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Entropy 2014, 16(12), 6515-6523;

Geometric Thermodynamics: Black Holes and the Meaning of the Scalar Curvature

Facultad de Ciencias Físico Matemáticas, Universidad Autónoma de Puebla, Apartado Postal 1152, 72000 Puebla, Mexico
Departamento de Física, Cinvestav, Instituto Politécnico Nacional 2508, San Pedro Zacatenco, 07360 Gustavo A. Madero, Ciudad de Mexico, Mexico
Departamento de Física Matemática, Instituto de Ciencias, Universidad Autónoma de Puebla, 72570 Puebla, Mexico
Author to whom correspondence should be addressed.
Received: 9 October 2014 / Revised: 2 December 2014 / Accepted: 4 December 2014 / Published: 11 December 2014
(This article belongs to the Special Issue Entropy and Spacetime)
Full-Text   |   PDF [199 KB, uploaded 24 February 2015]


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. View Full-Text
Keywords: Ruppeiner’s metrics; phase transitions; black hole thermodynamics Ruppeiner’s metrics; phase transitions; black hole thermodynamics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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García-Ariza, M.Á.; Montesinos, M.; Torres del Castillo, G.F. Geometric Thermodynamics: Black Holes and the Meaning of the Scalar Curvature. Entropy 2014, 16, 6515-6523.

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