Thermodynamics of rotating black holes and black rings: phase transitions and thermodynamic volume

TL;DR

This review explores the thermodynamics of higher-dimensional rotating black holes and rings, revealing complex phase transitions and confirming the thermodynamic volume's properties, including the reverse isoperimetric inequality.

Contribution

It provides a comprehensive analysis of phase transitions and thermodynamic volume in rotating black holes and rings, extending thermodynamic concepts to non-spherical horizons.

Findings

Reentrant phase transitions in Kerr-AdS and Myers-Perry black holes.

Confirmation of the reverse isoperimetric inequality for black rings.

Numerical and analytical study of the equation of state P(V,T).

Abstract

In this review we summarize, expand, and set in context recent developments on the thermodynamics of black holes in extended phase space, where the cosmological constant is interpreted as thermodynamic pressure and treated as a thermodynamic variable in its own right. We specifically consider the thermodynamics of higher-dimensional rotating asymptotically flat and AdS black holes and black rings in a canonical (fixed angular momentum) ensemble. We plot the associated thermodynamic potential-the Gibbs free energy-and study its behaviour to uncover possible thermodynamic phase transitions in these black hole spacetimes. We show that the multiply-rotating Kerr-AdS black holes exhibit a rich set of interesting thermodynamic phenomena analogous to the "every day thermodynamics" of simple substances, such as reentrant phase transitions of multicomponent liquids, multiple first-order solid/liquid/gas phase transitions, and liquid/gas phase transitions of the Van der Waals type. Furthermore, the reentrant phase transitions also occur for multiply-spinning asymptotically flat Myers-Perry black holes. The thermodynamic volume, a quantity conjugate to the thermodynamic pressure, is studied for AdS black rings and demonstrated to satisfy the reverse isoperimetric inequality; this provides a first example of calculation confirming the validity of isoperimetric inequality conjecture for a black hole with non-spherical horizon topology. The equation of state P=P(V,T) is studied for various black holes both numerically and analytically-in the ultraspinning and slow rotation regimes.