Thermodynamic curvature and phase transitions in Kerr-Newman black holes

By George Ruppeiner. 2008

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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. Away from the extremal case, $R$ diverges to $+\ensuremath{\infty}$ along curves of diverging heat capacities ${C}_{J,\ensuremath{\Phi}}$ and ${C}_{\ensuremath{\Omega},Q}$, 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 $|R|$.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/6f2a7b2da754f9357c2d7069977871bec006571a

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