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The interior of charged black holes and the problem of uniqueness in general relativity

Mihalis Dafermos
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Abstract

We consider a spherically symmetric characteristic initial value problem for the Einstein-Maxwell-scalar field equations. On the initial outgoing characteristic, the data is assumed to satisfy the Price law decay widely believed to hold on an event horizon arising from the collapse of an asymptotically flat Cauchy surface. We establish that the heuristic mass inflation scenario put forth by Israel and Poisson is mathematically correct in the context of this initial value problem. In particular, the maximal domain of development has a future boundary, over which the spacetime is extendible as a continuous metric, but along which the Hawking mass blows up identically; thus, the spacetime is inextendible as a differentiable metric. In view of recent results of the author in collaboration with I. Rodnianski (gr-qc/0309115), which rigorously establish the validity of Price's law as an upper bound for the decay of scalar field hair, the continuous extendibility result applies to the collapse of complete asymptotically flat spacelike data where the scalar field is compactly supported on the initial hypersurface. This shows that under Christodoulou's C^0 formulation, the strong cosmic censorship conjecture is false for this system.

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Mihalis Dafermos. 2004-11-06. The interior of charged black holes and the problem of uniqueness in general relativity. https://arxiv.org/abs/gr-qc/0307013

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