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Mathematical Physics

arXiv:1804.04934 (math-ph)
[Submitted on 13 Apr 2018 (v1), last revised 28 Feb 2019 (this version, v2)]

Title:Stable cosmological Kaluza-Klein Spacetimes

Authors:Volker Branding, David Fajman, Klaus Kroencke
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Abstract:We consider the Einstein flow on a product manifold with one factor being a compact quotient of 3-dimensional hyperbolic space without boundary and the other factor being a flat torus of fixed arbitrary dimension. We consider initial data symmetric with respect to the toroidal directions. We obtain effective Einsteinian field equations coupled to a wave map type and a Maxwell type equation by the Kaluza-Klein reduction. The Milne universe solves those field equations when the additional parts arising from the toroidal dimensions are chosen constant. We prove future stability of the Milne universe within this class of spacetimes, which establishes stability of a large class of cosmological Kaluza-Klein vacua. A crucial part of the proof is the implementation of a new gauge for Maxwell-type equations in the cosmological context, which we refer to as slice-adapted gauge.
Subjects: Mathematical Physics (math-ph); General Relativity and Quantum Cosmology (gr-qc); Analysis of PDEs (math.AP); Differential Geometry (math.DG)
Cite as: arXiv:1804.04934 [math-ph]
  (or arXiv:1804.04934v2 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1804.04934
Related DOI: https://doi.org/10.1007/s00220-019-03319-5

Submission history

From: Volker Branding [view email]
[v1] Fri, 13 Apr 2018 13:35:21 UTC (30 KB)
[v2] Thu, 28 Feb 2019 16:22:07 UTC (31 KB)
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