Phase Transitions, Shadows, and Microstructure of Kerr-anti-de Sitter Black Holes from Geometrothermodynamics

TL;DR

This paper uses geometrothermodynamics to analyze phase transitions, microstructure, and shadow properties of Kerr-anti-de Sitter black holes, revealing critical phenomena and their relation to shadow features.

Contribution

It introduces a thermodynamic framework incorporating shadow analysis to connect black hole microstructure with phase transitions and geometric curvature singularities.

Findings

Identification of critical points and phase transitions in different ensembles.

Analytical expressions for black hole shadow parameters.

Correlation between thermodynamic curvature singularities and shadow features.

Abstract

Using the formalism of geometrothermodynamics, we investigate the phase-transition structure and microstructure of the Kerr-anti-de Sitter black hole and show the relationship with its shadow structure. By treating the curvature radius as a thermodynamic variable, we ensure scaling consistency and model the system as quasi-homogeneous. In the canonical ensemble, we identify critical points and characterize both first- and second-order phase transitions independently of pressure. In the grand-canonical ensemble, we reveal a distinct phase structure, including the Hawking-Page transition. We derive analytical expressions for the Kerr-anti-de Sitter black hole shadow and its critical parameters, using shadow thermodynamics to construct asymmetric shadow profiles that capture the phase-transition structure. Finally, we show that the singularities of the geometrothermodynamic curvature in the shadow align with divergences in thermodynamic response functions, confirming the correspondence between shadows, phase transitions, and microstructure.