Black hole analogue of triple point and reentrant phase transition
Abstract: We study the thermodynamic behavior of doubly-spinning d=6 Kerr-anti de Sitter black holes in the canonical ensemble of fixed angular momenta, interpreting the cosmological constant as thermodynamic pressure. We find, dependent on the ratio of the two angular momenta q=J2/J1, qualitatively different interesting phenomena known from the ''every day thermodynamics of simple substances''. In particular, for certain q's the system displays the presence of a large/intermediate/small black hole phase transition with one triple and two critical points. This behavior is reminiscent of the solid/liquid/gas phase transition except that the coexistence line of small and intermediate black holes does not continue for an arbitrary value of pressure (similar to the solid/liquid coexistence line) but rather terminates at one of the critical points. Even more interestingly, for q=0 we find a reentrant phase transition, 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.
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