Self-gravitating fluid flows with Gowdy symmetry near cosmological singularities

TL;DR

This paper investigates the behavior of self-gravitating fluids with Gowdy symmetry near cosmological singularities, solving the Einstein-Euler system with initial data at the singularity and analyzing different regimes based on sound speed.

Contribution

It extends the analysis of inhomogeneous spacetimes to include fluids, solving the singular initial value problem for the Einstein-Euler system with Gowdy symmetry.

Findings

Solutions constructed in sub-critical and critical regimes for linear equations of state.

Identification of conditions on sound speed leading to different regimes.

Analysis of asymptotic behavior of geometric and matter variables near singularity.

Abstract

We consider self-gravitating fluids in cosmological spacetimes with Gowdy symmetry on the torus $T^3$ and, in this class, we solve the singular initial value problem for the Einstein-Euler system of general relativity, when an initial data set is prescribed on the hypersurface of singularity. We specify initial conditions for the geometric and matter variables and identify the asymptotic behavior of these variables near the cosmological singularity. Our analysis of this class of nonlinear and singular partial differential equations exhibits a condition on the sound speed, which leads us to the notion of sub-critical, critical, and super-critical regimes. Solutions to the Einstein-Euler systems when the fluid is governed by a linear equation of state are constructed in the first two regimes, while additional difficulties arise in the latter one. All previous studies on inhomogeneous spacetimes concerned vacuum cosmological spacetimes only.