Gravitational Instabilities of Uniform Black Strings in AdS

Understand

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.