The Phase Transition between Caged Black Holes and Black Strings - A Review

TL;DR

This review discusses the phase transition between caged black holes and black strings in higher-dimensional gravity, highlighting recent numerical results, critical dimensions, and topology changes, and emphasizing the end-state of the Gregory-Laflamme instability.

Contribution

It summarizes recent numerical phase diagram determinations and insights into the black-hole/black-string transition, including critical dimensions and topology change phenomena.

Findings

Numerical phase diagram confirms merger of black-hole and black string phases.

Strong evidence that the Gregory-Laflamme instability ends in a black hole.

Identification of critical dimensions where system behavior changes.

Abstract

Black hole uniqueness is known to fail in higher dimensions, and the multiplicity of black hole phases leads to phase transitions physics in General Relativity. The black-hole black-string transition is a prime realization of such a system and its phase diagram has been the subject of considerable study in the last few years. The most surprising results seem to be the appearance of critical dimensions where the qualitative behavior of the system changes, and a novel kind of topology change. Recently, a full phase diagram was determined numerically, confirming earlier predictions for a merger of the black-hole and black string phases and giving very strong evidence that the end-state of the Gregory-Laflamme instability is a black hole (in the dimension range 4<D<14). Here this progress is reviewed, illustrated with figures, put into a wider context, and the still open questions are listed.