Thermodynamic topology of Kerr-Sen black holes via Rényi statistics

Abstract: In the present study, we investigate the topological properties of black holes in terms of R\'{e}nyi statistics as an extension of the Gibbs-Boltzmann (GB) statistics, aiming to characterize the non-Boltzmannian thermodynamic topology of Kerr-Sen and dyonic Kerr-Sen black holes. Through this research, we discover that the topological number derived via R\'{e}nyi statistics differs from that obtained through GB statistics. Interestingly, although the non-extended parameter $\lambda$ changes the topological number, the topological classification of the Kerr-Sen and dyonic Kerr-Sen black holes remains consistent under both GB and R\'{e}nyi statistics. In addition, the topological numbers associated with these two types of black holes without cosmological constant using R\'{e}nyi entropy processes are the same as the AdS cases of them by considering the GB entropy, as further evidenced by such a study found here. This indicates the cosmological constant has some potential connections the with the nonextensive R\'{e}nyi parameter from the perspective of thermodynamic topology.