Thermodynamic Metrics and Black Hole Physics

Understand

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.