Einstein’s Equations

1996 ◽  
pp. 524-605
Author(s):  
Michael E. Taylor
Keyword(s):  
Einstein’S Equations ◽  
Einstein's Equations

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.

Ambi-twistors and Einstein's equations

1985 ◽  
Vol 2 (4) ◽  
pp. 555-563 ◽  
Author(s):  
C R LeBrun
Keyword(s):  
Einstein’S Equations ◽  
Einstein's Equations
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