Topology of black hole thermodynamics in Gauss-Bonnet gravity

Thermodynamics of black holes in anti de Sitter (AdS) spacetimes typically contains 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 [arXiv:2112.01706] on using Duan's $\phi$-mapping theory, we classify the critical points of six dimensional charged Gauss-Bonnet black holes in AdS spacetime. We find that the higher derivative corrections from 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.