2013/05/23 by Carlos A. R. Herdeiro, Juan Carlos Degollado, Helgi Freyr Rúnarsson
Physics and Astronomy · #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.88.063003
7 pages, 3 figures
arxiv created 2013/05/23 · arxiv updated 2013/09/11
Confined scalar fields, either by a mass term or by a mirror-like boundary condition, have unstable modes in the background of a Kerr black hole. Assuming a time dependence as e-iωt, the growth time-scale of these unstable modes is set by the inverse of the (positive) imaginary part of the frequency, Im(ω), which reaches a maximum value of the order of Im(ω)M∼ 10-5, attained for a mirror-like boundary condition, where M is the black hole mass. In this paper we study the minimally coupled Klein-Gordon equation for a charged scalar field in the background of a Reissner-Nordström black hole and show that the unstable modes, due to a mirror-like boundary condition, can grow several orders of magnitude faster than in the rotating case: we have obtained modes with up to Im(ω)M∼ 0.07. We provide an understanding, based on an analytic approximation, to why the instability in the charged case has a smaller timescale than in the rotating case. This faster growth, together with the spherical symmetry, makes the charged case a promising model for studies of the fully non-linear development of superradiant instabilities.