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2019 The interior of dynamical extremal black holes in spherical symmetry
Dejan Gajic, Jonathan Luk
Pure Appl. Anal. 1(2): 263-326 (2019). DOI: 10.2140/paa.2019.1.263

Abstract

We study the nonlinear stability of the Cauchy horizon in the interior of extremal Reissner–Nordström black holes under spherical symmetry. We consider the Einstein–Maxwell–Klein–Gordon system such that the charge of the scalar field is appropriately small in terms of the mass of the background extremal Reissner–Nordström black hole. Given spherically symmetric characteristic initial data which approach the event horizon of extremal Reissner–Nordström sufficiently fast, we prove that the solution extends beyond the Cauchy horizon in C 0 , 1 2 W loc 1 , 2 , in contrast to the subextremal case (where generically the solution is C 0 ( C 0 , 1 2 W loc 1 , 2 ) ). In particular, there exist nonunique spherically symmetric extensions which are moreover solutions to the Einstein–Maxwell–Klein–Gordon system. Finally, in the case that the scalar field is chargeless and massless, we additionally show that the extension can be chosen so that the scalar field remains Lipschitz.

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Dejan Gajic. Jonathan Luk. "The interior of dynamical extremal black holes in spherical symmetry." Pure Appl. Anal. 1 (2) 263 - 326, 2019. https://doi.org/10.2140/paa.2019.1.263

Information

Received: 12 January 2019; Accepted: 12 February 2019; Published: 2019
First available in Project Euclid: 14 May 2019

zbMATH: 07079480
MathSciNet: MR3949375
Digital Object Identifier: 10.2140/paa.2019.1.263

Subjects:
Primary: 35L51 , 83C05 , 83C57 , 83C75

Keywords: black hole interior , Cauchy horizon , extremal black hole , strong cosmic censorship conjecture

Rights: Copyright © 2019 Mathematical Sciences Publishers

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