Universality of small black hole instability in AdS/CFT

Abstract

$Ad{S}_5$ type IIb supergravity compactifications on five-dimensional Einstein manifolds ${\mathcal{V}}_5$ 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) $Ad{S}_5$, they are expected to suffer Gregory-Laflamme instability with respect to localization on ${\mathcal{V}}_5$. Previously, the instability was demonstrated for gravitational dual of $\mathcal{N}=4$ SYM, where ${\mathcal{V}}_5=S^5$. We extend stability analysis to arbitrary ${\mathcal{V}}_5$. We point out that the quasinormal mode equation governing the instabilities is universal. The precise onset of the instability is ${\mathcal{V}}_5$-sensitive, as it is governed by the lowest non-vanishing eigenvalue ${\lambda }_{min}$ of its Laplacian.

arXiv comment11 pages, 2 figures