Phases of Kaluza-Klein Black Holes: A Brief Review

TL;DR

This review summarizes recent advances in understanding the phase structure of static, neutral Kaluza-Klein black holes, including various phases, stability, and the rich solution landscape with non-uniqueness phenomena.

Contribution

It provides a comprehensive overview of the phase diagram, solution types, and transitions in Kaluza-Klein black holes, highlighting new insights into their stability and topology changes.

Findings

Identification of solution phases: uniform, non-uniform, localized black holes.

Discussion of classical instabilities and horizon topology transitions.

Revelation of infinite non-uniqueness in solutions for fixed mass and tension.

Abstract

We review the latest progress in understanding the phase structure of static and neutral Kaluza-Klein black holes, i.e. static and neutral solutions of pure gravity with an event horizon that asymptote to a d-dimensional Minkowski-space times a circle. We start by reviewing the (mu,n) phase diagram and the split-up of the phase structure into solutions with an internal SO(d-1) symmetry and solutions with Kaluza-Klein bubbles. We then discuss the uniform black string, non-uniform black string and localized black hole phases, and how those three phases are connected, involving issues such as classical instability and horizon-topology changing transitions. Finally, we review the bubble-black hole sequences, their place in the phase structure and interesting aspects such as the continuously infinite non-uniqueness of solutions for a given mass and relative tension.