The phase transition and triple points of charged Gauss–Bonnet-AdS black holes in the canonical ensemble

This study investigates the phase transition behavior and triple point characteristics of charged AdS black holes in Gauss–Bonnet gravity within the extended phase space, considering a thermal AdS space background. In four-dimensional spherically symmetric space–time, the system exhibits a multistage phase transition structure, comprising the Hawking–Page phase transitions and first-order small/large black hole phase transitions, accompanied by triple points where massless, small-mass and large-mass black hole phases coexist. The corresponding [Formula: see text] phase diagram demonstrates remarkable similarity to classical solid-liquid-gas phase transitions. Further analysis reveals that charge asymmetrically modulates the phase transition temperatures: while enhancing the Hawking–Page transition temperature, it suppresses the first-order small/large phase transition temperature. In contrast, higher-dimensional spherically symmetric space–time exhibits only the classical Hawking–Page phase transition. Within the hyperbolic symmetric space–time framework, the system displays reentrant phase transition behavior, involving two distinct-temperature Hawking–Page transitions and triple points. According to the AdS/CFT correspondence, this phenomenon may correspond to reentrant phase transitions and triple point structures in QCD phase diagrams. Notably, charge increases the higher Hawking–Page temperature while decreasing the lower one. Through analytical and numerical methods, this work systematically determines the coexistence curves, triple points, critical points and phase transition conditions under various space–time symmetries, providing new theoretical insights into quantum gravity.