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Open AccessArticle

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

1
Facultad de Ciencias Físico Matemáticas, Universidad Autónoma de Puebla, Apartado Postal 1152, 72000 Puebla, Mexico
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Departamento de Física, Cinvestav, Instituto Politécnico Nacional 2508, San Pedro Zacatenco, 07360 Gustavo A. Madero, Ciudad de Mexico, Mexico
3
Departamento de Física Matemática, Instituto de Ciencias, Universidad Autónoma de Puebla, 72570 Puebla, Mexico
*
Author to whom correspondence should be addressed.
Entropy 2014, 16(12), 6515-6523; https://doi.org/10.3390/e16126515
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)
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
MDPI and ACS Style

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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