2012/12/31 by James Lucietti, Keiju Murata, Harvey S. Reall +1
Physics and Astronomy · #gr-qc #hep-th
paper · pdf · doi:10.1007/jhep03(2013)035
44 pages, 19 figures
arxiv created 2013/04/23 · arxiv updated 2015/06/12
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.