On the stability of AdS black strings

TL;DR

This work analyzes the classical stability of AdS black strings under linearized perturbations to address the Gregory-Laflamme instability in the presence of a negative cosmological constant. Using a perturbative ansatz around the AdS uniform black string, the authors derive an eigenvalue problem for the GL mode, solve it numerically across dimensions $5\le d\le8$ and topologies $\kappa=0,\pm1$, and map the instability region as a function of horizon radius $r_h$ and cosmological scale $\ell$. They find that AdS UBSs with horizon topology $S^{d-3}\times S^1$ are unstable below a critical configuration, whereas topological strings $\kappa=0,-1$ are classically stable, with the onset of instability coinciding with the GM conjecture’s thermodynamic criteria via the $(S,T_H)$ diagram. The results provide an explicit AdS realization of the GM conjecture and suggest broader implications for AdS black rings and other AdS black objects.

Abstract

We explore via linearized perturbation theory the Gregory-Laflamme instability of the black string solutions of Einstein's equations with negative cosmological constant recently discussed in literature. Our results indicate that the black strings whose conformal infinity is the product of time and $S^{d-3}\times S^1$ are stable for large enough values of the event horizon radius. All topological black strings are also classically stable. We argue that this provides an explicit realization of the Gubser-Mitra conjecture.