Notes on the thermodynamics of superentropic AdS black holes

The superentropic black hole, which possesses a noncompact horizon topology and violates the reverse isoperimetric inequality, has been found to satisfy both the thermodynamic first law and the Bekenstein-Smarr mass formula. In this paper, we first derive a new Christodoulou-Ruffini-like squared-mass formula for the four-dimensional Kerr-Newman-AdS superentropic black hole and then establish a set of very simple relations between thermodynamic quantities of the superentropic Kerr-Newman-AdS(4) black hole and its usual counterparts. Using these relations, the thermodynamic quantities of the Kerr-Newman-AdS(4) superentropic black hole can be obtained from those of the usual protype by taking the ultraspinning limit properly. Then these relations are extended to the singly rotating Kerr-AdS black holes in arbitrary dimensions and the double-rotating charged black hole in the five-dimensional minimal gauged super-gravity. It can be inferred that the thermodynamic quantities of all superentropic black holes obey similar limiting relations to those of their corresponding conventional rotating AdS black holes and thus can be obtained by taking the ultraspinning limit appropriately.