Thermodynamics of Kerr-Newman-AdS Black Holes and Conformal Field Theories

TL;DR

This paper analyzes the thermodynamics and phase transitions of Kerr-Newman-AdS black holes in four dimensions, exploring their stability, phase diagrams, and implications for dual conformal field theories via the AdS/CFT correspondence.

Contribution

It provides a comprehensive phase diagram including Hawking-Page and small-large black hole transitions, and connects these to dual CFT states, especially in supersymmetric limits.

Findings

Identified stability conditions and phase transitions for Kerr-Newman-AdS black holes.

Mapped the phase diagram including Hawking-Page transition and critical points.

Linked black hole thermodynamics to dual CFT states in rotating Einstein universes.

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.