Abstract
We first review Weinhold information geometry and Ruppeiner information geometry of 3D charged-dilaton black hole. Then, we use the Legendre invariant to introduce a 2-dimensional thermodynamic metric in the space of equilibrium states, which becomes singular at those points. According to the analysis of the heat capacities, these points are the places where phase transitions occur. This result is valid for the black hole, therefore, provides a geometrothermodynamics description of black hole phase transitions in terms of curvature singularities.
Highlights
Since Ferrara et al [1] investigated the critical points of moduli space by using Weinhold metric and Ruppeiner metric; the black hole thermodynamic in geometry framework becomes a hot spot of theoretical physics
We investigated the Weinhold metric and the Ruppeiner metric as well as the geometrothermodynamics of a 3D Charged-Dilaton Black Hole
Our results showed that the thermodynamic curvature is in general different, indicating the presence of thermodynamic interaction
Summary
Since Ferrara et al [1] investigated the critical points of moduli space by using Weinhold metric and Ruppeiner metric; the black hole thermodynamic in geometry framework becomes a hot spot of theoretical physics. Since Weinhold and Ruppeiner metrics are not Legendre invariant, one of the first results in the Advances in High Energy Physics context of GTD was the derivation of simple Legendre invariant generalizations of these metrics and their application to black hole thermodynamics [19,20,21,22,23,24,25,26]. These results end the controversy regarding the application of geometric structures in black hole thermodynamics.
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