On the area of the symmetry orbits in weakly regular Einstein-Euler spacetimes with Gowdy symmetry

2014/11/12 by Nastasia Grubic, Philippe G. LeFloch, Grubic, Nastasia +1
Mathematics · Physics and Astronomy · #35L65 #76L05 #83C05 #83C35 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc #math.AP #msc:35L65 #msc:76L05 #msc:83C05 #msc:83C35

paper · pdf · doi:10.48550/arxiv.1411.3269

18 pages

arxiv created 2014/11/12 · arxiv updated 2014/11/13

Abstract

This paper establishes novel bounds for Gowdy-symmetric Einstein-Euler spacetimes and completes the analysis, initiated by LeFloch and Rendall, of the global areal foliation for these spacetimes. We thus consider the initial value problem for the Einstein-Euler equations under the assumption of Gowdy symmetry. We establish that, for the maximal Cauchy development of future contracting initial data, the area of the group orbits approaches zero toward the future. This property holds as one approaches the future boundary of the spacetime, provided a geometry invariant associated with the Gowdy symmetry property is initially non-vanishing. Our condition is sharp within the class of spatially homogeneous spacetimes.

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