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

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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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Authors and Affiliations

  1. ISCTE, Instituto Universitário de Lisboa, Av. das Forças Armadas, 1649-026, Lisbon, Portugal

    João L. Costa

  2. CAMGSD, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001, Lisbon, Portugal

    João L. Costa, Pedro M. Girão, José Natário & Jorge Drumond Silva

Authors
  1. João L. Costa
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  2. Pedro M. Girão
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  3. José Natário
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  4. Jorge Drumond Silva
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Corresponding author

Correspondence to Jorge Drumond Silva.

Additional information

Communicated by P. Chrusciel

This work was partially supported by FCT/Portugal through UID/MAT/04459/2013 and Grant (GPSEinstein) PTDC/MAT-ANA/1275/2014.

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Costa, J.L., Girão, P.M., Natário, J. et al. On the Occurrence of Mass Inflation for the Einstein–Maxwell-Scalar Field System with a Cosmological Constant and an Exponential Price Law. Commun. Math. Phys. 361, 289–341 (2018). https://doi.org/10.1007/s00220-018-3122-z

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  • DOI: https://doi.org/10.1007/s00220-018-3122-z

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