https://doi.org/10.1140/epjc/s10052-025-14389-2
Regular Article - Theoretical Physics
Thermodynamic topology of AdS black holes in rainbow gravity
Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, 410081, Changsha, Hunan, People’s Republic of China
Received:
24
April
2025
Accepted:
31
May
2025
Published online:
15
June
2025
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 
-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 
does not affect the total topological number of black holes, which always remains 
, but there is one novel critical point appearing in GCE. And we also find the topological number of black hole is in CE, while in GCE, the topological number can be 0 or , 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.
© The Author(s) 2025
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