It is shown that the equations governing linearized gravitational (or
electromagnetic) perturbations of the near-horizon geometry of any known
extreme vacuum black hole (allowing for a cosmological constant) can be
Kaluza-Klein reduced to give the equation of motion of a charged scalar field
in AdS\_2 with an electric field. One can define an effective
Breitenlohner-Freedman bound for such a field. We conjecture that if a
perturbation preserves certain symmetries then a violation of this bound should
imply an instability of the full black hole solution. Evidence in favour of
this conjecture is provided by the extreme Kerr solution and extreme
cohomogeneity-1 Myers-Perry solution. In the latter case, we predict an
instability in seven or more dimensions and, in 5d, we present results for
operator conformal weights assuming the existence of a CFT dual. We sketch a
proof of our conjecture for scalar field perturbations.
%0 Journal Article
%1 Durkee2011Perturbations
%A Durkee, Mark
%A Reall, Harvey S.
%D 2011
%J Physical Review D
%K arxiv, kerr-cft, kerrbh
%N 10
%R 10.1103/physrevd.83.104044
%T Perturbations of near-horizon geometries and instabilities of Myers-Perry black holes
%U http://dx.doi.org/10.1103/physrevd.83.104044
%V 83
%X It is shown that the equations governing linearized gravitational (or
electromagnetic) perturbations of the near-horizon geometry of any known
extreme vacuum black hole (allowing for a cosmological constant) can be
Kaluza-Klein reduced to give the equation of motion of a charged scalar field
in AdS\_2 with an electric field. One can define an effective
Breitenlohner-Freedman bound for such a field. We conjecture that if a
perturbation preserves certain symmetries then a violation of this bound should
imply an instability of the full black hole solution. Evidence in favour of
this conjecture is provided by the extreme Kerr solution and extreme
cohomogeneity-1 Myers-Perry solution. In the latter case, we predict an
instability in seven or more dimensions and, in 5d, we present results for
operator conformal weights assuming the existence of a CFT dual. We sketch a
proof of our conjecture for scalar field perturbations.
@article{Durkee2011Perturbations,
abstract = {{It is shown that the equations governing linearized gravitational (or
electromagnetic) perturbations of the near-horizon geometry of any known
extreme vacuum black hole (allowing for a cosmological constant) can be
Kaluza-Klein reduced to give the equation of motion of a charged scalar field
in AdS\_2 with an electric field. One can define an effective
Breitenlohner-Freedman bound for such a field. We conjecture that if a
perturbation preserves certain symmetries then a violation of this bound should
imply an instability of the full black hole solution. Evidence in favour of
this conjecture is provided by the extreme Kerr solution and extreme
cohomogeneity-1 Myers-Perry solution. In the latter case, we predict an
instability in seven or more dimensions and, in 5d, we present results for
operator conformal weights assuming the existence of a CFT dual. We sketch a
proof of our conjecture for scalar field perturbations.}},
added-at = {2019-02-26T10:37:35.000+0100},
archiveprefix = {arXiv},
author = {Durkee, Mark and Reall, Harvey S.},
biburl = {https://www.bibsonomy.org/bibtex/2a0dd525d4da5625ddc875eaaf1969c07/acastro},
citeulike-article-id = {8473005},
citeulike-linkout-0 = {http://arxiv.org/abs/1012.4805},
citeulike-linkout-1 = {http://arxiv.org/pdf/1012.4805},
citeulike-linkout-2 = {http://dx.doi.org/10.1103/physrevd.83.104044},
day = 22,
doi = {10.1103/physrevd.83.104044},
eprint = {1012.4805},
interhash = {b9e9958644166501d8be2f5f90d973ae},
intrahash = {a0dd525d4da5625ddc875eaaf1969c07},
issn = {1550-7998},
journal = {Physical Review D},
keywords = {arxiv, kerr-cft, kerrbh},
month = apr,
number = 10,
posted-at = {2010-12-23 03:09:30},
priority = {2},
timestamp = {2019-02-26T10:37:35.000+0100},
title = {{Perturbations of near-horizon geometries and instabilities of Myers-Perry black holes}},
url = {http://dx.doi.org/10.1103/physrevd.83.104044},
volume = 83,
year = 2011
}