Self-gravitating fluid flows with Gowdy symmetry near cosmological singularities

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.

41 pages

References in corpus (5)

• Analytic description of singularities in Gowdy spacetimes
• Observational Challenges for the Standard FLRW Model
• Spikes in the Mixmaster regime of G_2 cosmologies
• Asymptotic Behavior in Polarized {\bf T}${}^2$-symmetric Vacuum Spacetimes
• Generalized relativistic hydrodynamics with a convex extension

Cited by in corpus (10)

• Future instability of FLRW fluid solutions for linear equations of state $p=K\rho$ with $1/3<K<1$
• Localized big bang stability for the Einstein-scalar field equations
• A numerical algorithm for Fuchsian equations and fluid flows on cosmological spacetimes
• Past instability of FLRW solutions of the Einstein-Euler-scalar field equations for linear equations of state $p=K\rho$ with $0\le K<1/3$
• Stability of AVTD Behavior within the Polarized $T^2$-symmetric vacuum spacetimes
• Wave asymptotics at a cosmological time-singularity: classical and quantum scalar fields
• Cyclic spacetimes through singularity scattering maps. The laws of quiescent bounces
• Stability of Asymptotic Behavior Within Polarised $T^2$-Symmetric Vacuum Solutions with Cosmological Constant
• Asymptotic structure of cosmological fluid flows in one and two space dimensions: a numerical study
• Analysis of a Bianchi-like equation satisfied by the Mars-Simon tensor