General thermodynamic geometry approach for rotating Kerr anti-de Sitter black holes

Abstract

Combining with the small-large black hole phase transition, the thermodynamic geometry has been well applied to study the microstructure for the charged AdS black hole. In this paper, we extend the geometric approach to the rotating Kerr-AdS black hole and aim to develop a general approach for the Kerr-AdS black hole. Treating the entropy and pressure as the fluctuation coordinates, we construct the Ruppeiner geometry for the Kerr-AdS black hole by making the use of the Christodoulou-Ruffini-like squared-mass formula, which is quite different from the charged case. Employing the empirical observation of the corresponding scalar curvature, we find that, for the near-extremal Kerr-AdS black hole, the repulsive interaction dominates among its microstructure. While for far-from-extremal Kerr-AdS black hole, the attractive interaction dominates. The critical phenomenon is also observed for the scalar curvature. These results uncover the characteristic microstructure of the Kerr-AdS black hole. Such general thermodynamic geometry approach is worth generalizing to other rotating AdS black holes, and more interesting microstructure is expected to be discovered.

13 pages and 6 figures

References in corpus (15)

• Multiple Reentrant Phase Transitions and Triple Points in Lovelock Thermodynamics
• Critical phenomena and thermodynamic geometry of charged Gauss-Bonnet AdS black holes
• Superfluid Black Holes
• Thermodynamic curvature and phase transitions in Kerr-Newman black holes
• Extended phase space thermodynamics for third order Lovelock black holes in diverse dimensions
• Isolated critical point from Lovelock gravity
• Critical behaviour and microscopic structure of charged AdS black holes via an alternative phase space
• Clapeyron equations and fitting formula of the coexistence curve in the extended phase space of charged AdS black holes
• Thermodynamical Metrics and Black Hole Phase Transitions
• Hessian matrix, specific heats, Nambu brackets, and thermodynamic geometry
• Intriguing microstructures of five-dimensional neutral Gauss-Bonnet AdS black hole
• Observing dynamic oscillatory behavior of triple points among black hole thermodynamic phase transitions
• Ruppeiner Geometry, Phase Transitions and Microstructures of Black Holes in Massive Gravity
• Analytic phase structures and thermodynamic curvature for the charged AdS black hole in alternative phase space
• Testing the microstructure of $d$-dimensional charged Gauss-Bonnet anti-de Sitter black holes