Stability of rapidly-rotating charged black holes in $AdS_5 \times S^5$

TL;DR

This paper investigates the stability of extremal charged rotating black holes in AdS_5 x S^5, finding they become unstable when their angular velocity exceeds a certain threshold, with implications for their thermodynamic behavior.

Contribution

It provides a detailed analysis of the quasi-normal modes and stability regimes of these black holes, linking dynamical and thermodynamic instabilities in this setting.

Findings

Black holes are unstable when angular velocity exceeds 1.

Thermodynamic instability coincides with dynamical instability.

Results suggest possible endpoints for the instability process.

Abstract

We study the stability of charged rotating black holes in a consistent truncation of Type $IIB$ Supergravity on $AdS_5 \times S^5$ that degenerate to extremal black holes with zero entropy. These black holes have scaling properties between charge and angular momentum similar to those of Fermi surface-like operators in a subsector of ${\cal N}=4$ SYM. By solving the equation of motion for a massless scalar field in this background, using matched asymptotic expansion followed by a numerical solution scheme, we are able to compute its Quasi-Normal modes, and analyze it's regime of (in)stability. We find that the black hole is unstable when its angular velocity with respect to the horizon exceeds 1 (in units of $1/l_{AdS}$). A study of the relevant thermodynamic Hessian reveals a local thermodynamic instability which occurs at the same region of parameter space. We comment on the endpoints of this instability.