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