Quasinormal Modes from Penrose Limits

TL;DR

This paper introduces a novel method using Penrose limits to approximate and analyze quasinormal modes of black holes, revealing symmetries and matching numerical results for large real frequencies.

Contribution

It applies Penrose limits to study quasinormal modes, demonstrating symmetry contractions and providing analytical approximations that agree with numerical data.

Findings

Symmetry algebra contracts to that of the plane wave in the limit.

The method matches numerical quasinormal modes for large real frequencies.

Penrose limits reveal geometric and symmetry properties of quasinormal modes.

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 $\rm{AdS}_3$, 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.