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

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Abstract

We consider a spherically symmetric, double characteristic initial value problem for the (real) 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 future development has a future boundary over which the space-time is extendible as a C 0 metric but along which the Hawking mass blows up identically; thus, the space-time is inextendible as a C 1 metric. In view of recent results of the author in collaboration with I. Rodnianski, which rigorously establish the validity of Price's law as an upper bound for the decay of scalar field hair, the C 0 extendibility result applies to the collapse of complete, asymptotically flat, spacelike initial data where the scalar field is compactly supported. This shows that under Christodoulou's C 0 formulation, the strong cosmic censorship conjecture is false for this system.

Original languageEnglish (US)
Pages (from-to)445-504
Number of pages60
JournalCommunications on Pure and Applied Mathematics
Volume58
Issue number4
DOIs
StatePublished - Apr 1 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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