Critical behavior of the black hole / black string transition

Abstract

We numerically construct static localized black holes in five and six spacetime dimensions which are solutions to Einstein's vacuum field equations with one compact periodic dimension. In particular, we investigate the critical regime in which the poles of the localized black hole are about to merge. A well adapted multi-domain pseudo-spectral scheme provides us with accurate results and enables us to investigate the phase diagram of those localized solutions within the critical regime, which goes far beyond previous results. We find that in this regime the phase diagram possesses a spiral structure adapting to the one recently found for non-uniform black strings. When approaching the common endpoint of both phases, the behavior of physical quantities is described by complex critical exponents giving rise to a discrete scaling symmetry. The numerically obtained values of the critical exponents agree remarkably well with those derived from the double-cone metric.

arXiv commentVersion 4: matched with journal version but fixed a sign error in equation (16) (accidentally, version 3 does not contain changes compared to version 2)

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Cited by in corpus (16)

• Phases and Stability of Non-Uniform Black Strings
• Einstein-Gauss-Bonnet Black Strings at Large $D$
• Partial-Symmetry-Breaking Phase Transitions
• Generalized Hawking-Page transitions
• Topology-changing horizons at large D as Ricci flows
• Phases of Holographic Hawking Radiation on spatially compact spacetimes
• Gregory-Laflamme and Superradiance encounter Black Resonator Strings
• Critical Kaluza-Klein black holes and black strings in D = 10
• Discrete scale invariance in holography revisited
• Notes on ten-dimensional localized black holes and deconfined states in two-dimensional SYM
• String Theory in a Pinch: Resolving the Gregory-Laflamme Singularity
• Spectral methods for the spin-2 equation near the cylinder at spatial infinity
• Little String Theories on Curved Manifolds
• Critical lumpy black holes in AdS${}_p\times S^q$
• Radial perturbations of scalar-Gauss-Bonnet black holes beyond spontaneous scalarization
• The Low Energy Limit of BFSS Quantum Mechanics