A class of plane symmetric perfect-fluid cosmologies with a Kasner-like singularity

TL;DR

This paper proves the existence of a new class of plane symmetric perfect-fluid cosmological solutions with a Kasner-like singularity, constructed via solving a symmetric hyperbolic Fuchsian system.

Contribution

It introduces a novel class of solutions to Einstein's equations characterized by specific Kasner-like singularities, dependent on two smooth functions.

Findings

Existence of solutions with Kasner-like singularity proven.

Solutions depend on two smooth functions of one coordinate.

Constructed using symmetric hyperbolic Fuchsian systems.

Abstract

We prove the existence of a class of plane symmetric perfect-fluid cosmologies with a (-1/3, 2/3, 2/3) Kasner-like singularity. These solutions of the Einstein equations depend on two smooth functions of one space coordinate. They are constructed by solving a symmetric hyperbolic system of Fuchsian equations.