Gravitational Instabilities of Uniform Black Strings in AdS

TL;DR

This paper investigates the stability of uniform black strings in Anti-de Sitter space, revealing linear instabilities in higher dimensions and proposing potential end states, including black holes or non-uniform strings, with implications for cosmic censorship.

Contribution

It provides analytic and numerical evidence that AdS uniform black strings are unstable in dimensions greater than four, challenging previous assumptions about their stability.

Findings

AdS$_{d-1}$ uniform black strings are unstable in $d>4$.

Stable in $d=4$, as with BTZ$_3$ strings.

Potential end states include black hole tunneling or non-uniform black strings.

Abstract

Locally AdS$_{d-1}\times\mathbb{R}$ uniform black strings (UBS) in the presence of a massless scalar field are believed to avoid the onset of the Gregory-Laflamme (GL) instability in $d\ge4$ as no tachyonic modes exist in the spectrum of the Laplace-Beltrami operator. We present analytic and numerical evidence of GL modes in the Lichnerowicz spectrum indicating that AdS$_{d-1}$ UBSs are classically and thermodynamically unstable at the linear level in $d>4$. In $d=4$, we confirm that uniform BTZ$_3$ strings are indeed stable as previously suggested. We propose that linear instabilities of black strings are triggered if and only if a tachyonic mode exists in the Lichnerowicz spectrum. At the end state of the instability, AdS$_{d-1}$ UBSs of finite length may tunnel to a SAdS$_d$ black hole or converge onto a novel non-uniform AdS$_d$ black string. We conjecture that weak cosmic censorship is violated if the non-uniform solution is an exact AdS$_d$ black funnel and compute entropy estimates in $d>4$ as evidence.