The compressibility of rotating black holes in D-dimensions

TL;DR

This paper explores the thermodynamic properties of rotating black holes in higher-dimensional anti-de Sitter space, focusing on their volume, compressibility, and the speed of sound, revealing bounds and explicit formulas related to their angular momenta.

Contribution

It provides explicit calculations of thermodynamic volume and compressibility for rotating black holes in D dimensions, extending previous work and deriving new bounds and formulas involving angular momenta.

Findings

Thermodynamic volume matches previous Smarr relation calculations.

Compressibility is non-negative and bounded.

Speed of sound is bounded and expressed via angular momenta as Casimir invariants.

Abstract

Treating the cosmological constant as a pressure, in the context of black hole thermodynamics, a thermodynamic volume for the black hole can be defined as being the thermodynamic variable conjugate to the pressure, in the sense of a Legendre transform. The thermodynamic volume is explicitly calculated, as the Legendre transform of the pressure in the enthalpy for a rotating asymptotically anti-de Sitter Myers-Perry black hole in D space-time dimensions. The volume obtained is shown to agree with previous calculations using the Smarr relation. The compressibility is calculated and shown to be non-negative and bounded. Taking the limit of zero cosmological constant, the compressibility of a rotating black hole in asymptotically flat space-times is determined and the corresponding speed of sound computed. The latter is bounded above and has an elegant expression purely in terms of the angular momenta, in the form of quartic and quadratic Casimirs of the rotation group, SO(D-1).