Topology of black hole thermodynamics in Gauss-Bonnet gravity

Thermodynamics of black holes in anti???de Sitter (AdS) spacetimes typically contain critical points in the phase diagram, some of which correspond to the first order transition ending in a second order one. Following the recent proposal in [Phys. Rev. D 105, 104003 (2022)] on using Duan???s 0-mapping theory, we classify the critical points of six dimensional charged Gauss-Bonnet black holes in AdS spacetime. We find that the higher derivative curvature terms in the form of Gauss-Bonnet gravity do not change the topological class of critical points in charged black holes in AdS, unlike the case of Born-Infeld corrections noted earlier. The connection between the topological nature of critical points and existence of first order phase transitions breaks down in a certain parameter regime. A resolution is proposed by treating the novel and conventional critical points as phase creation and phase annihilation points, respectively. Examples are provided to support the proposal.