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

TL;DR

This paper links near-horizon geometry perturbations of extreme black holes to scalar field equations in AdS_2, proposing a stability criterion based on a Breitenlohner-Freedman bound and providing evidence for potential instabilities in higher dimensions.

Contribution

It introduces a Kaluza-Klein reduction approach to relate black hole perturbations to charged scalar fields in AdS_2 and conjectures a stability criterion based on this framework.

Findings

Evidence of instability in 7+ dimensions for Myers-Perry black holes.

Predictions of operator conformal weights in 5d with CFT dual.

Sketch of proof for the scalar field perturbation conjecture.

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.