Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data. I: The interior of the black hole region
type: Item
instance of: scholarly article
title: Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data. I: The interior of the black hole region
zbMATH Open document ID: 1429.83046
author: Jonathan Luk
author: Sungjin Oh
published in: Annals of Mathematics. Second Series
publication date: 2019-08-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/1702.05715
review text: The article is of actual interest. In spite of the authors do not write about, it is of interest, of course, for science-fiction writers, which imagine flies inside black holes interiors, after traversing the exterior events horizon. They divide their research in 2 parts: the first one concerns Reissner-Nordström's Cauchy (internal) horizon and the second one, forthcoming, the Kerr's Cauchy (internal) horizon. The problem was investigated before, since 1974 and 1980 by many authors, including the authors of the actual paper, and some results of interest were obtained. The first one rigorous formulation was given by \textit{M. Dafermos} [Commun. Math. Phys. 332, No. 2, 729--757 (2014; Zbl 1301.83021)] and \textit{M. Dafermos} and \textit{I. Rodnianski} [Commun. Pure Appl. Math. 62, No. 7, 859--919 (2009; Zbl 1169.83008); in: XVIth international congress on mathematical physics, Prague, Czech Republic, August 3--8, 2009. Hackensack, NJ: World Scientific. 421--432 (2010; Zbl 1211.83019)]. The authors introduce some new notions as: extendibility and non-extendibility of a space-time. Both papers, from which the second is in press, are designed to confer mathematical rigourousity to previous results by formulation and proof of some theorems, which according to the authors should elucidate the problem. Particularly, key to the proof are appropriate stability and instability results in the interior of the black hole region, whose proofs are in turn based on ideas from the work of \textit{M. Dafermos} and the first author [``The interior of dynamical vacuum black holes. I: The \(C^0\)-stability of the Kerr Cauchy horizon'', Preprint, \url{arXiv:1710.01722}] on the stability of the Kerr Cauchy horizon (without symmetry) and from the author's previous paper on linear instability of the Reissner-Nordström Cauchy horizon.
Mathematics Subject Classification ID: 83C75
Mathematics Subject Classification ID: 35Q75
Mathematics Subject Classification ID: 83C05
Mathematics Subject Classification ID: 83C57
Mathematics Subject Classification ID: 83C22
zbMATH DE Number: 7097496
zbMATH Keywords: black hole interior
zbMATH Keywords: strong cosmic censorship
zbMATH Keywords: Cauchy horizon
zbMATH Keywords: null singularities
reviewed by: Alex B. Gaina
MaRDI profile type: Publication
OpenAlex ID: W2962878655
arXiv ID: 1702.05715
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Wikidata QID: Q127552032
DOI: 10.4007/ANNALS.2019.190.1.1
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