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arXiv · 1012.4805

Perturbations of near-horizon geometries and instabilities of Myers-Perry black holes

Mark Durkee·Harvey S. Reall
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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.

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Mark Durkee, Harvey S. Reall. 2010-12-21. Perturbations of near-horizon geometries and instabilities of Myers-Perry black holes. https://doi.org/10.1103/physrevd.83.104044

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