The Reissner-Nordström black hole with the fastest relaxation rate

Abstract

Numerous {\it numerical} investigations of the quasinormal resonant spectra of Kerr-Newman black holes have revealed the interesting fact that the characteristic relaxation times $\tau (\bar{a},\bar{Q})$ of these canonical black-hole spacetimes can be described by a two-dimensional function $\bar{\tau }\equiv \tau /M$ which increases monotonically with increasing values of the dimensionless angular-momentum parameter $\bar{a}\equiv J/M^2$ and, in addition, is characterized by a non-trivial ({\it non}-monotonic) functional dependence on the dimensionless charge parameter $\bar{Q}\equiv Q/M$. In particular, previous numerical investigations have indicated that, within the family of spherically symmetric charged Reissner-Nordström spacetimes, the black hole with $\bar{Q}\simeq 0.7$ has the {\it fastest} relaxation rate. In the present paper we use {\it analytical} techniques in order to investigate this intriguing non-monotonic functional dependence of the Reissner-Nordström black-hole relaxation rates on the dimensionless physical parameter $\bar{Q}$. In particular, it is proved that, in the eikonal (geometric-optics) regime, the black hole with $\bar{Q}=\frac{\sqrt{51-3\sqrt{33}}}{8}\simeq 0.73$ is characterized by the {\it fastest} relaxation rate (the smallest dimensionless relaxation time $\bar{\tau }$) within the family of charged Reissner-Nordström black-hole spacetimes.

5 pages

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• Bekenstein-Hod Universal Bound on Information Emission Rate Is Obeyed by LIGO-Virgo Binary Black Hole Remnants
• Analytical studies on the hoop conjecture in charged curved spacetimes
• The fastest relaxation rate of higher-dimensional Reissner--Nordström black hole
• Relaxation rate of RNdS black hole
• On the five-dimensional non-extremal Reissner-Nordström black hole: Retractions and scalar quasibound states