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

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".

20 pages (plus 17 pages for Appendix on Kaluza-Klein Holography), 14 figures

References in corpus (10)

• Instabilities of Black Strings and Branes
• An instability of higher-dimensional rotating black holes
• Kaluza-Klein Holography
• Anatomy of bubbling solutions
• Ultraspinning instability of rotating black holes
• Holographic Coulomb branch vevs
• Stable non-uniform black strings below the critical dimension
• Bumpy black holes
• Multi-black hole configurations on the cylinder
• Analytic Evidence for Continuous Self Similarity of the Critical Merger Solution

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• Height-function-based 4D reference metrics for hyperboloidal evolution
• Superradiance and black resonator strings encounter helical black strings
• The Fate of Instability of de Sitter Black Holes at Large $D$
• Spontaneous Deformation of an AdS Spherical Black Hole
• Small black holes in $Ad{S}_5\times S^5$
• Critical lumpy black holes in AdS${}_p\times S^q$
• New asymptotically (Anti)-de Sitter black holes in (super)gravity
• The Canonical Ensemble Reloaded: The Complex-Stability of Euclidean quantum gravity for Black Holes in a Box
• The Low Energy Limit of BFSS Quantum Mechanics