Instability in near-horizon geometries of even-dimensional Myers-Perry black holes

TL;DR

This paper investigates the stability of near-horizon geometries of even-dimensional extremal Myers-Perry black holes, finding potential instabilities due to gravitational perturbations that violate the Breitenl"ohner-Freedman bound in AdS$_2$.

Contribution

It provides the first analysis of perturbations in these geometries, revealing possible instabilities and discussing implications for the Kerr-CFT correspondence.

Findings

Some gravitational modes violate the Breitenl"ohner-Freedman bound in AdS$_2$

Near-horizon geometries of even-dimensional extremal Myers-Perry black holes are potentially unstable

Results have implications for the Kerr-CFT correspondence

Abstract

We study the gravitational, electromagnetic and scalar field perturbations on the near-horizon geometries of the even-dimensional extremal Myers-Perry black holes. By dimensional reduction, the perturbation equations are reduced to effective equations of motion in AdS$_2$. We find that some modes in the gravitational perturbations violate the Breitenl\"ohner-Freedman bound in AdS$_2$. This result suggests that the even-dimensional (near-)extremal Myers-Perry black holes are unstable against gravitational perturbations. We also discuss implications of our results to the Kerr-CFT correspondence.