Exact solutions of the spherically symmetric gravitational field equations

2006 ◽  
Vol 1 (2) ◽  
pp. 169-177 ◽  
Author(s):  
He-sheng Hu
Keyword(s):  
Gravitational Field ◽  
Exact Solutions ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Symmetric Gravitational Field

scholarly journals PARAMETRIC NONHOLONOMIC FRAME TRANSFORMS AND EXACT SOLUTIONS IN GRAVITY

2007 ◽  
Vol 04 (08) ◽  
pp. 1285-1334 ◽  
Author(s):  
SERGIU I. VACARU
Keyword(s):  
Gravitational Field ◽  
Exact Solutions ◽  
General Scheme ◽  
Nonlinear Partial Differential Equations ◽  
Killing Vector ◽  
Field Equations ◽  
Finsler Spaces ◽  
Gravitational Field Equations ◽  
Pp Wave ◽  
Physical Consequences

A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for nonholonomic manifolds and Finsler spaces) when the gravitational field equations transform into systems of nonlinear partial differential equations which can be integrated in general form. The new classes of solutions are defined by generic off-diagonal metrics depending on integration functions on one, two and three (or three and four) variables if we consider four (or five) dimensional spacetimes. Second, we use a general scheme when one (two) parameter families of exact solutions are defined by any source-free solutions of Einstein's equations with one (two) Killing vector field(s). A successive iteration procedure results in new classes of solutions characterized by an infinite number of parameters for a non-Abelian group involving arbitrary functions on one variable. Five classes of exact off-diagonal solutions are constructed in vacuum Einstein and in string gravity describing solitonic pp-wave interactions. We explore possible physical consequences of such solutions derived from primary Schwarzschild or pp-wave metrics.

The First Solutions and the Challenge of Their Interpretation

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Gravitational Field ◽  
Exact Solutions ◽  
De Sitter ◽  
Field Equations ◽  
Gravitational Field Equations ◽  
Nonlinear Character ◽  
Georges Lemaître

This chapter discusses the first wave of the exploration of exact solutions to Einstein's gravitational field equations. When Einstein published the final form of the field equations in 1915, only an approximate solution was known. Given the complicated nonlinear character of the field equations, he did not expect that exact solutions could easily be found. He was all the more surprised when the astronomer Karl Schwarzschild presented him with just such an exact solution. Thus, this chapter presents a series of these solutions, beginning with the work of Karl Schwarzschild, Johannes Droste, Willem de Sitter, Alexander Friedmann, Hans Reissner, Gunnar Nordström, and finally, Georges Lemaître.

scholarly journals Approximate Solutions of the Relativistic Gravitational Field Equations to Describe Clusters of Galaxies

1972 ◽  
Vol 25 (3) ◽  
pp. 299 ◽  
Author(s):  
MW Cook
Keyword(s):  
Gravitational Field ◽  
Approximate Solutions ◽  
Spherically Symmetric ◽  
Clusters Of Galaxies ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Stellar Objects ◽  
Gravitational Field Equations ◽  
Local Fluctuations ◽  
Region 10

Approximate solutions to the Einstein field equations are found which describe a spherically symmetric inhomogeneity in a general Robertson?Walker model, i.e. one with an arbitrary equation of state. The approximation hypothesis is that the pressure deviates only slightly from uniformity, and it is found that the density may have quite large local fluctuations, e.g. by a factor of 106 over a region 10-2 Mpc in diameter. Reference is made to observed data to determine which categories of stellar objects may be described by the results.

Thermodynamics of traversable wormholes in f(R,T) gravity

2021 ◽  
pp. 2150175
Author(s):  
Mudassar Rehman ◽  
Khalid Saifullah
Keyword(s):  
Gravitational Field ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Matter Coupling ◽  
Gravitational Field Equations ◽  
Traversable Wormholes ◽  
Local Coordinates ◽  
Stress Energy ◽  
Minimal Curvature ◽  
Trapping Horizons

In this paper, we discuss thermodynamics for spherically symmetric and static traversable wormholes which include Morris–Thorne wormholes and charged wormholes in the background of [Formula: see text] gravity. The local coordinates have been used to find trapping horizons of these objects and generalized surface gravity has been worked out on the trapping horizons. The expression for the unified first law has also been derived from the gradient of Misner–Sharp energy with the help of gravitational field equations and from this law the first law of wormhole dynamics has been obtained. We have done this analysis for the simplest case of [Formula: see text] gravity where [Formula: see text], [Formula: see text] and [Formula: see text] being the traces of the Ricci and stress–energy tensors. Also, we have extended these thermodynamic results to non-minimal curvature-matter coupling.

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