Exact solutions of the Einstein equations for an infinite slab with a constant energy density
Abstract
We find exact static solutions of the Einstein equations in the spacetime with plane symmetry, where an infinite slab with finite thickness and homogeneous energy (mass) density is present. In the first solution the pressure is isotropic, while in the second solution the tangential components of the pressure are equal to zero. In both cases the pressure vanishes at the boundaries of the slab. Outside the slab these solutions are matched with the Rindler spacetime and with the WeylLeviCivita spacetime, which represent special cases of the Kasner solution.
 Publication:

Physics Letters B
 Pub Date:
 May 2019
 DOI:
 10.1016/j.physletb.2019.02.050
 arXiv:
 arXiv:1811.09493
 Bibcode:
 2019PhLB..792..430K
 Keywords:

 Einstein equations;
 Plane symmetry;
 Singularities;
 General Relativity and Quantum Cosmology
 EPrint:
 Final version, published in Physics Letters B