Exact quasi-normal modes for the near horizon Kerr metric

Abstract

We study the quasi-normal modes of a massless scalar field in a general sub-extreme Kerr back- ground by exploiting the hidden SL(2, R) x SL(2, R) x SO(3) symmetry of the subtracted geometry approximation. This faithfully models the near horizon geometry but locates the black hole in a confining asymptotically conical box analogous to the anti-de-Sitter backgrounds used in string the- ory. There are just two series of modes, given in terms of hypergeometric functions and spherical harmonics, reminiscent of the left-moving and right-moving degrees in string theory: one is over- damped, the other is underdamped and exhibits rotational splitting. The remarkably simple exact formulae for the complex frequencies would in principle allow the determination of the mass and angular momentum from observations of a black hole. No black hole bomb is possible because the Killing field which co-rotates with the horizon is everywhere timelike outside the black hole.

4 pages

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