Quantum-statistical constraints on Kerr-anti-de Sitter thermodynamics

TL;DR

This paper develops a framework for understanding Kerr-anti-de Sitter black hole thermodynamics, linking geometric, quantum, and statistical aspects, and clarifying the uniqueness of certain thermodynamic descriptions.

Contribution

It introduces a comprehensive approach that unifies geometric and quantum-statistical perspectives on KadS thermodynamics, identifying unique and physically meaningful descriptions.

Findings

Quantum statistical relation restricts KadS thermodynamics to a specific subclass.

Identifies unique thermodynamic descriptions: co-rotating frame and volume-coinciding volume.

Provides a coherent interpretation reconciling geometric and quantum considerations.

Abstract

We develop a general framework for interpreting the thermodynamic descriptions of Kerr-anti de Sitter black holes (KadS). These descriptions satisfy a first law and respect the homogeneity required by scaling properties. Additionally, they are subject to restrictions from semiclassical arguments. We show that temperature and angular velocity are kinematic quantities tied to a reference frame, identified through the Euclidean formalism. However, the pressure-volume contribution is a dynamical term that requires a gauge fixing of the potential mass and volume. It is established that the observer associated with a given thermodynamic description is directly encoded in the Killing vector that generates the horizon. We demonstrate that the quantum statistical relation restricts the infinite family of KadS descriptions to a subclass that reduces to Schwarzschild-adS and Kerr thermodynamics in the limits of vanishing cosmological constant and angular momentum. Furthermore, we establish the uniqueness of both the description associated with a frame co-rotating with infinity, and the description whose thermodynamic and geometric volumes coincide. Thus, our framework provides a coherent interpretation of the variety of KadS thermodynamics, reconciling geometric and quantum-statistical considerations.