Thermodynamics of Kerr-Newman-AdS Black Holes and Conformal Field Theories
Marco M. Caldarelli, Guido Cognola, Dietmar Klemm
TL;DR
The work analyzes the thermodynamics of four-dimensional Kerr-Newman-AdS black holes within the AdS/CFT framework, across canonical and grand-canonical ensembles. By employing a counterterm-regularized Euclidean action, it derives the thermodynamic potentials $G$ and $F$ and establishes a generalized Smarr relation that includes AdS corrections, consistent with the first law $dM=TdS+\\Omega dJ+\\Phi dQ$. The resulting phase structure features a Hawking-Page transition in the grand-canonical ensemble and a first-order small/large black hole transition in the canonical ensemble that ends at a critical point as charge or angular momentum increase, with a BPS limit corresponding to zero-temperature, highly degenerate boundary states. These findings connect bulk KNAdS thermodynamics to the dual CFT on a rotating Einstein universe, including supersymmetric limits and rotating boundary dynamics.
Abstract
We study the thermodynamics of four-dimensional Kerr-Newman-AdS black holes both in the canonical and the grand-canonical ensemble. The stability conditions are investigated, and the complete phase diagrams are obtained, which include the Hawking-Page phase transition in the grand-canonical ensemble. In the canonical case, one has a first order transition between small and large black holes, which disappears for sufficiently large electric charge or angular momentum. This disappearance corresponds to a critical point in the phase diagram. Via the AdS/CFT conjecture, the obtained phase structure is also relevant for the corresponding conformal field theory living in a rotating Einstein universe, in the presence of a global background U(1) current. An interesting limit arises when the black holes preserve some supersymmetry. These BPS black holes correspond to highly degenerate zero temperature states in the dual CFT, which lives in an Einstein universe rotating with the speed of light.