Quasinormal Modes from Penrose Limits

Abstract

We use Penrose limits to approximate quasinormal modes with large real frequencies. The Penrose limit associates a plane wave to a region of spacetime near a null geodesic. This plane wave can be argued to geometrically realize the geometrical optics approximation. Therefore, when applied to the bound null orbits around black holes, the Penrose limit can be used to study quasinormal modes. For instance, this Penrose limit point of view makes manifest the symmetry that emerges in the geometrical optics approximation of quasinormal modes in terms of isometries of the resulting plane wave spacetime. We apply the procedure to warped AdS3, Schwarzschild black holes and Kerr black holes. In the former we show explicitly how the symmetry algebra contracts to that of the limiting plane wave while in the latter we find the expected agreement with numerically computed quasinormal modes for large (real) frequencies. Contents 1. Introduction 2. Warped AdS 3 3. The Schwarzschild black hole 4. The Kerr black hole 5. Conclusion and outlook References

Tidal forces in Kerr-AdS and Grey galaxies

“…In general, this plane wave metric is time-dependent and not diagonal. It is identical to the plane wave limit of the Kerr black hole recently reported in [28]. Curiously enough, all the L dependences drop out and the answer (3.83)-(3.84) for the Kerr-AdS is identical to the Kerr case.…”