Gravitational Instabilities of Uniform Black Strings in AdS

  Locally AdS_d-1xR 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≥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 BTZ₃ strings are indeed stable as previously suggested. This supports that linear instabilities of black strings are triggered only if tachyonic modes exist 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.