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

Understand

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.