Criticality and topological classes of neutral Gauss-Bonnet AdS black holes in 5D

This work investigates the thermodynamics, phase transition, and topological classes of Neutral Gauss-Bonnet (GB) AdS black holes (BHs) in 5D. We obtain equations for several thermody-namic quantities for the Neutral GB of AdS BHs by using the well-known properties of BH thermodynamics. We find thermal stability and other significant thermodynamical parameters that assist us study stability and criticality. Thermodynamic features of Neutral GB AdS BHs are graphically explored by utilizing (Cp), (T - S), (P - rh), and G, volume expansivity (3), isothermal compressibility (x). Second-order phase transitions, like Cp - S illustrates the divergence behavior. In addition, the swallow tail behavior finds the stability and instability of small black holes (SBH), intermediate black holes (IBH), and large black holes (LBH). Also, our investigation focuses on analyzing the topology of thermodynamic critical points and calculating their respective topological charges within the canonical and grand canonical ensembles. This analysis allows us to discuss the ensemble dependence of the Neutral GB-AdS BH exists.