Topology of thermodynamics in R-charged black holes

We study the topology of black hole thermodynamics in four-, five-, and seven-dimensional R-charged black holes. While the 4D R-charged black hole possesses four charges, the 5D and 7D R-charged black holes have three and two charges, respectively. In our study, we investigate the influence of charge configuration of the R-charged black holes on the topology of their thermodynamics. In each of these black holes, we consider a number of different charge configurations and compute the topological charges associated with the critical points. Based on the values of the topological charges, we classify the critical points into conventional and novel critical points. We find that the number of critical points and their nature depends on the charge configuration of the R-charged black holes irrespective of their dimensionality. However, the total topological charge for all the charge configurations in 4D, 5D, and 7D remains the same, Q=-1. This indicates that the R-charged black holes in 4D, 5D, and 7D are thermodynamically in the same topological class. We also conclude that the variation of charge configurations does not have any impact on the topological class of thermodynamics for R-charged black holes.