Strong Cosmic Censorship in Spherical Symmetry for Two-Ended Asymptotically Flat Initial Data II: The Exterior of the Black Hole Region View Full Text


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Article Info

DATE

2019-06

AUTHORS

Jonathan Luk, Sung-Jin Oh

ABSTRACT

This is the second and last paper of a two-part series in which we prove the C2-formulation of the strong cosmic censorship conjecture for the Einstein–Maxwell–(real)–scalar–field system in spherical symmetry for two-ended asymptotically flat data. In the first paper, we showed that the maximal globally hyperbolic future development of an admissible asymptotially flat Cauchy initial data set is C2-future-inextendible provided that an L2-averaged (inverse) polynomial lower bound for the derivative of the scalar field holds along each horizon. In this paper, we show that this lower bound is indeed satisfied for solutions arising from a generic set of Cauchy initial data. Roughly speaking, the generic set is open with respect to a (weighted) C1 topology and is dense with respect to a (weighted) C∞ topology. The proof of the theorem is based on extensions of the ideas in our previous work on the linear instability of Reissner–Nordström Cauchy horizon, as well as a new large data asymptotic stability result which gives good decay estimates for the difference of the radiation fields for small perturbations of an arbitrary solution. More... »

PAGES

6

Journal

TITLE

Annals of PDE

ISSUE

1

VOLUME

5

From Grant

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    http://scigraph.springernature.com/pub.10.1007/s40818-019-0062-7

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