Lumpy AdS$\bf{_5\times}$ S$\bf{^5}$ Black Holes and Black Belts

TL;DR

This paper constructs new 'lumpy' black hole solutions in AdS$_5 imes$ S$^5$ that break symmetry and explores their stability, topology, and phase transitions, revealing complex behaviors and dominant phases at different energies.

Contribution

It introduces new families of black hole solutions with broken symmetry and analyzes their phase structure and topology changes in AdS$_5 imes$ S$^5$.

Findings

Lumpy solutions bifurcate from the Gregory-Laflamme instability.

The $ ext{S}^8$ black holes likely dominate at low energies.

Two branches of solutions with $ ext{l} = 2$ are identified.

Abstract

Sufficiently small Schwarzschild black holes in global AdS$_5\times$S$^5$ 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 S$^5$ down to SO$(5)$. These new "lumpy" solutions are labelled by the harmonics $\ell$. We find evidence that the $\ell = 1$ branch never dominates the microcanonical/canonical ensembles and connects through a topology-changing merger to a localised black hole solution with S$^8$ topology. We argue that these S$^8$ 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 $\ell = 2$. 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 $\mathrm S^4\times\mathrm S^4$ which we call a "black belt".