An exact solution to Einstein’s equations with a stiff equation of state

1978 ◽  
Vol 19 (11) ◽  
pp. 2283-2284 ◽  
Author(s):  
Paul S. Wesson
Keyword(s):  
Exact Solution ◽  
Equation Of State ◽  
Einstein’S Equations ◽  
Einstein's Equations ◽  
Stiff Equation

PETROV TYPE I, STATIONARY, AXISYMMETRIC, PERFECT FLUID SOLUTION OF EINSTEIN'S EQUATIONS

1999 ◽  
Vol 14 (01) ◽  
pp. 7-14
Author(s):  
E. KYRIAKOPOULOS
Keyword(s):  
Equation Of State ◽  
General Solution ◽  
Perfect Fluid ◽  
Petrov Type ◽  
Type I ◽  
Fluid Solution ◽  
Einstein’S Equations ◽  
Perfect Fluid Solution ◽  
Einstein's Equations ◽  
Static Limit

We present a four-parameter, algebraically general solution for the interior of a rigidly rotating, axisymmetric perfect fluid, with the equation of state μ = p + const . The solution is analytically simple and has a static limit.

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.

scholarly journals ALL "STATIC" SPHERICALLY SYMMETRIC PERFECT FLUID SOLUTIONS OF EINSTEIN'S EQUATIONS WITH CONSTANT EQUATION OF STATE PARAMETER AND FINITE POLYNOMIAL "MASS FUNCTION"

2011 ◽  
Vol 23 (08) ◽  
pp. 865-882 ◽  
Author(s):  
İBRAHİM SEMİZ
Keyword(s):  
Black Hole ◽  
Equation Of State ◽  
Perfect Fluid ◽  
State Parameter ◽  
Phantom Energy ◽  
Mass Function ◽  
Spherically Symmetric ◽  
Einstein’S Equations ◽  
Standard Case ◽  
Einstein's Equations

We look for "static" spherically symmetric solutions of Einstein's Equations for perfect fluid source with equation of state p = wρ, for constant w. We consider all four cases compatible with the standard ansatz for the line element, discussed in previous work. For each case, we derive the equation obeyed by the mass function or its analogs. For these equations, we find all finite-polynomial solutions, including possible negative powers. For the standard case, we find no significantly new solutions, but show that one solution is a static phantom solution, another a black hole-like solution. For the dynamic and/or tachyonic cases we find, among others, dynamic and static tachyonic solutions, a Kantowski–Sachs (KS) class phantom solution, another KS-class solution for dark energy, and a second black hole-like solution. The black hole-like solutions feature segregated normal and tachyonic matter, consistent with the assertion of previous work. In the first black hole-like solution, tachyonic matter is inside the horizon, in the second, outside. The static phantom solution, a limit of an old one, is surprising at first, since phantom energy is usually associated with super-exponential expansion. The KS-phantom solution stands out since its "mass function" is a ninth order polynomial.

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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