General Cosmological Solutions of Einstein's Equations for Spherical, Plane and Hyperbolic Symmetric Space

2000 ◽  
Vol 17 (2) ◽  
pp. 79-81
Author(s):  
Mohammed Ashraful Islam
Keyword(s):  
Symmetric Space ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Cosmological Solutions

Inhomogeneous solutions in cosmology

1990 ◽  
Vol 68 (9) ◽  
pp. 824-826
Author(s):  
Paul S. Wesson
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
General Relativity ◽  
Particle Physics ◽  
Quantum Field ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Cosmological Solutions ◽  
The Universe ◽  
Friedmann Robertson Walker

The standard cosmological solutions of Einstein's equations of general relativity describe a fluid that is homogeneous and isotropic in density and pressure. These solutions, often called the Friedmann–Robertson–Walker solutions, are believed to be good descriptions of the universe at the present time. But early on, processes connected with particle physics and quantum field theory may have caused localized inhomogeneities, and recently some new kinds of solution of Einstein's equations have been found, which may describe such regions. In one solution being studied by Wesson and Ponce de Leon (Phys. Rev. D: Part. Fields, 39, 420 (1989)), the density is still uniform but the pressure is nonuniform about a centre. The mass is given by a relation that looks like the familiar Newtonian relation m = (4/3)πR3ρ. However, the solution has other properties that are quite strange (e.g. a region of negative pressure and a kind of dipolar geometry). It is not known if solutions like this are merely mathematical curiosities or imply something about the behaviour of real matter in extreme situations.

The C -field as a direct particle field

1964 ◽  
Vol 282 (1389) ◽  
pp. 178-183 ◽  
Keyword(s):  
Steady State ◽  
Riemannian Space ◽  
Electromagnetic Theory ◽  
Action Principle ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Particle Field ◽  
Asymptotic Case ◽  
The World ◽  
Cosmological Solutions

It has been known for some years that a C -field, generated by a certain source equation, leads to interesting changes in the cosmological solutions of Einstein’s equations. The steady-state cosmology appears as an asymptotic case. The source equation has so far only been given in the macroscopic case of a smooth fluid. In the present paper we derive the source equation in terms of discrete particles. The method adopted is similar to that we have recently given for the generalization to Riemannian space of the Fokker action principle in the electromagnetic theory. In the latter, a 4-vector is defined in terms of the world lines of particles. The definition is such that the four-dimensional curl of the vector satisfies Maxwell’s equations, which are therefore identities. Similarly, C is a scalar defined in terms of the world-lines of particles, and the source equation used formerly then follows as an identity.

COVARIANT CONFORMAL DECOMPOSITION OF EINSTEIN EQUATIONS

2002 ◽  
Vol 17 (20) ◽  
pp. 2762-2762
Author(s):  
E. GOURGOULHON ◽  
J. NOVAK
Keyword(s):  
Numerical Simulations ◽  
Extrinsic Curvature ◽  
Einstein Equations ◽  
Numerical Implementation ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Tensor Density ◽  
Dirac Gauge ◽  
Ill Posed ◽  
Isolated Systems

It has been shown1,2 that the usual 3+1 form of Einstein's equations may be ill-posed. This result has been previously observed in numerical simulations3,4. We present a 3+1 type formalism inspired by these works to decompose Einstein's equations. This decomposition is motivated by the aim of stable numerical implementation and resolution of the equations. We introduce the conformal 3-"metric" (scaled by the determinant of the usual 3-metric) which is a tensor density of weight -2/3. The Einstein equations are then derived in terms of this "metric", of the conformal extrinsic curvature and in terms of the associated derivative. We also introduce a flat 3-metric (the asymptotic metric for isolated systems) and the associated derivative. Finally, the generalized Dirac gauge (introduced by Smarr and York5) is used in this formalism and some examples of formulation of Einstein's equations are shown.

scholarly journals LOCAL COSMIC STRING AND C-FIELD

2006 ◽  
Vol 21 (18) ◽  
pp. 3727-3732 ◽  
Author(s):  
F. RAHAMAN ◽  
R. MONDAL ◽  
M. KALAM
Keyword(s):  
Cosmic String ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Einstein’S Equations ◽  
Einstein's Equations

We investigate a local cosmic string with a phenomenological energy–momentum tensor as prescribed by Vilenkin, in the presence of C-field. The solutions of full nonlinear Einstein's equations for exterior and interior regions of such a string are presented.

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