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Communications in Mathematical Physics

, Volume 361, Issue 1, pp 289–341 | Cite as

On the Occurrence of Mass Inflation for the Einstein–Maxwell-Scalar Field System with a Cosmological Constant and an Exponential Price Law

  • João L. Costa
  • Pedro M. Girão
  • José Natário
  • Jorge Drumond Silva
Article

Abstract

In this paper we study the spherically symmetric characteristic initial data problem for the Einstein–Maxwell-scalar field system with a positive cosmological constant in the interior of a black hole, assuming an exponential Price law along the event horizon. More precisely, we construct open sets of characteristic data which, on the outgoing initial null hypersurface (taken to be the event horizon), converges exponentially to a reference Reissner–Nördstrom black hole at infinity. We prove the stability of the radius function at the Cauchy horizon, and show that, depending on the decay rate of the initial data, mass inflation may or may not occur. In the latter case, we find that the solution can be extended across the Cauchy horizon with continuous metric and Christoffel symbols in \({L^2_{{\rm loc}}}\), thus violating the Christodoulou–Chruściel version of strong cosmic censorship.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • João L. Costa
    • 1
    • 2
  • Pedro M. Girão
    • 2
  • José Natário
    • 2
  • Jorge Drumond Silva
    • 2
  1. 1.ISCTE, Instituto Universitário de LisboaLisbonPortugal
  2. 2.CAMGSD, Instituto Superior TécnicoUniversidade de LisboaLisbonPortugal

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