Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-12-09
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, 6 figures; version to appear in JHEP, added one figure, references and discussion
Scientific paper
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 $\mu M\ll1$ and $\mu M\gg1$ regimes, where $\mu$ 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 $\mu M\sim 1$. 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.
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