The microstructure and Ruppeiner geometry of charged anti-de Sitter black holes in Gauss-Bonnet gravity:from the critical point to the triple point

Ruppeiner geometry has been successfully applied in the study of the black hole microstructure by combining with the small-large black hole phase transition,and the potential interactions among the molecular-like constituent degrees of freedom are uncovered.In this paper,we will extend the study to the triple point,where three black hole phases coexist acting as a typical feature of black hole systems quite different from the small-large black hole phase transition.For the six-dimensional charged Gauss-Bonnet anti-de Sitter black hole,we thoroughly investigate the swallow tail behaviors of the Gibbs free energy and the equal area laws.After obtaining the black hole triple point in a complete parameter space,we exhibit its phase structures both in the pressure-temperature and temperature-horizon radius diagrams.Quite different from the liquid-vapor phase transition,a double peak behavior is present in the temperature-horizon radius phase diagram.Then we construct the Ruppeiner geometry and calculate the corresponding normalized curvature scalar.Near the triple point,we observe multiple negatively divergent behaviors.Positive curvature scalar is observed for the small black hole with high temperature,which indicates that the repulsive interaction dominates among the microstructure.Furthermore,we consider the variation of the curvature scalar along the coexisting intermediate and large black hole curves.Combining with the observation for different fluids,the result suggests that this black hole system behaves more like the argon or methane.Our study provides a first and preliminary step towards understanding black hole microstructure near the triple point,as well as uncovering the particular properties of the Gauss-Bonnet gravity.

Microstructure of charged AdS black hole with minimal length effects

In this work,the microstructure of charged AdS black holes under minimal length effects is investigated.We study the thermodynamics of black holes in the extended phase space,where the cosmological constant is regarded as the thermodynamic pressure.The modified Hawking temperature and phase transition are obtained based on the generalized uncertainty principle(GUP).Then,using thermodynamic geometry,the microstructure of black holes can be determined by the ratio of the GUP parameter to charge.For a small ratio,the black hole exhibits the typical RN-AdS microstructure with van der Waals phase transition and repulsive/attractive interactions.As the ratio increases,the reentrant phase transition is observed,and both the repulsion-attraction coexisted and the attraction dominated black holes are noted.For a large ratio,the black hole behaves like a Schwarzchild-AdS black hole in which neither phase transition nor repulsive interaction are observed.These results suggest that the GUP effect will reduce the repulsive interaction presented by the charged AdS black hole.