The Reissner\u2013Nordstr\xf6m black hole with the fastest relaxation rate

Abstract

Numerous 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 (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 fastest relaxation rate. In the present paper we use 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}}={{sqrt{51-3sqrt{33}}}over {8}}simeq 0.73 is characterized by the fastest relaxation rate (the smallest dimensionless relaxation time {{bar{tau }}}) within the family of charged Reissner–Nordström black-hole spacetimes.