The Reissner-Nordstr”om black hole with the fastest relaxation rate. (arXiv:1812.01014v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Hod_S/0/1/0/all/0/1">Shahar Hod</a>
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-Nordstr”om 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-Nordstr”om
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 {it fastest} relaxation rate (the smallest dimensionless
relaxation time ${bar tau}$) within the family of charged
Reissner-Nordstr”om black-hole spacetimes.
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-Nordstr”om 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-Nordstr”om
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 {it fastest} relaxation rate (the smallest dimensionless
relaxation time ${bar tau}$) within the family of charged
Reissner-Nordstr”om black-hole spacetimes.
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