Reentrant phase transitions in rotating anti–de Sitter black holes

We study the thermodynamics of higher-dimensional singly spinning asymptotically AdS black holes in the canonical (fixed $J$) ensemble of extended phase space, where the cosmological constant is treated as pressure and the corresponding conjugate quantity is interpreted as thermodynamic volume. Along with the usual small/large black hole phase transition, we find a new phenomenon of reentrant phase transitions for all $d\ensuremath{\ge}6$ dimensions, in which a monotonic variation of the temperature yields two phase transitions from large to small and back to large black holes. This situation is similar to that seen in multicomponent liquids.