On the stability of AdS black strings

We explore via linearized perturbation theory the Gregory-Laflamme instability of the black string solutions of Einstein's equations with negative cosmological constant recently discussed in literature. Our results indicate that the black strings whose conformal infinity is the product of time and $S^{d-3}\times S^1$ are stable for large enough values of the event horizon radius. All topological black strings are also classically stable. We argue that this provides an explicit realization of the Gubser-Mitra conjecture.