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 Cosmological models through spatial Ricci-flow

2016 ◽  
Vol 13 (05) ◽  
pp. 1650069
Author(s):  
Ramesh Sharma
Keyword(s):  
Equation Of State ◽  
Perfect Fluid ◽  
Ricci Flow ◽  
Quadratic Equation ◽  
Space Time ◽  
Cosmological Models ◽  
Fluid Solution ◽  
Perfect Fluid Solution ◽  
Quadratic Equation Of State

We consider the synchronization of the Einstein’s flow with the Ricci-flow of the standard spatial slices of the Robertson–Walker space–time and show that associated perfect fluid solution has a quadratic equation of state and is either spherical and collapsing, or hyperbolic and expanding.

A GENERALIZATION OF THE WAHLQUIST SOLUTION

1998 ◽  
Vol 07 (06) ◽  
pp. 927-941 ◽  
Author(s):  
TAXIARCHIS PAPAKOSTAS
Keyword(s):  
Equation Of State ◽  
Perfect Fluid ◽  
Fluid Solution ◽  
Perfect Fluid Solution ◽  
Type D ◽  
Petrov Classification

We present a new perfect fluid solution belonging to (1,1) subfamily of Hauser–Mahlist spaces, rigidly rotating, type D in Petrov classification which reduces to the Wahlquist metric for particular values of our constants of integration. Unfortunately it is characterized by the equation of state of the Wahlquist solution: e + 3p = constant .

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.

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