Thermodynamic curvature and phase transitions in Kerr-Newman black holes

George Ruppeiner

doi:10.1103/PhysRevD.78.024016

paper

Thermodynamic curvature and phase transitions in Kerr-Newman black holes

arXiv:0802.1326 · doi:10.1103/PhysRevD.78.024016

Abstract

Singularities in the thermodynamics of Kerr-Newman black holes are commonly associated with phase transitions. However, such interpretations are complicated by a lack of stability and, more significantly, by a lack of conclusive insight from microscopic models. Here, I focus on the later problem. I use the thermodynamic Riemannian curvature scalar $R$ as a try to get microscopic information from the known thermodynamics. The hope is that this could facilitate matching black hole thermodynamics to known models of statistical mechanics. For the Kerr-Newman black hole, the sign of $R$ is mostly positive, in contrast to that for ordinary thermodynamic models, where $R$ is mostly negative. Cases with negative $R$ include most of the simple critical point models. An exception is the Fermi gas, which has positive $R$ . I demonstrate several exact correspondences between the two-dimensional Fermi gas and the extremal Kerr-Newman black hole. $R$ diverges to $+ \infty$ along curves of diverging heat capacities $C_{J, Φ}$ and $C_{Ω, Q}$ , but not along the Davies curve of diverging $C_{J, Q}$ . Finding statistical mechanical models with like behavior might yield additional insight into the microscopic properties of black holes. I also discuss a possible physical interpretation of $∣ R ∣$ .

arXiv comment29 pages, 8 figures

Thermodynamic curvature and phase transitions in Kerr-Newman black holes

Abstract

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