A REVIEW ON THE GEOMETRIC FORMULATION OF TOLMAN–BONDI EQUATIONS IN GENERAL RELATIVITY

2009 ◽  
Vol 06 (04) ◽  
pp. 595-617 ◽  
Author(s):  
IVANA BOCHICCHIO ◽  
MAURO FRANCAVIGLIA ◽  
ETTORE LASERRA
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Exact Solutions ◽  
Structural Properties ◽  
Spherically Symmetric ◽  
Principal Curvatures ◽  
Spherical Shells ◽  
Geometric Formulation ◽  
Dust Universe

This work is focused on spherically symmetric space-times. More precisely, geometric and structural properties of spatially spherical shells of a dust universe are analyzed in detail considering recent results of our research. Moreover, exact solutions, obtained for constant Ricci principal curvatures, are inferred and qualitatively analyzed through suitable classic analogies.

Stable wormhole models in general relativity under conformal symmetry

2021 ◽  
Vol 18 (03) ◽  
pp. 2150041
Author(s):  
Asifa Ashraf ◽  
Zhiyue Zhang
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Conformal Symmetry ◽  
Energy Condition ◽  
Null Energy Condition ◽  
Anisotropic Fluid ◽  
Spherically Symmetric ◽  
Shape Functions ◽  
The Stability ◽  
Tov Equation

In this study, we shall explore conformal symmetry to examine the wormhole models by considering traceless fluid. In this regard, we shall take anisotropic fluid with spherically symmetric space-time. Further, we shall calculate the properties of shape-functions, which are necessary for the existence of wormhole geometry. The presence of exotic matter is confirmed in all the cases through the violation of the Null Energy Condition. Furthermore, we have discussed the stability of wormhole solutions through the Tolman–Oppenheimer–Volkoff (TOV) equation. It is observed that our acquired solutions are stable under the particular values of involved parameters in different cases in conformal symmetry.

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.

XIX.—A Theory of Regraduation in General Relativity

1946 ◽  
Vol 62 (2) ◽  
pp. 164-174
Author(s):  
A. G. Walker
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Special Form ◽  
The Other ◽  
Spherically Symmetric ◽  
Conservation Equations ◽  
Interesting Paper ◽  
Equivalence Theory ◽  
Two Alternatives

1. It was remarked by me a few years ago that temporal regraduations, other than trivial changes of zero and unit, had not so far been considered in General Relativity. An interesting paper by Dr G. C. McVittie has now appeared in which regraduations are examined in certain spherically symmetric space-times. Under the assumptions made by McVittie it is shown that regraduations can exist for some but not all space-times, those for which they can exist being of a very special form which excludes many space-times generally regarded as significant or interesting. In the present paper I take the matter further and discuss the problem with more generality. It will be shown that the existence of non-trivial regraduations depends firstly upon which theory is being assumed for the derivation of the conservation equations There are two alternatives, and regraduations are found to be excluded by one, the “geodesic” theory, but not necessarily by the other, the “equivalence” theory.

XVII.—The Regraduation of Clocks in Spherically Symmetric Space-times of General Relativity.

1946 ◽  
Vol 62 (2) ◽  
pp. 147-155
Author(s):  
G. C. McVittie
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Coordinate Transformation ◽  
Riemannian Space ◽  
Space Time ◽  
Spherically Symmetric ◽  
Dynamical Time

SummaryThe changes in his description of events brought about by an arbitrary regraduation of an observer's clock are examined, taking the axioms of general relativity as fundamental. It is shown that regraduation does not imply a change from one Riemannian space-time to another but merely a coordinate transformation within space-time. A generalisation of the “dynamical time” of kinematical relativity is a by-product of the investigation.

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.

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