Three-Charge Black Holes on a Circle

TL;DR

This paper analyzes the phases of five-dimensional three-charge black holes on a circle, providing analytical corrections to their thermodynamics and numerically exploring their phase structure, including new non-uniform phases.

Contribution

It offers the first detailed analytical and numerical study of three-charge black holes on a circle, revealing new phases and corrections to entropy consistent with microscopic models.

Findings

Analytical corrections to black hole metrics and thermodynamics for small mass.

Agreement of entropy corrections with microscopic models in near-extremal limit.

Discovery of a new non-uniform phase of three-charge black holes on a circle.

Abstract

We study phases of five-dimensional three-charge black holes with a circle in their transverse space. In particular, when the black hole is localized on the circle we compute the corrections to the metric and corresponding thermodynamics in the limit of small mass. When taking the near-extremal limit, this gives the corrections to the constant entropy of the extremal three-charge black hole as a function of the energy above extremality. For the partial extremal limit with two charges sent to infinity and one finite we show that the first correction to the entropy is in agreement with the microscopic entropy by taking into account that the number of branes shift as a consequence of the interactions across the transverse circle. Beyond these analytical results, we also numerically obtain the entire phase of non- and near-extremal three- and two-charge black holes localized on a circle. More generally, we find in this paper a rich phase structure, including a new phase of three-charge black holes that are non-uniformly distributed on the circle. All these three-charge black hole phases are found via a map that relates them to the phases of five-dimensional neutral Kaluza-Klein black holes.