Ruppeiner Geometry of Black Hole Thermodynamics

Abstract

The Hessian of the entropy function can be thought of as a metric tensor on state space. In the context of thermodynamical fluctuation theory Ruppeiner has argued that the Riemannian geometry of this metric gives insight into the underlying statistical mechanical system; the claim is supported by numerous examples. We study these geometries for some families of black holes and find that the Ruppeiner geometry is flat for Reissner--Nordström black holes in any dimension, while curvature singularities occur for the Kerr black holes. Kerr black holes have instead flat Weinhold curvature.

5 pages, 2 figures. Talk given at 30th Spanish Relativity Meeting (ERE 2007): Relativistic Astrophysics And Cosmology, 10-14 Sep 2007, Puerto de La Cruz, Tenerife, Spain

References in corpus (8)

• A rotating black ring in five dimensions
• Instability of Ultra-Spinning Black Holes
• Geometry of black hole thermodynamics
• Geometry of Higher-Dimensional Black Hole Thermodynamics
• Stability and Critical Phenomena of Black Holes and Black Rings
• Ruppeiner Geometry of RN Black Holes: Flat or Curved?
• Flat Information Geometries in Black Hole Thermodynamics
• Ruppeiner theory of black hole thermodynamics

Cited by in corpus (7)

• The intrinsic curvature of thermodynamic potentials for black holes with critical points
• Thermodynamic Information Geometry and Complexity Growth of Warped AdS Black Hole and the WAdS${}_3$/CFT${}_2$ Correspondence
• Information Geometry on the Space of Equilibrium States of Black Holes in Higher Derivative Theories
• Geometric thermodynamics: black holes and the meaning of the scalar curvature
• Interaction Between AdS Black Hole Molecules
• Thermodynamic Stability of the Stationary Lifshitz Black Hole of New Massive Gravity
• Geometric curvatures of plane symmetry black hole