English
Related papers

Related papers: On Spherically Symmetric Solutions of the Einstein…

200 papers

We consider a general non-linear sigma model coupled to Einstein gravity and show that in spherical symmetry and for a simple realization of self-similarity, the spacetime can be completely determined. We also examine some more specific…

General Relativity and Quantum Cosmology · Physics 2009-07-07 Eric W. Hirschmann , Anzhong Wang

We survey many of the important properties of spherically symmetric spacetimes as follows. We present several different ways of describing a spherically symmetric spacetime and the resulting metrics. We then focus our discussion on an…

General Relativity and Quantum Cosmology · Physics 2014-10-10 Alan R. Parry

We are concerned with spherically symmetric solutions to the Euler equations for the multi-dimensional compressible fluids, which have many applications in diverse real physical situations. The system can be reduced to one dimensional…

Analysis of PDEs · Mathematics 2019-08-20 Feimin Huang , Tianhong Li , Difan Yuan

This paper develops a method for solving Einstein's equation numerically on multi-cube representations of manifolds with arbitrary spatial topologies. This method is designed to provide a set of flexible, easy to use computational…

General Relativity and Quantum Cosmology · Physics 2015-06-18 Lee Lindblom , Bela Szilagyi , Nicholas W. Taylor

The properties of LRS class II perfect fluid space-times are analyzed using the description of geometries in terms of the Riemann tensor and a finite number of its covariant derivatives. In this manner it is straightforward to obtain the…

General Relativity and Quantum Cosmology · Physics 2009-10-31 M. Marklund , M. Bradley

We consider spherically symmetric, asymptotically flat space-times with a collisionless gas as matter model. Many properties of the resulting Vlasov-Einstein system are not yet accessible by purely analytical means. We present a discretized…

Numerical Analysis · Mathematics 2025-10-20 Gerhard Rein , Thomas Rodewis

We get the general static, spherically symmetric solutions of the d-dimensional Einstein-Maxwell-Dilaton theories by dimensionally reducing them to a class of 2-dimensional dilaton gravity theories. By studying the symmetries of the actions…

High Energy Physics - Theory · Physics 2010-11-19 Youngjai Kiem , Dahl Park

In this article, we provide a discussion on a composite class of exact static spherically symmetric vacuum solutions of Einstein's equations. We construct the composite solution of Einstein field equation by match the interior vacuum metric…

General Relativity and Quantum Cosmology · Physics 2010-06-15 S. M. Kozyrev

In a previous paper two of the authors (G. R. and A. D. R.) showed that there exist global, classical solutions of the spherically symmetric Vlasov-Einstein system for small initial data. The present paper continues this investigation and…

General Relativity and Quantum Cosmology · Physics 2015-06-25 Gerhard Rein , Alan D. Rendall , Jack Schaeffer

In this paper we revise two classical examples of Relativistic Hydrodynamics in order to illustrate in detail the numerical methods commonly used in fluid dynamics, specifically those designed to deal with shocks, which are based on a…

General Relativity and Quantum Cosmology · Physics 2012-12-07 F. S. Guzman , F. D. Lora-Clavijo , M. D. Morales

We consider solutions of the semi-classical Einstein-Klein-Gordon system with a cosmological constant $\Lambda\in\mathbb{R}$, where the spacetime is given by Einstein's static metric on $\mathbb{R}\times\mathbb{S}^3$ with a round sphere of…

Mathematical Physics · Physics 2021-10-22 Ko Sanders

We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate $r$ between two…

General Relativity and Quantum Cosmology · Physics 2021-04-16 Jorge L. deLyra , Rodrigo de A. Orselli , C. E. I. Carneiro

We prove the existence of static, spherically symmetric solutions of the stellar dynamic Vlasov-Poisson and Vlasov-Einstein systems, which have the property that their spatial support is a finite, spherically symmetric shell with a vacuum…

Mathematical Physics · Physics 2007-05-23 Gerhard Rein

The structure of the Einstein field equations describing the gravitational collapse of spherically symmetric isotropic fluids is analyzed here for general equations of state. A suitable system of coordinates is constructed which allows us,…

General Relativity and Quantum Cosmology · Physics 2015-03-24 Roberto Giambò , Giulio Magli

Axially symmetric stationary metrics governed by the Einstein-Euler equations for slowly rotating perfect fluids have been constructed in an arbitrarily large bounded domain containing the support of the mass density. However the problem of…

Analysis of PDEs · Mathematics 2019-07-23 Tetu Makino

We exhibit a simple and explicit formula for the metric of an arbitrary static spherically symmetric perfect fluid spacetime. This class of metrics depends on one freely specifiable monotone non-increasing generating function. We also…

General Relativity and Quantum Cosmology · Physics 2009-11-07 Shahinur Rahman , Matt Visser

We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing…

General Physics · Physics 2018-02-14 S. Thirukkanesh , F. C. Ragel , Ranjan Sharma , Shyam Das

In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention…

General Relativity and Quantum Cosmology · Physics 2010-05-07 Evgeny Sorkin , Matthew W. Choptuik

Solutions of field equations in $f(R)$ gravity are found for a spherically symmetric and static spacetime in the Born-Infeld (BI) non-linear electrodynamics. It is found that the models supported in this configuration must have the…

General Relativity and Quantum Cosmology · Physics 2020-11-18 Roger A. Hurtado , Jose R. Arenas

We consider the conformal Einstein equations for massless collisionless gas cosmologies which admit an isotropic singularity. After developing the general theory, we restrict to spatially-homogeneous cosmologies. We show that the Cauchy…

General Relativity and Quantum Cosmology · Physics 2009-10-31 K. Anguige , K. P. Tod