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On the horizon instability of an extreme Reissner-Nordström black hole

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Abstract

Aretakis has proved that a massless scalar field has an instability at the horizon of an extreme Reissner-Nordström black hole. We show that a similar instability occurs also for a massive scalar field and for coupled linearized gravitational and electromagnetic perturbations. We present numerical results for the late time behaviour of massless and massive scalar fields in the extreme RN background and show that instabilities are present for initial perturbations supported outside the horizon, e.g. an ingoing wavepacket. For a massless scalar we show that the numerical results for the late time behaviour are reproduced by an analytic calculation in the near-horizon geometry. We relate Aretakis’ conserved quantities at the future horizon to the Newman-Penrose conserved quantities at future null infinity.

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Author information

Authors and Affiliations

  1. School of Mathematics and Maxwell Institute of Mathematical Sciences, University of Edinburgh, Edinburgh, EH9 3JZ, U.K.

    James Lucietti

  2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, U.K.

    Keiju Murata & Harvey S. Reall

  3. Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 608-8502, Japan

    Keiju Murata

  4. Department of Physics, University of California, Davis, CA, 95616, U.S.A.

    Norihiro Tanahashi

Authors
  1. James Lucietti
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  2. Keiju Murata
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  3. Harvey S. Reall
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  4. Norihiro Tanahashi
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Corresponding author

Correspondence to Keiju Murata.

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ArXiv ePrint: 1212.2557

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Lucietti, J., Murata, K., Reall, H.S. et al. On the horizon instability of an extreme Reissner-Nordström black hole. J. High Energ. Phys. 2013, 35 (2013). https://doi.org/10.1007/JHEP03(2013)035

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  • DOI: https://doi.org/10.1007/JHEP03(2013)035

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