Geometric thermodynamics: black holes and the meaning of the scalar curvature

Abstract

In this paper we show that the vanishing of the scalar curvature of Ruppeiner-like metrics does not characterize the ideal gas. Furthermore, we claim through an example that flatness is not a sufficient condition to establish the absence of interactions in the underlying microscopic model of a thermodynamic system, which poses a limitation on the usefulness of Ruppeiner's metric and conjecture. Finally, we address the problem of the choice of coordinates in black hole thermodynamics. We propose an alternative energy representation for Kerr-Newman black holes that mimics fully Weinhold's approach. The corresponding Ruppeiner's metrics become degenerate only at absolute zero and have non-vanishing scalar curvatures.

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References in corpus (4)

• Thermodynamic curvature and phase transitions in Kerr-Newman black holes
• Thermodynamical Metrics and Black Hole Phase Transitions
• A Commentary on Ruppeiner Metrics for Black Holes
• Ruppeiner Geometry of Black Hole Thermodynamics

Cited by in corpus (5)

• New perspective for black hole thermodynamics in Gauss-Bonnet-Born-Infeld massive gravity
• Dilatonic BTZ black holes with power-law field
• Ruppeiner thermodynamic geometry for the Schwarzschild-AdS black hole
• Thermal fluctuations of (non)linearly charged BTZ black hole in massive gravity
• Interacting systems with zero thermodynamic curvature