# Stability analysis of rotating black holes with equal angular momenta

We study the dynamical stability of five-dimensional Myers-Perry black holes with equal angular momenta which have an enlarged symmetry, U(2). Using this symmetry, we derive master equations for a part of metric perturbations which are relevant to the stability. Based on the master equations, we prove the stability of Myers-Perry black holes under these perturbations. Our result gives strong evidence for the stability of Myers-Perry black holes with equal angular momenta. We also apply the formalism to the Kerr-AdS$_5\times S^5$ spacetime with equal angular momenta. In this spacetime, we found the two types of classical instability, superradiant and Gregory-Laflamme. We discuss the gauge dual of these instabilities.

This talk is part of the DAMTP Friday GR Seminar series.