Analytic Study of Rotating Black-Hole Quasinormal Modes

TL;DR

This paper derives a Bohr-Sommerfeld quantization condition for the highly-damped quasinormal modes of rotating black holes, providing a new analytical approach to understanding their frequency spectrum.

Contribution

It introduces a novel Bohr-Sommerfeld equation for quasinormal modes of rotating black holes, linking classical geodesic properties to quantum-like mode frequencies.

Findings

Derived a quantization condition for high damping modes.

Expressed mode frequencies in terms of black hole parameters.

Discussed physical implications of the mode spectrum.

Abstract

A Bohr-Sommerfeld equation is derived for the highly-damped quasinormal mode frequencies omega(n>>1) of rotating black holes. It may be written as 2\int_C(p_r+ip_0)dr=(n+1/2)h, where p_r is the canonical momentum conjugate to the radial coordinate r along null geodesics of energy hbar*omega and angular momentum hbar*m, p_0=O(omega^0), and the contour C connects two complex turning points of p_r. The solutions are omega(n) = - m*omega_0 - i(phi + n*delta), where {omega_0,delta}>0 are functions of the black-hole parameters alone. Some physical implications are discussed.