Thermodynamic topology of AdS black holes in rainbow gravity - Ping Yin; Yaqin Liu; Juhua Chen; Yongjiu Wang (European Physical Journal C: Particles and Fields)
Abstract In this paper, we study the topology of four-dimensional AdS black holes with nonlinear sources in the framework of rainbow gravity. We apply the Duan’s $$φ $$ φ -mapping theory and the method of generalized free energy to study the topological charges related to critical points and the local and global topology at black hole thermodynamic defects, respectively. By analyzing the critical points of black holes in the canonical ensemble (CE) and the grand canonical ensemble (GCE), we find the nonlinear parameter $$p$$ p does not affect the total topological number of black holes, which always remains $$+1$$ + 1 , but there is one novel critical point appearing in GCE. And we also find the topological number of black hole is $$+1$$ + 1 in CE, while in GCE, the topological number can be 0 or $$+1$$ + 1 , depending on the system pressure and the electric potential, respectively. Our results show that the topological classification of AdS black holes depends significantly on the ensemble selection, and the rainbow gravity effect has no effect on its topological number.