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

  • James Lucietti
  • Keiju MurataEmail author
  • Harvey S. Reall
  • Norihiro Tanahashi
Article

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.

Keywords

Classical Theories of Gravity Black Holes Black Holes in String Theory 

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Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  • James Lucietti
    • 1
  • Keiju Murata
    • 2
    • 3
    Email author
  • Harvey S. Reall
    • 2
  • Norihiro Tanahashi
    • 4
  1. 1.School of Mathematics and Maxwell Institute of Mathematical SciencesUniversity of EdinburghEdinburghU.K.
  2. 2.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeU.K.
  3. 3.Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan
  4. 4.Department of PhysicsUniversity of CaliforniaDavisU.S.A.

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