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

Entropy

Miguel Ángel Garc໚-Ariza¹  Merced Montesinos² 

[1]Facultad de Ciencias Físico Matemáticas, Universidad Autónoma de Puebla, Apartado Postal 1152, 72000 Puebla, Mexico

[2] E-Mail:

[3]Departamento de Física, Cinvestav, Instituto Politécnico Nacional 2508, San Pedro Zacatenco, 07360 Gustavo A. Madero, Ciudad de Mexico, México

关键词: Ruppeiner’s metrics;    phase transitions;    black hole thermodynamics;   

DOI  :  10.3390/e16126515

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland