Asymptotic quasinormal modes of Reissner-Nordstr\"om and Kerr black holes

TL;DR

This paper numerically computes highly-damped quasinormal modes of charged and rotating black holes, revealing oscillatory behaviors and limits that connect classical black hole properties with quantum gravity insights.

Contribution

It provides the first numerical analysis of highly damped QNM frequencies for Reissner-Nordström and Kerr black holes, uncovering new oscillatory patterns and asymptotic behaviors.

Findings

QNM frequencies show oscillatory behavior with charge and mode order.

QNM spirals tend towards a limit as black holes become extremal.

Kerr QNM frequencies relate to horizon angular velocity and temperature.

Abstract

According to a recent proposal, the so-called Barbero-Immirzi parameter of Loop Quantum Gravity can be fixed, using Bohr's correspondence principle, from a knowledge of highly-damped black hole oscillation frequencies. Such frequencies are rather difficult to compute, even for Schwarzschild black holes. However, it is now quite likely that they may provide a fundamental link between classical general relativity and quantum theories of gravity. Here we carry out the first numerical computation of very highly damped quasinormal modes (QNM's) for charged and rotating black holes. In the Reissner-Nordstr\"om case QNM frequencies and damping times show an oscillatory behaviour as a function of charge. The oscillations become faster as the mode order increases. At fixed mode order, QNM's describe spirals in the complex plane as the charge is increased, tending towards a well defined limit as the hole becomes extremal. Kerr QNM's have a similar oscillatory behaviour when the angular index $m=0$. For $l=m=2$ the real part of Kerr QNM frequencies tends to $2\Omega$, $\Omega$ being the angular velocity of the black hole horizon, while the asymptotic spacing of the imaginary parts is given by $2\pi T_H$.