A cylindrically symmetric solution of Einstein’s equations describing gravitational collapse of stiff fluid

1993 ◽  
Vol 34 (5) ◽  
pp. 1908-1913 ◽  
Author(s):  
W. Davidson
Keyword(s):  
Gravitational Collapse ◽  
Symmetric Solution ◽  
Einstein’S Equations ◽  
Stiff Fluid ◽  
Einstein's Equations ◽  
Cylindrically Symmetric

Cylindrically symmetric relativistic fluids and the purely electric Weyl tensor

2015 ◽  
Vol 12 (10) ◽  
pp. 1550103 ◽  
Author(s):  
Rajesh Kumar ◽  
S. K. Srivastava ◽  
V. C. Srivastava
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Weyl Tensor ◽  
Einstein’S Equations ◽  
Relativistic Fluids ◽  
Einstein's Equations ◽  
Cylindrically Symmetric ◽  
Expansion Scalar

In General Relativity (GR), the analysis of electric and magnetic Weyl tensors has been studied by various authors. The present study deals with cylindrically symmetric relativistic fluids in GR characterized by the vanishing of magnetic Weyl tensor-purely electric (PE) fields. A very new assumption has been adapted to solve the Einstein's equations and the obtained solution is shearing at all. We signified the importance of PE fields in the context of expansion scalar, energy density, shear and acceleration.

scholarly journals THE SINGULARITY IN GENERIC GRAVITATIONAL COLLAPSE IS SPACELIKE, LOCAL AND OSCILLATORY

1998 ◽  
Vol 13 (19) ◽  
pp. 1565-1573 ◽  
Author(s):  
B. K. BERGER ◽  
D. GARFINKLE ◽  
J. ISENBERG ◽  
V. MONCRIEF ◽  
M. WEAVER
Keyword(s):  
Numerical Simulations ◽  
Gravitational Collapse ◽  
Evolution Equations ◽  
Oscillatory Behavior ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Spatial Point ◽  
Spatially Inhomogeneous ◽  
Homogeneous Universe ◽  
Spatially Homogeneous

A longstanding conjecture by Belinskii, Khalatnikov and Lifshitz that the singularity in generic gravitational collapse is spacelike, local and oscillatory is explored analytically and numerically in spatially inhomogeneous cosmological space–times. With a convenient choice of variables, it can be seen analytically how nonlinear terms in Einstein's equations control the approach to the singularity and cause oscillatory behavior. The analytic picture requires the drastic assumption that each spatial point evolves toward the singularity as an independent spatially homogeneous universe. In every case, detailed numerical simulations of the full Einstein evolution equations support this assumption.

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.

Sign in / Sign up

Export Citation Format

Share Document