Perfect fluid spheres in general relativity

1983 ◽  
Vol 15 (1) ◽  
pp. 65-77 ◽  
Author(s):  
D. C. Srivastava ◽  
S. S. Prasad
Keyword(s):  
General Relativity ◽  
Perfect Fluid ◽  
Fluid Spheres

scholarly journals Generating perfect fluid spheres in general relativity

2005 ◽  
Vol 71 (12) ◽  
Author(s):  
Petarpa Boonserm ◽  
Matt Visser ◽  
Silke Weinfurtner
Keyword(s):  
General Relativity ◽  
Perfect Fluid ◽  
Fluid Spheres

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>

scholarly journals PHYSICAL PROPERTIES OF TOLMAN–BAYIN SOLUTIONS: SOME CASES OF STATIC CHARGED FLUID SPHERES IN GENERAL RELATIVITY

2007 ◽  
Vol 16 (11) ◽  
pp. 1745-1759 ◽  
Author(s):  
SAIBAL RAY ◽  
BASANTI DAS ◽  
FAROOK RAHAMAN ◽  
SUBHARTHI RAY
Keyword(s):  
General Relativity ◽  
Physical Properties ◽  
Perfect Fluid ◽  
Mass Density ◽  
Fluid Pressure ◽  
Matter Distribution ◽  
Electromagnetic Mass ◽  
Charged Fluid ◽  
Maxwell Space ◽  
Fluid Spheres

In this article, Einstein–Maxwell space–time is considered in connection with some of the astrophysical solutions previously obtained by Tolman (1939) and Bayin (1978). The effect of inclusion of charge in these solutions is investigated thoroughly and the nature of fluid pressure and mass density throughout the sphere is discussed. Mass–radius and mass–charge relations are derived for various cases of the charged matter distribution. Two cases are obtained where perfect fluid with positive pressures gives rise to electromagnetic mass models such that gravitational mass is of purely electromagnetic origin.

scholarly journals Cosmological Milestones and Gravastars - Topics in General Relativity

2021 ◽  
Author(s):  
◽  
Celine Cattoen
Keyword(s):  
General Relativity ◽  
Perfect Fluid ◽  
Thin Shells ◽  
Generalized Power Series ◽  
Friedmann Equations ◽  
Usual Concept ◽  
Transverse Stresses ◽  
Necessary And Sufficient ◽  
Differential Curvature ◽  
Fluid Spheres

<p>In this thesis, we consider two different problems relevant to general relativity. Overthe last few years, opinions on physically relevant singularities occurring in FRWcosmologies have considerably changed. We present an extensive catalogue of suchcosmological milestones using generalized power series both at the kinematical anddynamical level. We define the notion of “scale factor singularity” and explore its relationto polynomial and differential curvature singularities. We also extract dynamicalinformation using the Friedmann equations and derive necessary and sufficient conditionsfor the existence of cosmological milestones such as big bangs, big crunches, bigrips, sudden singularities and extremality events. Specifically, we provide a completecharacterization of cosmological milestones for which the dominant energy conditionis satisfied. The second problem looks at one of the very small number of seriousalternatives to the usual concept of an astrophysical black hole, that is, the gravastarmodel developed by Mazur and Mottola. By considering a generalized class of similarmodels with continuous pressure (no infinitesimally thin shells) and negative centralpressure, we demonstrate that gravastars cannot be perfect fluid spheres: anisotropcpressures are unavoidable. We provide bounds on the necessary anisotropic pressureand show that these transverse stresses that support a gravastar permit a higher compactnessthan is given by the Buchdahl–Bondi bound for perfect fluid stars. We alsocomment on the qualitative features of the equation of state that such gravastar-likeobjects without any horizon must have.</p>

Sign in / Sign up

Export Citation Format

Share Document