Phases of Five-Dimensional Black Holes

TL;DR

This paper explores the phase structure of five-dimensional black holes, revealing that maximal entropy configurations are black Saturns with a central black hole and thin black ring, with implications for thermodynamic stability.

Contribution

It introduces the concept of black Saturn configurations as maximal entropy solutions and analyzes their phase space and thermodynamic properties in five-dimensional gravity.

Findings

Maximal entropy configurations are black Saturns with a central black hole and thin ring.

The entropy upper bound matches that of a static black hole of the same mass.

High-entropy phases are not in thermal equilibrium, but equilibrium reduces possible phases.

Abstract

We argue that the configurations that approach maximal entropy in five-dimensional asymptotically flat vacuum gravity, for fixed mass and angular momentum, are `black Saturns' with a central, close to static, black hole and a very thin black ring around it. For any value of the angular momentum, the upper bound on the entropy is equal to the entropy of a static black hole of the same total mass. For fixed mass, spin and area there are families of multi-ring solutions with an arbitrarily large number of continuous parameters, so the total phase space is infinite-dimensional. Somewhat surprisingly, the phases of highest entropy are not in thermal equilibrium. Imposing thermodynamical equilibrium drastically reduces the phase space to a finite, small number of different phases.