Gravitational Instabilities of Uniform Black Strings in AdS

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 $d\ge 4$ 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.

v1: 6 Pages; 2 Figures; Comments are welcome; v2: Corrected typos. Added references. Added a note. Submitted to PRL; v3: Added a figure

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