%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 }