Abstract
We consider the thermodynamics and geometrothermodynamics of the Myers-Perry black holes in five dimensions for three different cases, depending on the values of the angular momenta. We follow Davies approach to study the thermodynamics of black holes and find a nontrivial thermodynamic structure in all cases, which is fully reproduced by the analysis performed with the techniques of Geometrothermodynamics. Moreover, we observe that in the cases when only one angular momentum is present or the two angular momenta are fixed to be equal, that is, when the thermodynamic system is two dimensional, there is a complete agreement between the divergences of the generalized susceptibilities and the singularities of the equilibrium manifold, whereas when the two angular momenta are fully independent, that is, when the thermodynamic system is three dimensional, additional singularities in the curvature appear. However, we prove that such singularities are due to the changing from a stable phase to an unstable one.
Highlights
Black holes are very special thermodynamic systems
We find out that the GTD thermodynamic geometry is always curved for the considered cases, showing the presence of thermodynamic interaction and that its singularities always correspond to divergences of the susceptibilities or to points where there is a change from a stable to an unstable phase
We extend the work in [41] to the case of Myers-Perry black holes in five dimensions, with the aim of both to analyze their thermodynamic geometry from a new perspective and to focus on the idea of checking what happens with a change of the potential from Φ = M to Φ = S in the GTD analysis and when the equilibrium manifold is 3 dimensional
Summary
Black holes are very special thermodynamic systems. They are thermodynamic system since they have a temperature, the celebrated Hawking temperature [1], and a definition of entropy via the Bekenstein area law [2], from which one can prove that the laws of thermodynamics apply to black holes [3]. They are very special thermodynamic systems, and since, for instance, the entropy is not extensive, they cannot be separated into small subsystems, and perhaps the worst fact, their thermodynamics does not possess a microscopic description yet (see, e.g., [4] for a clear description of these problems) In this puzzling situation, one of the most successful and at the same time discussed approach to the study of black holes phase transitions is the work of Davies [5]. We find out that the GTD thermodynamic geometry is always curved for the considered cases, showing the presence of thermodynamic interaction and that its singularities always correspond to divergences of the susceptibilities or to points where there is a change from a stable to an unstable phase This will allow us to infer new results on the physical meaning of the equilibrium manifold of GTD.
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