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Strong cosmic
censorship in the presence of matter: the decisive effect of
horizon oscillations on the black hole interior geometry
Christoph Kehle and Maxime Van de Moortel |
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Vol. 17 (2024), No. 5, 1501–1592
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Abstract |
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Motivated by the strong cosmic censorship conjecture in the presence of matter, we study the Einstein equations coupled with a charged/massive scalar field with spherically symmetric characteristic data relaxing to a Reissner–Nordström event horizon. Contrary to the vacuum case, the relaxation rate is conjectured to be slow (nonintegrable), opening the possibility that the matter fields and the metric coefficients blow up in amplitude at the Cauchy horizon, not just in energy. We show that whether this blow-up in amplitude occurs or not depends on a novel oscillation condition on the event horizon which determines whether or not a resonance is excited dynamically:
Heuristic arguments in the physics literature indicate that the oscillation condition should be satisfied generically on the event horizon. If these heuristics are true, then our result falsifies the -formulation of strong cosmic censorship by means of oscillation. |
Keywords
strong cosmic censorship, black hole, Einstein equations,
scattering, charged scalar field
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Mathematical Subject Classification
Primary: 35Q75, 35Q76, 83C05, 83C57, 83C75
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Milestones
Received: 31 May 2021
Revised: 7 April 2022
Accepted: 21 December 2022
Published: 20 June 2024
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Authors |
| Christoph Kehle | |
| Institute for Theoretical
Studies ETH Zürich Zürich Switzerland |
Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States |
| Maxime Van de Moortel | |
| Department of Mathematics Princeton University Princeton, NJ United States |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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