Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-12-21
Phys.Rev.D83:104044,2011
Physics
High Energy Physics
High Energy Physics - Theory
24 pages (+ 16 pages appendices), 2 figures. v2: Corrected error in CFT operator dimensions (they are all integers). v3: Vario
Scientific paper
10.1103/PhysRevD.83.104044
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.
Durkee Mark
Reall Harvey S.
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