Gravitational instabilities of uniform black strings in AdS space

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