The extremal black hole bomb

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Abstract

We analyze the spectrum of massive scalar bound states in the background of extremal Kerr black holes, focusing on modes in the superradiant regime, which grow exponentially in time and quickly deplete the black hole’s mass and spin. Previous analytical estimates for the growth rate of this instability were limited to the μM ≪ 1 and μM ≫ 1 regimes, where μ and M denote the scalar field and black hole masses, respectively. In this work, we discuss an analytical method to compute the superradiant spectrum for generic values of these parameters, namely in the phenomenologically interesting regime μM ∼ 1. To do this, we solve the radial mode equation in two overlapping regions and match the solutions in their common domain of validity. We show that matching the functional forms of these functions involves approximations that are not valid for the whole range of scalar masses, exhibiting unphysical poles that produce a large enhancement of the growth rate. Alternatively, we match the functions at a single point and show that, despite the uncertainty in the choice of the match point, this method eliminates the spurious poles and agrees with previous numerical computations of the spectrum using a continued-fraction method.

Keywords

Black Holes Classical Theories of Gravity Black Holes in String Theory 
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Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  1. 1.Rudolf Peierls Centre for Theoretical Physics, Department of PhysicsUniversity of OxfordOxfordU.K.

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