, we propose a real-time moving target tracking algorithm which utilizes spatial histograms taking into account symmetric Kullback-Leibler metric. In the proposed algorithm, the key spatial histograms are extracted and taken into particle filtering framework. Once the target is identified, an image-based control scheme is implemented to drive bionic spherical parallel mechanism such that the identified target is to be tracked at the center of the captured images. Meanwhile, the robot motion information is fed forward to develop an adaptive smooth tracking controller inspired by the Vestibuloocular Reflex mechanism. The proposed tracking system is designed to make the robot track dynamic objects when the robot travels through transmittable terrains, especially bumpy environment. To perform bumpy-resist capability under the condition of violent attitude variation when the robot works in the bumpy environment mentioned, experimental results demonstrate the effectiveness and robustness of our bioinspired tracking system using bionic spherical parallel mechanism inspired by head-eye coordination.
Properties of spatial wormholes and other splittable spacetimes
NASA Astrophysics Data System (ADS)
Price, Richard H.
2016-03-01
The usefulness of the Morris-Thorne spatial wormhole motivates a consideration of a generalization to a class of similarly simple spacetime geometries. In this generalization, a "splittable" spacetime can be considered to be built of a parallel stack of identical 3-geometries. Such spacetimes do not have the usual manifestation of gravity, but in Einstein's theory they will in general have mass-energy density.
Numerical study of spherical Taylor-Couette flow
NASA Technical Reports Server (NTRS)
Yang, R.-J.
1989-01-01
A new technique to simulate Taylor vortices in a spherical gap between a rotating inner sphere and a stationary outer one has been developed and tested. Paths leading to zero-, one-, and two-vortex flows are designed heuristically. Fictitious symmetric boundaries near the equator are imposed, and the choice of the location of the fictitious boundaries is determined by either one- or two-vortex flow being stimulated. The imposition of one or two fictitious boundaries during the initial calculation generates the state suitable for one-or two-vortex flow to exist. After removing the fictitious boundaries, the flow settles down into its own attractor. Using this method, the three steady flow modes can be simulated by using a half domain. The technique can converge to desired flows very fast, and its results show excellent agreement with experimental ones.
Measurement of Poloidal Velocity on the National Spherical Torus Experiment
Ronald E. Bell and Russell Feder
2010-06-04
A diagnostic suite has been developed to measure impurity poloidal flow using charge exchange recombination spectroscopy on the National Spherical Torus Experiment. Toroidal and poloidal viewing systems measure all quantities required to determine the radial electric field. Two sets of up/down symmetric poloidal views are used to measure both active emission in the plane of the neutral heating beams and background emission in a radial plane away from the neutral beams. Differential velocity measurements isolate the line-integrated poloidal velocity from apparent flows due to the energy-dependent chargeexchange cross section. Six f/1.8 spectrometers measure 276 spectra to obtain 75 active and 63 background channels every 10 ms. Local measurements from a similar midplane toroidal viewing system are mapped into two dimensions to allow the inversion of poloidal line-integrated measurements to obtain local poloidal velocity profiles. Radial resolution after inversion is 0.6-1.8 cm from the plasma edge to the center.
Spherical perfect lens: Solutions of Maxwell's equations for spherical geometry
NASA Astrophysics Data System (ADS)
Anantha Ramakrishna, S.; Pendry, J. B.
2004-03-01
It has been recently proved that a slab of negative refractive index material acts as a perfect lens in that it makes accessible the subwavelength image information contained in the evanescent modes of a source. Here we elaborate on perfect lens solutions to spherical shells of negative refractive material where magnification of the near-field images becomes possible. The negative refractive materials then need to be spatially dispersive with ɛ(r)˜1/r and μ(r)˜1/r. We concentrate on lenslike solutions for the extreme near-field limit. Then the conditions for the TM and TE polarized modes become independent of μ and ɛ, respectively.
Comparison of spacetime defects which are homeomorphic but not diffeomorphic
Klinkhamer, F. R. Sorba, F.
2014-11-15
Certain remnants of a quantum spacetime foam can be modeled by a distribution of defects embedded in a flat classical spacetime. The presence of such spacetime defects affects the propagation of elementary particles. In this article, we show explicitly that both topology and differential structure of the defects are important for the particle motion. Specifically, we consider three types of spacetime defects which are described by the same topological manifold R×(RP{sup 3}−(point)) but which are not diffeomorphic to each other. We investigate the propagation of a massless scalar field over the three different manifolds and find different solutions of the Klein–Gordon equation.
Gravitational tension, spacetime pressure and black hole volume
NASA Astrophysics Data System (ADS)
Armas, Jay; Obers, Niels A.; Sanchioni, Marco
2016-09-01
We study the first law of black hole thermodynamics in the presence of surrounding gravitational fields and argue that variations of these fields are naturally incorporated in the first law by defining gravitational tension or gravitational binding energy. We demonstrate that this notion can also be applied in Anti-de Sitter spacetime, in which the surrounding gravitational field is sourced by a cosmological fluid, therefore showing that spacetime volume and gravitational tension encode the same physics as spacetime pressure and black hole volume. We furthermore show that it is possible to introduce a definition of spacetime pressure and black hole volume for any spacetime with characteristic length scales which does not necessarily require a cosmological constant sourcing Einstein equations. However, we show that black hole volume is non-universal in the flat spacetime limit, questioning its significance. We illustrate these ideas by studying the resulting black hole volume of Kaluza-Klein black holes and of a toy model for a black hole binary system in five spacetime dimensions (the black saturn solution) as well as of several novel perturbative black hole solutions. These include the higher-dimensional Kerr-Newman solution in Anti-de Sitter spacetime as well as other black holes in plane wave and Lifshitz spacetimes.
Constant mean curvature slicings of Kantowski-Sachs spacetimes
Heinzle, J. Mark
2011-04-15
We investigate existence, uniqueness, and the asymptotic properties of constant mean curvature (CMC) slicings in vacuum Kantowski-Sachs spacetimes with positive cosmological constant. Since these spacetimes violate the strong energy condition, most of the general theorems on CMC slicings do not apply. Although there are in fact Kantowski-Sachs spacetimes with a unique CMC foliation or CMC time function, we prove that there also exist Kantowski-Sachs spacetimes with an arbitrary number of (families of) CMC slicings. The properties of these slicings are analyzed in some detail.
Exotic spacetimes, superconducting strings with linear momentum, and (not quite) all that
NASA Astrophysics Data System (ADS)
Gleiser, Reinaldo J.; Tiglio, Manuel H.
2000-05-01
We derive the general exact vacuum metrics associated with a stationary (nonstatic), nonrotating, cylindrically symmetric source. An analysis of the geometry described by these vacuum metrics shows that they contain a subfamily of metrics that, although admitting a consistent time orientation, displays ``exotic'' properties, such as ``trapping'' of geodesics and closed causal curves through every point. The possibility that such spacetimes could be generated by a superconducting string, endowed with a neutral current and momentum, has recently been considered by Thatcher and Morgan. Our results, however, differ from those found by Thatcher and Morgan, and the discrepancy is explained. We also analyze the general possibility of constructing physical sources for the exotic metrics, and find that, under certain restrictions, they must always violate the dominant energy condition (DEC). We illustrate our results by explicitly analyzing the case of concentric shells, where we find that in all cases the external vacuum metric is nonexotic if the matter in the shells satisfies the DEC.
Martingale Rosenthal inequalities in symmetric spaces
Astashkin, S V
2014-12-31
We establish inequalities similar to the classical Rosenthal inequalities for sequences of martingale differences in general symmetric spaces; a central role is played here by the predictable quadratic characteristic of a martingale. Bibliography: 26 titles.
PT-Symmetric Quantum Field Theory
NASA Astrophysics Data System (ADS)
Bender, Carl M.
2011-09-01
In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H†) can be weakened and generalized to the requirement that a Hamiltonian be PT symmetric ([H,PT] = 0); that is, invariant under combined space reflection and time reversal. Weakening the constraint of Hermiticity allows one to consider new kinds of physically acceptable Hamiltonians and, in effect, it amounts to extending quantum mechanics from the real (Hermitian) domain into the complex domain. Much work has been done on the analysis of various PT-symmetric quantum-mechanical models. However, only very little analysis has been done on PT-symmetric quantum-field-theoretic models. Here, we describe some of what has been done in the context of PT-symmetric quantum field theory and describe some possible fundamental applications.
Origin of symmetric PMNS and CKM matrices
NASA Astrophysics Data System (ADS)
Rodejohann, Werner; Xu, Xun-Jie
2015-03-01
The Pontecorvo-Maki-Nakagawa-Sakata and Cabibbo-Kobayashi-Maskawa matrices are phenomenologically close to symmetric, and a symmetric form could be used as zeroth-order approximation for both matrices. We study the possible theoretical origin of this feature in flavor symmetry models. We identify necessary geometric properties of discrete flavor symmetry groups that can lead to symmetric mixing matrices. Those properties are actually very common in discrete groups such as A4 , S4 , or Δ (96 ) . As an application of our theorem, we generate a symmetric lepton mixing scheme with θ12=θ23=36.21 ° ; θ13=12.20 ° , and δ =0 , realized with the group Δ (96 ) .
A method of spherical harmonic analysis in the geosciences via hierarchical Bayesian inference
NASA Astrophysics Data System (ADS)
Muir, J. B.; Tkalčić, H.
2015-11-01
The problem of decomposing irregular data on the sphere into a set of spherical harmonics is common in many fields of geosciences where it is necessary to build a quantitative understanding of a globally varying field. For example, in global seismology, a compressional or shear wave speed that emerges from tomographic images is used to interpret current state and composition of the mantle, and in geomagnetism, secular variation of magnetic field intensity measured at the surface is studied to better understand the changes in the Earth's core. Optimization methods are widely used for spherical harmonic analysis of irregular data, but they typically do not treat the dependence of the uncertainty estimates on the imposed regularization. This can cause significant difficulties in interpretation, especially when the best-fit model requires more variables as a result of underestimating data noise. Here, with the above limitations in mind, the problem of spherical harmonic expansion of irregular data is treated within the hierarchical Bayesian framework. The hierarchical approach significantly simplifies the problem by removing the need for regularization terms and user-supplied noise estimates. The use of the corrected Akaike Information Criterion for picking the optimal maximum degree of spherical harmonic expansion and the resulting spherical harmonic analyses are first illustrated on a noisy synthetic data set. Subsequently, the method is applied to two global data sets sensitive to the Earth's inner core and lowermost mantle, consisting of PKPab-df and PcP-P differential traveltime residuals relative to a spherically symmetric Earth model. The posterior probability distributions for each spherical harmonic coefficient are calculated via Markov Chain Monte Carlo sampling; the uncertainty obtained for the coefficients thus reflects the noise present in the real data and the imperfections in the spherical harmonic expansion.
van Vleck determinants: Traversable wormhole spacetimes
Visser, M. )
1994-04-15
Prompted by various questions regarding the putative existence, stability, and chronological properties of traversable wormholes, a number of authors have presented calculations of the renormalized stress-energy tensor in wormhole spacetimes. In particular, the use of point-splitting techniques leads to expressions that contain the van Vleck determinant as a common prefactor. Recent technical advances permit one to undertake extensive computations of the van Vleck determinant in traversable wormhole spacetimes, at least in the short-throat flat-space approximation. This paper presents several such computations for various model spacetimes. Implications with regard to Hawking's chronology protection conjecture are discussed. In particular, any attempt to transform a single isolated wormhole into a time machine results in large vacuum polarization effects. These vacuum polarization effects are sufficient to disrupt the internal structure of the wormhole long before the onset of Planck scale physics, and before the onset of time travel. Thus for isolated wormholes, vacuum polarization effects are sufficient to enforce Hawking's chronology protection conjecture. On the other hand, it is possible to conceive of a putative time machine built out of two or more wormholes, each of which taken in isolation is not itself a time machine. Such Roman configurations'' are much more subtle to analyze. For reasonable'' configurations (traversable by humans) the vacuum polarization effects in such multiple wormhole putative time machines become large long before the onset of Planck scale physics. The disruption scale for would-be traversable time machines'' is well above the Planck length. On the other hand, for some particularly bizarre configurations (not traversable by humans) the vacuum polarization effects can be arranged to be arbitrarily small at the onset of Planck scale physics.
Ultraintense Laser-Driven Relativistic Hydrodynamics for Plane Symmetric Systems
NASA Astrophysics Data System (ADS)
Talamo, James
We consider the relativistic hydrodynamics of a plane symmetric, charged fluid system driven by an ultra-violent, ultra-intense laser. The resulting particle motion will be relativistic due to the strength of the laser. The fluid will accelerate violently with respect to an observer in the laboratory, so although the arena for the evolution is a smooth Minkowski spacetime, methods of general relativity will be invoked. Many systems in relativity can be cast into field theories, and we first extend the variational formulation of special relativity to laser-matter interactions. From this, a full set of four Euler equations arise that govern the hydrodynamics of a general 4-dimensional laser-matter system. The plane symmetry, however, naturally gives rise to two Killing vectors. This allows for a 2+2 reduction process to be used to analyze the system. This will allow for a reformulation of the 4-dimensional system of interacting particles as a 2-dimensional system of interacting plasma sheets. The transverse particle motion is shown to produce a change in the "effective mass" of the plasma sheets, which allows one to consider the sheets as a single entity. To achieve this, we first give the details of this 2+2 formalism and show how it can be used to write the underlying space time as a product of a base manifold and transverse Euclidean planes. We then establish a natural isomorphism between the geometrical objects (vectors, covectors, and tensors) on these manifolds. By examining the effects of this procedure in the LAB and comoving coordinate systems, we establish a coordinate transformation between them. Finally, we apply the results of the 2+2 split to the 4-dimensional Euler equations, which admit two constants of motion. This allows for us to define a plasma sheet as an equivalence class of particles whose spacetime positions differ only longitudinally and define a sheet proper time. Furthermore, the notion of particle thermodynamics can be, and is, generalized
Symmetric states: Their nonlocality and entanglement
Wang, Zizhu; Markham, Damian
2014-12-04
The nonlocality of permutation symmetric states of qubits is shown via an extension of the Hardy paradox and the extension of the associated inequality. This is achieved by using the Majorana representation, which is also a powerful tool in the study of entanglement properties of symmetric states. Through the Majorana representation, different nonlocal properties can be linked to different entanglement properties of a state, which is useful in determining the usefulness of different states in different quantum information processing tasks.
World-sheet stability, space-time horizons and cosmic censorship
NASA Astrophysics Data System (ADS)
Pollock, M. D.
2014-11-01
Previously, we have analyzed the stability and supersymmetry of the heterotic superstring world sheet in the background Friedmann space-time generated by a perfect fluid with energy density ρ and pressure p = ( γ - 1) ρ. The world sheet is tachyon-free within the range 2/3 ≤ γ ≤ ∞, and globally supersymmetric in the Minkowski-space limit ρ = ∞, or when γ = 2/3, which is the equation of state for stringy matter and corresponds to the Milne universe, that expands along its apparent horizon. Here, this result is discussed in greater detail, particularly with regard to the question of horizon structure, cosmic censorship, the TCP theorem, and local world-sheet supersymmetry. Also, we consider the symmetric background space-time generated by a static, electrically (or magnetically) charged matter distribution of total mass and charge Q, and containing a radially directed macroscopic string. We find that the effective string mass m satisfies the inequality m 2 ≥ 0, signifying stability, provided that , which corresponds to the Reissner-Nordström black hole. The case of marginal string stability, m 2 = 0, is the extremal solution , which was shown by Gibbons and Hull to be supersymmetric, and has a marginal horizon. If , the horizon disappears, m 2 < 0, and the string becomes unstable.
Dirac Hamiltonian and Reissner-Nordström metric: Coulomb interaction in curved space-time
NASA Astrophysics Data System (ADS)
Noble, J. H.; Jentschura, U. D.
2016-03-01
We investigate the spin-1 /2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordström space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordström geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational and electrogravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electrogravitational correction terms to the potential proportional to αnG , where α is the fine-structure constant and G is the gravitational coupling constant. The particle-antiparticle symmetry found for the Dirac-Schwarzschild geometry (and for other geometries which do not include electromagnetic interactions) is shown to be explicitly broken due to the electrostatic coupling. The resulting spectrum of radially symmetric, electrostatically bound systems (with gravitational corrections) is evaluated for example cases.
Tools for the study of dynamical spacetimes
NASA Astrophysics Data System (ADS)
Zhang, Fan
This thesis covers a range of topics in numerical and analytical relativity, centered around introducing tools and methodologies for the study of dynamical spacetimes. The scope of the studies is limited to classical (as opposed to quantum) vacuum spacetimes described by Einstein's general theory of relativity. The numerical works presented here are carried out within the Spectral Einstein Code (SpEC) infrastructure, while analytical calculations extensively utilize Wolfram's Mathematica program. We begin by examining highly dynamical spacetimes such as binary black hole mergers, which can be investigated using numerical simulations. However, there are difficulties in interpreting the output of such simulations. One difficulty stems from the lack of a canonical coordinate system (henceforth referred to as gauge freedom) and tetrad, against which quantities such as Newman-Penrose Psi4 (usually interpreted as the gravitational wave part of curvature) should be measured. We tackle this problem in Chapter 2 by introducing a set of geometrically motivated coordinates that are independent of the simulation gauge choice, as well as a quasi-Kinnersley tetrad, also invariant under gauge changes in addition to being optimally suited to the task of gravitational wave extraction. Another difficulty arises from the need to condense the overwhelming amount of data generated by the numerical simulations. In order to extract physical information in a succinct and transparent manner, one may define a version of gravitational field lines and field strength using spatial projections of the Weyl curvature tensor. Introduction, investigation and utilization of these quantities will constitute the main content in Chapters 3 through 6. For the last two chapters, we turn to the analytical study of a simpler dynamical spacetime, namely a perturbed Kerr black hole. We will introduce in Chapter 7 a new analytical approximation to the quasi-normal mode (QNM) frequencies, and relate various
Discrete symmetries and de Sitter spacetime
Cotăescu, Ion I. Pascu, Gabriel
2014-11-24
Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries- a criterion which selects a single state out of the α-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries- states between which exists a well-known thermality relation.
Apparent horizons in binary black hole spacetimes
NASA Astrophysics Data System (ADS)
Shoemaker, Deirdre Marie
Over the last decade, advances in computing technology and numerical techniques have lead to the possible theoretical prediction of astrophysically relevant waveforms in numerical simulations. With the building of gravitational wave detectors such as the Laser Interferometric Gravitational-Wave Observatory, we stand at the epoch that will usher in the first experimental study of strong field general relativity. One candidate source for ground based detection of gravitational waveforms, the orbit and merger of two black holes, is of great interest to the relativity community. The binary black hole problem is the two-body problem in general relativity. It is a stringent dynamical test of the theory. The problem involves the evolution of the Einstein equation, a complex system of non-linear, dynamic, elliptic-hyperbolic equations intractable in closed form. Numerical relativists are now developing the technology to evolve the Einstein equation using numerical simulations. The generation of these numerical I codes is a ``theoretical laboratory'' designed to study strong field phenomena in general relativity. This dissertation reports the successful development and application of the first multiple apparent horizon tracker applied to the generic binary black hole problem. I have developed a method that combines a level set of surfaces with a curvature flow method. This method, which I call the level flow method, locates the surfaces of any apparent horizons in the spacetime. The surface location then is used to remove the singularities from the computational domain in the evolution code. I establish the following set of criteria desired in an apparent horizon tracker: (1)The robustness of the tracker due to its lack of dependence on small changes to the initial guess; (2)The generality of the tracker in its applicability to generic spacetimes including multiple back hole spacetimes; and (3)The efficiency of the tracker algorithm in CPU time. I demonstrate the apparent
NASA Technical Reports Server (NTRS)
Villarreal, James A.; Shelton, Robert O.
1991-01-01
Introduced here is a novel technique which adds the dimension of time to the well known back propagation neural network algorithm. Cited here are several reasons why the inclusion of automated spatial and temporal associations are crucial to effective systems modeling. An overview of other works which also model spatiotemporal dynamics is furnished. A detailed description is given of the processes necessary to implement the space-time network algorithm. Several demonstrations that illustrate the capabilities and performance of this new architecture are given.
Polyhedra in spacetime from null vectors
NASA Astrophysics Data System (ADS)
Neiman, Yasha
2014-01-01
We consider convex spacelike polyhedra oriented in the Minkowski space. These are the classical analogues of spinfoam intertwiners. We point out a parametrization of these shapes using null face normals, with no constraints or redundancies. Our construction is dimension-independent. In 3+1d, it provides the spacetime picture behind a well-known property of the loop quantum gravity intertwiner space in spinor form, namely that the closure constraint is always satisfied after some SL(2, C) rotation. As a simple application of our variables, we incorporate them in a 4-simplex action that reproduces the large-spin behavior of the Barrett-Crane vertex amplitude.
Spacetime Curvature and Higgs Stability after Inflation.
Herranen, M; Markkanen, T; Nurmi, S; Rajantie, A
2015-12-11
We investigate the dynamics of the Higgs field at the end of inflation in the minimal scenario consisting of an inflaton field coupled to the standard model only through the nonminimal gravitational coupling ξ of the Higgs field. Such a coupling is required by renormalization of the standard model in curved space, and in the current scenario also by vacuum stability during high-scale inflation. We find that for ξ≳1, rapidly changing spacetime curvature at the end of inflation leads to significant production of Higgs particles, potentially triggering a transition to a negative-energy Planck scale vacuum state and causing an immediate collapse of the Universe.
Spacetime Curvature and Higgs Stability after Inflation.
Herranen, M; Markkanen, T; Nurmi, S; Rajantie, A
2015-12-11
We investigate the dynamics of the Higgs field at the end of inflation in the minimal scenario consisting of an inflaton field coupled to the standard model only through the nonminimal gravitational coupling ξ of the Higgs field. Such a coupling is required by renormalization of the standard model in curved space, and in the current scenario also by vacuum stability during high-scale inflation. We find that for ξ≳1, rapidly changing spacetime curvature at the end of inflation leads to significant production of Higgs particles, potentially triggering a transition to a negative-energy Planck scale vacuum state and causing an immediate collapse of the Universe. PMID:26705621
Rehabilitating space-times with NUTs
NASA Astrophysics Data System (ADS)
Clément, Gérard; Gal'tsov, Dmitri; Guenouche, Mourad
2015-11-01
We revisit the Taub-NUT solution of the Einstein equations without time periodicity condition, showing that the Misner string is still fully transparent for geodesics. In this case, analytic continuation can be carried out through both horizons leading to a Hausdorff spacetime without a central singularity, and thus geodesically complete. Furthermore, we show that, in spite of the presence of a region containing closed time-like curves, there are no closed causal geodesics. Thus, some longstanding obstructions to accept the Taub-NUT solution as physically relevant are removed.
Penrose's singularity theorem in a Finsler spacetime
NASA Astrophysics Data System (ADS)
Babak Aazami, Amir; Javaloyes, Miguel Angel
2016-01-01
We translate Penrose's singularity theorem to a Finsler spacetime. To that end, causal concepts in Lorentzian geometry are extended, including definitions and properties of focal points and trapped surfaces, with careful attention paid to the differences that arise in the Finslerian setting. This activity is supported by the programme 'Young leaders in research' 18942/JLI/13 by Fundación Séneca, Regional Agency for Science and Technology from the Region of Murcia, and by the World Premier International Research Center Initiative (WPI), MEXT, Japan.
Lax pairs for deformed Minkowski spacetimes
NASA Astrophysics Data System (ADS)
Kyono, Hideki; Sakamoto, Jun-ichi; Yoshida, Kentaroh
2016-01-01
We proceed to study Yang-Baxter deformations of 4D Minkowski spacetime based on a conformal embedding. We first revisit a Melvin background and argue a Lax pair by adopting a simple replacement law invented in 1509.00173. This argument enables us to deduce a general expression of Lax pair. Then the anticipated Lax pair is shown to work for arbitrary classical r-matrices with Poincaré generators. As other examples, we present Lax pairs for pp-wave backgrounds, the Hashimoto-Sethi background, the Spradlin-Takayanagi-Volovich background.
Spacetime symmetries and Kepler's third law
NASA Astrophysics Data System (ADS)
Le Tiec, Alexandre
2012-11-01
The curved spacetime geometry of a system of two point masses moving on a circular orbit has a helical symmetry. We show how Kepler’s third law for circular motion, and its generalization in post-Newtonian theory, can be recovered from a simple, covariant condition on the norm of the associated helical Killing vector field. This unusual derivation can be used to illustrate some concepts of prime importance in a general relativity course, including those of Killing field, covariance, coordinate dependence and gravitational redshift.
A Spherical Aerial Terrestrial Robot
NASA Astrophysics Data System (ADS)
Dudley, Christopher J.
This thesis focuses on the design of a novel, ultra-lightweight spherical aerial terrestrial robot (ATR). The ATR has the ability to fly through the air or roll on the ground, for applications that include search and rescue, mapping, surveillance, environmental sensing, and entertainment. The design centers around a micro-quadcopter encased in a lightweight spherical exoskeleton that can rotate about the quadcopter. The spherical exoskeleton offers agile ground locomotion while maintaining characteristics of a basic aerial robot in flying mode. A model of the system dynamics for both modes of locomotion is presented and utilized in simulations to generate potential trajectories for aerial and terrestrial locomotion. Details of the quadcopter and exoskeleton design and fabrication are discussed, including the robot's turning characteristic over ground and the spring-steel exoskeleton with carbon fiber axle. The capabilities of the ATR are experimentally tested and are in good agreement with model-simulated performance. An energy analysis is presented to validate the overall efficiency of the robot in both modes of locomotion. Experimentally-supported estimates show that the ATR can roll along the ground for over 12 minutes and cover the distance of 1.7 km, or it can fly for 4.82 minutes and travel 469 m, on a single 350 mAh battery. Compared to a traditional flying-only robot, the ATR traveling over the same distance in rolling mode is 2.63-times more efficient, and in flying mode the system is only 39 percent less efficient. Experimental results also demonstrate the ATR's transition from rolling to flying mode.
Multishell model for Majumdar-Papapetrou spacetimes
Guerses, Metin; Himmetoglu, Burak
2005-07-15
Exact solutions to static and nonstatic Einstein-Maxwell equations in the presence of extremely charged dust embedded on thin shells are constructed. Singularities of multi-black-hole Majumdar- Papapetrou and Kastor-Traschen solutions are removed by placing the matter on thin shells. Double spherical thin shell solution is given as an illustration and the matter densities on the shells are derived.
Physics of Spherical Torus Plasmas
Peng, Yueng Kay Martin
2000-01-01
Broad and important progress in plasma tests, theory, new experiments, and future visions of the spherical torus (ST, or very low aspect ratio tokamaks) have recently emerged. These have substantially improved our understanding of the potential properties of the ST plasmas, since the preliminary calculation of the ST magnetohydrodynamic equilibria more than a decade ago. Exciting data have been obtained from concept exploration level ST experiments of modest capabilities (with major radii up to 35 cm), making important scientific contributions to toroidal confinement in general. The results have helped approval and construction of new and/or more powerful ST experiments, and stimulated an increasing number of theoretical calculations of interest to magnetic fusion energy. Utilizing the broad knowledge base from the successful tokamak and advanced tokamak research, a wide range of new ST physics features has been suggested. These properties of the ST plasma will be tested at the 1 MA level with major radius up to similar to 80 cm in the new proof of principle devices National Spherical Torus Experiment (NSTX, U.S.) [M. Peng , European Conf. Abst. 22C, 451 (1998); S. M. Kaye , Fusion Technol. 36, 16 (1999); M. Ono , "Exploration of Spherical Torus Physics in the NSTX Device," 17th IAEA Fusion Energy Conf., paper IAEA-CN-69/ICP/01 (R), Yokohama, Japan (1998)], Mega Ampere Spherical Tokamak (MAST, U.K.) [A. C. Darke , Fusion Technol. 1, 799 (1995); Q. W. Morris , Proc. Int. Workshop on ST (Ioffe Inst., St. Petersburg, 1997), Vol. 1, p. 290], and Globus-M (R.F.) [V. K. Gusev , European Conf. Abst. 22C, 576 (1998)], which have just started full experimental operation. New concept exploration experiments, such as Pegasus (University of Wisconsin) [R. Fonck and the PEGASUS Team, Bull. Am. Phys. Soc. 44, 267 (1999)], Helicity Injected Tokamak-II (HIT-II, University of Washington) [T. R. Jarboe , Phys. Plasmas 5, 1807 (1998)], and Current Drive Experiment-Upgrade (CDX
APPARATUS FOR GRINDING SPHERICAL BODIES
Burch, R.F. Jr.
1963-09-24
A relatively inexpensive device is described for grinding rough ceramic bodies into accurate spherical shapes using a conventional drill press and a belt sander. A horizontal disk with an abrasive-surfaced recess in its lower face is mounted eccentrically on a vertical shaft which is forced downward against a stop by a spring. Bodies to be ground are placed in the recess and are subjected to the abrasive action of the belt sander as the disk is rotated by the drill press. (AEC)
Electronic switching spherical array antenna
NASA Technical Reports Server (NTRS)
Stockton, R.
1978-01-01
This work was conducted to demonstrate the performance levels attainable with an ESSA (Electronic Switching Spherical Array) antenna by designing and testing an engineering model. The antenna was designed to satisfy general spacecraft environmental requirements and built to provide electronically commandable beam pointing capability throughout a hemisphere. Constant gain and beam shape throughout large volumetric coverage regions are the principle characteristics. The model is intended to be a prototype of a standard communications and data handling antenna for user scientific spacecraft with the Tracking and Data Relay Satellite System (TDRSS). Some additional testing was conducted to determine the feasibility of an integrated TDRSS and GPS (Global Positioning System) antenna system.