Quasilocal thermodynamics of Kerr and Kerr–anti-de Sitter spacetimes and the AdS/CFT correspondence

We consider the quasilocal thermodynamics of rotating black holes in asymptotically flat and asymptotically anti--de Sitter (AdS) spacetimes. Using the minimal number of intrinsic boundary counterterms inspired by the AdS/conformal field theory correspondence, we find that we are able to carry out an analysis of the thermodynamics of these black holes for virtually all possible values of the rotation parameter and cosmological constant that leave the quasilocal boundary well defined, going well beyond what is possible with background subtraction methods. Specifically, we compute the quasilocal energy E and angular momentum J for arbitrary values of the rotation, mass, and cosmological constant parameters for the (3+1)-dimensional Kerr, Kerr-AdS black holes, and (2+1)-dimensional Banados-Teitelboim-Zannelli (BTZ) black hole. We perform a quasilocal stability analysis and find phase behavior that is commensurate with previous analyses carried out at infinity.