Exact Solutions for Shear-free Motion of Spherically Symmetric Charged Perfect Fluid Distributions in General Relativity

1992 ◽  
Vol 40 (1) ◽  
pp. 31-72 ◽  
Author(s):  
D. C. Srivastava
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Perfect Fluid ◽  
Free Motion ◽  
Spherically Symmetric

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.

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.

scholarly journals Some Exact Solutions in General Relativity

2021 ◽  
Author(s):  
◽  
Petarpa Boonserm
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Perfect Fluid ◽  
Fluid Sphere ◽  
Spacetime Geometry ◽  
Pressure Profiles ◽  
Coordinate Conditions ◽  
Pedagogical Discussion ◽  
Fluid Spheres ◽  
Tov Equation

<p><b>In this thesis four separate problems in general relativity are considered, dividedinto two separate themes: coordinate conditions and perfect fluid spheres. Regardingcoordinate conditions we present a pedagogical discussion of how the appropriateuse of coordinate conditions can lead to simplifications in the form of the spacetimecurvature — such tricks are often helpful when seeking specific exact solutions of theEinstein equations. Regarding perfect fluid spheres we present several methods oftransforming any given perfect fluid sphere into a possibly new perfect fluid sphere.</b></p> <p>This is done in three qualitatively distinct manners: The first set of solution generatingtheorems apply in Schwarzschild curvature coordinates, and are phrased in termsof the metric components: they show how to transform one static spherical perfectfluid spacetime geometry into another. A second set of solution generating theoremsextends these ideas to other coordinate systems (such as isotropic, Gaussian polar,Buchdahl, Synge, and exponential coordinates), again working directly in terms of themetric components. Finally, the solution generating theorems are rephrased in termsof the TOV equation and density and pressure profiles. Most of the relevant calculationsare carried out analytically, though some numerical explorations are also carriedout.</p>

scholarly journals Some Exact Solutions in General Relativity

2021 ◽  
Author(s):  
◽  
Petarpa Boonserm
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Perfect Fluid ◽  
Fluid Sphere ◽  
Spacetime Geometry ◽  
Pressure Profiles ◽  
Coordinate Conditions ◽  
Pedagogical Discussion ◽  
Fluid Spheres ◽  
Tov Equation

<p><b>In this thesis four separate problems in general relativity are considered, dividedinto two separate themes: coordinate conditions and perfect fluid spheres. Regardingcoordinate conditions we present a pedagogical discussion of how the appropriateuse of coordinate conditions can lead to simplifications in the form of the spacetimecurvature — such tricks are often helpful when seeking specific exact solutions of theEinstein equations. Regarding perfect fluid spheres we present several methods oftransforming any given perfect fluid sphere into a possibly new perfect fluid sphere.</b></p> <p>This is done in three qualitatively distinct manners: The first set of solution generatingtheorems apply in Schwarzschild curvature coordinates, and are phrased in termsof the metric components: they show how to transform one static spherical perfectfluid spacetime geometry into another. A second set of solution generating theoremsextends these ideas to other coordinate systems (such as isotropic, Gaussian polar,Buchdahl, Synge, and exponential coordinates), again working directly in terms of themetric components. Finally, the solution generating theorems are rephrased in termsof the TOV equation and density and pressure profiles. Most of the relevant calculationsare carried out analytically, though some numerical explorations are also carriedout.</p>

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