Thermodynamic Metrics and Black Hole Physics

Abstract

We give a brief survey of thermodynamic metrics, in particular the Hessian of the entropy function, and how they apply to black hole thermodynamics. We then provide a detailed discussion of the Gibbs surface of Kerr black holes. In particular we analyze its global properties, and extend it to take the entropy of the inner horizon into account. A brief discussion of Kerr-Newman black holes is included.

21 pages, new figures added

References in corpus (6)

• Thermodynamic curvature and phase transitions in Kerr-Newman black holes
• Unified geometric description of black hole thermodynamics
• Flat Information Geometries in Black Hole Thermodynamics
• A Commentary on Ruppeiner Metrics for Black Holes
• The intrinsic curvature of thermodynamic potentials for black holes with critical points
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Cited by in corpus (11)

• Killing Horizons: Negative Temperatures and Entropy Super-Additivity
• Restricted thermodynamic fluctuations and the Ruppeiner geometry of black holes
• Thermodynamic Black Holes
• Einstein-Maxwell-Dilatonic phantom black holes: Thermodynamics and geometrothermodynamics
• Geometrothermodynamics of van der Waals systems
• Thermodynamic geometry of static and rotating regular black holes in conformal massive gravity
• Thermodynamic optimization of a Penrose process: an engineers' approach to black hole thermodynamics
• On Black Hole Thermodynamics, Singularity, and Gravitational Entropy
• The Hookean Law of Black Holes and Fragmentation: Insights from Maximum Force Conjecture and Ruppeiner Geometry
• Degenerate Hessian structures on radiant manifolds
• Interacting systems with zero thermodynamic curvature