scholarly journals THE CONFORMALLY SPHERICALLY (PLANE-) SYMMETRIC ELECTRO-VACUUM SOLUTION TO EINSTEIN EQUATIONS

1989 ◽  
Vol 38 (7) ◽  
pp. 170
Author(s):  
FAN LI ◽  
LIANG CAN-BIN
Keyword(s):  
Vacuum Solution ◽  
Einstein Equations ◽  
Plane Symmetric

PLANE SYMMETRIC VISCOUS-FLUID COSMOLOGICAL MODELS WITH HEAT FLUX

1994 ◽  
Vol 03 (03) ◽  
pp. 639-645
Author(s):  
L.K. PATEL ◽  
LAKSHMI S. DESAI
Keyword(s):  
Heat Flux ◽  
Viscous Fluid ◽  
Vacuum Solution ◽  
Big Bang ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Plane Symmetric ◽  
Inhomogeneous Plane ◽  
Physical Features ◽  
Big Bang Singularity

A class of nonstatic inhomogeneous plane-symmetric solutions of Einstein field equations is obtained. The source for these solutions is a viscous fluid with heat flow. The fluid flow is irrotational and it has nonzero expansion, shear and acceleration. All these solutions have a big-bang singularity. The matter-free limit of the solutions is the well-known Kasner vacuum solution. Some physical features of the solutions are briefly discussed.

The Schwarzschild solution

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Vacuum Solution ◽  
Matter Density ◽  
Einstein Equations ◽  
Radial Coordinate ◽  
Spherically Symmetric ◽  
Schwarzschild Solution ◽  
Newtonian Theory ◽  
Schwarzschild Metric ◽  
The Poisson Equation ◽  
Symmetric Spacetime

This chapter deals with the Schwarzschild metric. To find the gravitational potential U produced by a spherically symmetric object in the Newtonian theory, it is necessary to solve the Poisson equation Δ‎U = 4π‎Gρ‎. Here, the matter density ρ‎ and U depend only on the radial coordinate r and possibly on the time t. Outside the source the solution is U = –GM/r, where M = 4π‎ ∫ ρ‎r2dr is the source mass. In general relativity the problem is to find the ‘spherically symmetric’ spacetime solutions of the Einstein equations, and the analog of the vacuum solution U = –GM/r is the Schwarzschild metric.

scholarly journals Classical Polymerization of the Schwarzschild Metric

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Babak Vakili
Keyword(s):  
Energy Momentum Tensor ◽  
Vacuum Solution ◽  
Equations Of Motion ◽  
Hamiltonian Function ◽  
Momentum Tensor ◽  
Einstein Equations ◽  
Spherically Symmetric ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Metric ◽  
Similarities And Differences

We study a spherically symmetric setup consisting of a Schwarzschild metric as the background geometry in the framework of classical polymerization. This process is an extension of the polymeric representation of quantum mechanics in such a way that a transformation maps classical variables to their polymeric counterpart. We show that the usual Schwarzschild metric can be extracted from a Hamiltonian function which in turn gets modifications due to the classical polymerization. Then, the polymer corrected Schwarzschild metric may be obtained by solving the polymer-Hamiltonian equations of motion. It is shown that while the conventional Schwarzschild space-time is a vacuum solution of the Einstein equations, its polymer-corrected version corresponds to an energy-momentum tensor that exhibits the features of dark energy. We also use the resulting metric to investigate some thermodynamical quantities associated with the Schwarzschild black hole, and in comparison with the standard Schwarzschild metric the similarities and differences are discussed.

Time-dependent solution from Myers–Perry

2016 ◽  
Vol 94 (2) ◽  
pp. 177-179
Author(s):  
L.A. López ◽  
Omar Pedraza ◽  
V.E. Ceron
Keyword(s):  
Rotational Symmetry ◽  
Space Time ◽  
Einstein Equations ◽  
Time Dependent ◽  
Wick Rotation ◽  
Five Dimensions ◽  
Asymptotically Flat ◽  
Plane Symmetric ◽  
New Interpretation ◽  
Time Dependent Solution

We present a three-parameter time-dependent solution of the vacuum Einstein equations in five dimensions. The solution is obtained by applying the Wick rotation to the Myers–Perry solution that represents a rotating black hole in five dimensions. The new interpretation of the Myers–Perry solution can be considered among the generalized Einstein–Rosen type that can be interpreted as plane-symmetric waves, cylindrical waves or cosmological space–time in five dimensions. In some limits the solution has boost-rotational symmetry and it is asymptotically flat. In the case that the solution represents a cylindrical space–time, the E-energy is analyzed.

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