Universality of small black hole instability in AdS/CFT

Abstract

[Formula: see text] Type IIb supergravity compactifications on five-dimensional Einstein manifolds [Formula: see text] 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) [Formula: see text], they are expected to suffer Gregory–Laflamme instability with respect to localization on [Formula: see text]. Previously, the instability was demonstrated for gravitational dual of [Formula: see text] SYM, where [Formula: see text]. We extend stability analysis to arbitrary [Formula: see text]. We point out that the quasinormal mode equation governing the instabilities is universal. The precise onset of the instability is [Formula: see text]-sensitive, as it is governed by the lowest nonvanishing eigenvalue [Formula: see text] of its Laplacian.