Lumpy AdS5× S5 black holes and black belts

Abstract

Sufficiently small Schwarzschild black holes in global AdS5×S5 are Gregory-Laflamme unstable. We construct new families of black hole solutions that bifurcate from the onset of this instability and break the full SO(6) symmetry group of the S5 down to SO(5). These new “lumpy” solutions are labelled by the harmonics ℓ. We find evidence that the ℓ = 1 branch never dominates the microcanonical/canonical ensembles and connects through a topology-changing merger to a localised black hole solution with S8 topology. We argue that these S8 black holes should become the dominant phase in the microcanonical ensemble for small enough energies, and that the transition to Schwarzschild black holes is first order. Furthermore, we find two branches of solutions with ℓ = 2. We expect one of these branches to connect to a solution containing two localised black holes, while the other branch connects to a black hole solution with horizon topology S4 × S4 which we call a “black belt”.