Spatial Kasner Solution and an Infinite Slab with a Constant Energy Density
Abstract
We study the solutions of the Einstein equations in the presence of a thick infinite slab with constant energy density. When there is an isotropy in the plane of the slab, we find an explicit exact solution that matches with the Rindler and WeylLeviCivita spacetimes outside the slab. We also show that there are solutions that can be matched with general anisotropic Kasner spacetime outside the slab. In any case, it is impossible to avoid the presence of the Kasner type singularities in contrast to the wellknown case of spherical symmetry, where by matching the internal Schwarzschild solution with the external one, the singularity in the center of coordinates can be eliminated.
 Publication:

Soviet Journal of Experimental and Theoretical Physics Letters
 Pub Date:
 May 2020
 DOI:
 10.1134/S0021364020060016
 arXiv:
 arXiv:2002.12916
 Bibcode:
 2020JETPL.111..306K
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 5 pages, to be published in JETP Letters