The initial singularity of ultrastiff perfect fluid spacetimes without symmetries

TL;DR

This paper proves the existence of a broad family of solutions to Einstein's equations coupled with ultrastiff perfect fluids that exhibit an initial singularity with isotropic structure, using Fuchsian reduction.

Contribution

It demonstrates the generic existence of isotropic initial singularity solutions without symmetry constraints in Einstein-Euler equations.

Findings

Existence of solutions with initial singularity of isotropic type.

Solutions depend on as many free functions as general solutions.

Method employs Fuchsian reduction for proof.

Abstract

We consider the Einstein equations coupled to an ultrastiff perfect fluid and prove the existence of a family of solutions with an initial singularity whose structure is that of explicit isotropic models. This family of solutions is `generic' in the sense that it depends on as many free functions as a general solution, i.e., without imposing any symmetry assumptions, of the Einstein-Euler equations. The method we use is a that of a Fuchsian reduction.