Einstein spaces as attractors for the Einstein flow

2009/08/06 by Andersson, Lars, Moncrief, Vincent · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.0908.0784

Abstract

In this paper we prove a global existence theorem, in the direction of cosmological expansion, for sufficiently small perturbations of a family of n+1-dimensional, n ≥ 3, spatially compact spacetimes which generalizes the k=-1 Friedmann--Robertson--Walker vacuum spacetime. Our results demonstrate causal geodesic completeness of the perturbed spacetimes, in the expanding direction, and show that the scale-free geometry converges towards an element in the moduli space of Einstein geometries, with a rate of decay depending on the stability properties of the Einstein geometry.

Cited by

• Future stability of solutions of the Einstein-nonlinear scalar field system with decelerated expansion
• Boundedness and decay of waves on spatially flat decelerated FLRW spacetimes

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