Thermodynamic curvature and phase transitions in Kerr-Newman black holes

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dc.creatorRuppeiner, George
dc.date2008-02-10
dc.date2008-07-10
dc.date.accessioned2026-07-07T11:55:56Z
dc.date.available2026-07-07T11:55:56Z
dc.descriptionSingularities 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 $|R|$.
dc.description29 pages, 8 figures
dc.identifierhttps://arxiv.org/abs/0802.1326
dc.identifierhttp://arxiv.org/abs/0802.1326
dc.identifierPhys.Rev.D78:024016,2008
dc.identifierdoi:10.1103/PhysRevD.78.024016
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/205414
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleThermodynamic curvature and phase transitions in Kerr-Newman black holes
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