Exact solution of einstein’s equations representing a spinning mass

1980 ◽  
Vol 28 (17) ◽  
pp. 566-568
Author(s):  
D. K. Ross
Keyword(s):  
Exact Solution ◽  
Einstein’S Equations ◽  
Einstein's Equations

scholarly journals The Localized Energy Distribution of Dark Energy Star Solutions

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Paul Halpern ◽  
Michael Pecorino
Keyword(s):  
Exact Solution ◽  
Dark Energy ◽  
Scalar Field ◽  
Energy Distribution ◽  
Phantom Energy ◽  
Energy Localization ◽  
Einstein’S Equations ◽  
Energy Distributions ◽  
Einstein's Equations ◽  
Energy Star

We examine the question of energy localization for an exact solution of Einstein's equations with a scalar field corresponding to the phantom energy interpretation of dark energy. We apply three different energy-momentum complexes, the Einstein, the Papapetrou, and the Møller prescriptions, to the exterior metric and determine the energy distribution for each. Comparing the results, we find that the three prescriptions yield identical energy distributions.

A generalized Kerr-Schild solution of Einstein's equations

1974 ◽  
Vol 75 (3) ◽  
pp. 383-390 ◽  
Author(s):  
P. C. Vaidya
Keyword(s):  
Exact Solution ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Einstein's Equation ◽  
Null Congruence

AbstractA very general exact solution of Einstein's equation Rik = σξiξk, is given in terms of the Kerr-Schild metric, gik = ηij + Hξiξk, where ξi is a shearfree geodetic null congruence. The Kerr-Schild solution for Rik = 0 is derived as a particular case.

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.

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