Strong cosmic censorship in spherical symmetry for two-ended asymptotically flat initial data. I: The interior of the black hole region
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.
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