On holonomy singularities in general relativity and the C^0,1_loc-inextendibility of spacetimes

2020/07/23 by Sbierski, Jan
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2007.12049

Abstract

This paper investigates the structure of gravitational singularities at the level of the connection. We show in particular that for FLRW spacetimes with particle horizons a local holonomy, which is related to a gravitational energy, becomes unbounded near the big-bang singularity. This implies the C^0,1_loc-inextendibility of such FLRW spacetimes. Again using an unbounded local holonomy we also give a general theorem establishing the C^0,1_loc-inextendibility of spherically symmetric weak null singularities which arise at the Cauchy horizon in the interior of black holes. Our theorem does not presuppose the mass-inflation scenario and in particular applies to the Reissner-Nordström-Vaidya spacetimes as well as to spacetimes which arise from small and generic spherically symmetric perturbations of two-ended subextremal Reissner-Nordström initial data for the Einstein-Maxwell-scalar field system. In [26], [27] Luk and Oh proved the C²-formulation of strong cosmic censorship for this latter class of spacetimes -- and based on their work we improve this to a C^0,1_loc-formulation of strong cosmic censorship.

Related

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• Lipschitz inextendibility of weak null singularities from curvature blow-up
• On Strong Cosmic Censorship
• A Primer on Spacetime Singularities I: Mathematical Framework
• Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data II. The exterior of the black hole region