scholarly journals Nonstatic Spherically Symmetric Solutions for a Perfect Fluid in General Relativity

1976 ◽  
Vol 29 (2) ◽  
pp. 113 ◽  
Author(s):  
N Chakravarty ◽  
SB Dutta Choudhury ◽  
A Banerjee
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Perfect Fluid ◽  
Dynamical Behaviour ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Spherically Symmetric Solutions ◽  
Spherically Symmetric Distribution ◽  
General Method

A general method is described by which exact solutions of Einstein's field equations are obtained for a nonstatic spherically symmetric distribution of a perfect fluid. In addition to the previously known solutions which are systematically derived, a new set of exact solutions is found, and the dynamical behaviour of the corresponding models is briefly discussed.

scholarly journals Radially symmetric distribution of matter

1966 ◽  
Vol 6 (2) ◽  
pp. 153-156 ◽  
Author(s):  
A. L. Mehra
Keyword(s):  
Perfect Fluid ◽  
Variable Density ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Spherically Symmetric Distribution

SummaryIn this paper a solution of the Einstein field equations for a spherically symmetric distribution of a perfect fluid of variable density has been obtained.

Exact solution of a static charged sphere in general relativity

1969 ◽  
Vol 47 (21) ◽  
pp. 2401-2404 ◽  
Author(s):  
S. J. Wilson
Keyword(s):  
Exact Solution ◽  
General Relativity ◽  
Gravitational Constant ◽  
The Self ◽  
Spherically Symmetric ◽  
Charged Sphere ◽  
Field Equations ◽  
First Order ◽  
Self Energy ◽  
Spherically Symmetric Distribution

An exact solution of the field equations of general relativity is obtained for a static, spherically symmetric distribution of charge and mass which can be matched with the Reissner–Nordström metric at the boundary. The self-energy contributions to the total gravitational mass are computed retaining only the first order terms in the gravitational constant.

SPHERICALLY SYMMETRIC SCALAR FIELD IN GENERAL RELATIVITY

1996 ◽  
Vol 11 (30) ◽  
pp. 2409-2415 ◽  
Author(s):  
FERNANDO KOKUBUN
Keyword(s):  
Exact Solution ◽  
General Relativity ◽  
Scalar Field ◽  
Field Distribution ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Ordinary Matter ◽  
Spherically Symmetric Distribution

We analyze the presence of a scalar field around a spherically symmetric distribution of an ordinary matter, obtaining an exact solution for a given scalar field distribution.

scholarly journals SEARCHING EXACT SOLUTIONS FOR COMPACT STARS IN BRANEWORLD: A CONJECTURE

2008 ◽  
Vol 23 (38) ◽  
pp. 3247-3263 ◽  
Author(s):  
J. OVALLE
Keyword(s):  
Exact Solution ◽  
General Relativity ◽  
Exact Solutions ◽  
Degrees Of Freedom ◽  
Compact Stars ◽  
Necessary Condition ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Internal Solution ◽  
Particular Solution

In the context of the braneworld, a method to find consistent solutions to Einstein's field equations in the interior of a spherically symmetric, static and non-uniform stellar distribution with Weyl stresses is developed. This method, based on the fact that any braneworld stellar solution must have the general relativity solution as a limit, produces a constraint which reduces the degrees of freedom on the brane. Hence the nonlocality and non-closure of the braneworld equations can be overcome. The constraint found is physically interpreted as a necessary condition to regain general relativity, and a particular solution for it is used to find an exact and physically acceptable analytical internal solution to no-uniform stellar distributions on the brane. It is shown that such an exact solution is possible due to the fact that bulk corrections to pressure, density and a metric component are a null source of anisotropic effects on the brane. A conjecture is proposed regarding the possibility of finding physically relevant exact solutions to non-uniform stellar distributions on the brane.

scholarly journals Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 830
Author(s):  
Evgeniya V. Goloveshkina ◽  
Leonid M. Zubov
Keyword(s):  
Nonlinear Theory ◽  
Hollow Sphere ◽  
Tensor Field ◽  
Exact Analytical Solution ◽  
Symmetric Tensor ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Tensor Fields ◽  
Spherically Symmetric Distribution ◽  
Nonlinear Elastic

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i. e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out.

Approximate solutions of the general relativity field equations with a scalar meson field

1963 ◽  
Vol 59 (4) ◽  
pp. 739-741 ◽  
Author(s):  
J. Hyde
Keyword(s):  
General Relativity ◽  
Scalar Meson ◽  
Empty Space ◽  
Approximate Solutions ◽  
Spherically Symmetric ◽  
Coordinate Transformations ◽  
Field Equations ◽  
Spherically Symmetric Solution ◽  
Image Position ◽  
Scalar Meson Field

It was shown by Birkhoff ((1), p. 253) that every spherically symmetric solution of the field equations of general relativity for empty space,may be reduced, by suitable coordinate transformations, to the static Schwarzschild form:where m is a constant. This result is known as Birkhoff's theorem and excludes the possibility of spherically symmetric gravitational radiation. Different proofs of the theorem have been given by Eiesland(2), Tolman(3), and Bonnor ((4), p. 167).

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