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

By Mihalis Dafermos. 2003

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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 C0 metric but along which the Hawking mass blows up identically; thus, the space‐time is inextendible as a C1 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 C0 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 C0 formulation, the strong cosmic censorship conjecture is false for this system. © 2005 Wiley Periodicals, Inc.

Subfields: Astronomy and Astrophysics, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/903dd6527ad4e728841e8f98bbb7f7937c8a23aa

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Citations in the corpus

The evolution problem in general relativity (2008, background): “For both the charged-scalar field system and the Bianchi IX vacuum system, even more ambitious than Open problem 13 would be to study the strong and weak cosmic censorship conjectures, possibly unifying the analysis of [40, 51, 52].”
On the viability of regular black holes (2018, background): “ area (see, for instance, the recent works [26{29]1), the main aspects were settled more than two decades ago [30{ 35], though formal proofs of a number of technical aspects were only available later [36] (see also [37] for a review). In brief terms, the central conclusion of these works is that the”
The interior of dynamical vacuum black holes I: The $C^0$-stability of the Kerr Cauchy horizon (2017, background): “Restricting to such spherically symmetric extensions, and under the additional assumption of a pointwise lower bound on the horizon H, one can show also that the Christoffel symbols are not in L(2)loc at CH + [27].”
Lectures on black holes and linear waves (2008, methodology): “ndedness (see Theorem 5.1) and decay (see Theorem 5.2) can be proven for the wave equation on suitable perturbations of Schwarzschild. As we shall see, the 47See for instance the relevance of this in [59]. 55 boundedness proof (See Section 5.2) turns out to be more robust and can be applied to a lar”
Silhouette of M87*: A new window to peek into the world of hidden dimensions (2019, background): “This includes existence of spacetime singularities, loss of predictability of Einstein’s equations beyond Cauchy horizons [10–15] and the necessity to invoke exotic forms of matter and energy like the dark matter and dark energy [16–19].”
A proof of Price’s law for the collapse of a self-gravitating scalar field (2003, methodology): “The motivation for this system has been discussed in previous work of the first author [22, 23 ].”
Quantum geometry and the Schwarzschild singularity (2005, background): “However, if the matter is charged, the generic singularity is not timelike as in the Reissner–Nordstrom case, but null [12].”
The red‐shift effect and radiation decay on black hole spacetimes (2005, methodology): “It is interesting to note that the decay rates (4)–(5) are sufficiently fast so as to suggest that the picture established in [ 7 ] may remain valid in the absense of symmetry assumptions, in particular, the existence of a marginally trapped tube which becomes achronal and terminates at i + , and a ”
A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds (2008, methodology): “The results of [ 17 ], when specialised to the simpler case of a scalar field on a fixed Schwarzschild or Reissner-Nordstrom background (with charge Q) lead to the statement that boundedness and decay properties propagate from H + to the region”