Universality of small black hole instability in AdS/CFT

TL;DR

This paper demonstrates that small black holes in AdS/CFT are universally unstable due to Gregory-Laflamme instability, with the onset depending on the eigenvalues of the internal manifold's Laplacian.

Contribution

It extends the stability analysis of small black holes in AdS/CFT to arbitrary five-dimensional Einstein manifolds, revealing a universal quasinormal mode equation governing the instability.

Findings

Instability occurs for small black holes in various AdS/CFT setups.

The onset of instability depends on the lowest eigenvalue of the Laplacian on the internal manifold.

The quasinormal mode equation is universal across different internal geometries.

Abstract

$AdS_5$ type IIb supergravity compactifications on five-dimensional Einstein manifolds ${\cal V}_5$ realize holographic duals to four-dimensional conformal field theories. Black holes in such geometries are dual to thermal states in these CFTs. When black holes become sufficiently small in (global) $AdS_5$, they are expected to suffer Gregory-Laflamme instability with respect to localization on ${\cal V}_5$. Previously, the instability was demonstrated for gravitational dual of ${\cal N}=4$ SYM, where ${\cal V}_5=S^5$. We extend stability analysis to arbitrary ${\cal V}_5$. We point out that the quasinormal mode equation governing the instabilities is universal. The precise onset of the instability is ${\cal V}_5$-sensitive, as it is governed by the lowest non-vanishing eigenvalue $\lambda_{min}$ of its Laplacian.