Abstract
In this paper, we investigate, in the framework of the topological approach to black hole thermodynamics, using the generalized off-shell Helmholtz free energy, the topological numbers of the static multi-charge AdS black holes in four- and five-dimensional gauged supergravities. We find that the topological number of the static-charged AdS black holes in four-dimensional Kaluza-Klein (K-K) gauged supergravity theory is W = 0, while that of the static-charged AdS black holes in four-dimensional gauged –iX0X1-supergravity and STU gauged supergravity theories, and five-dimensional Einstein-Maxwell-dilaton-axion (EMDA) gauged supergravity and STU gauged supergravity, and five-dimensional static-charged AdS Horowitz-Sen black hole are both W = 1. Furthermore, we observe a novel temperature-dependent thermodynamic topological phase transition that can happen in the four-dimensional static-charged AdS black hole in EMDA gauged supergravity theory, the four-dimensional static-charged AdS Horowitz-Sen black hole, and the five-dimensional static-charged AdS black hole in K-K gauged supergravity theory. We believe that the novel temperature-dependent thermodynamic topological phase transition could help us better understand black hole thermodynamics and, further, shed new light on the fundamental nature of gauged supergravity theories.
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Acknowledgments
We are greatly indebted to the anonymous referee for the constructive comments to improve the presentation of this work. We also thank Professor Shuang-QingWu for helpful suggestions and detailed discussions. This work is supported by the National Natural Science Foundation of China (NSFC) under Grants No. 12205243 and No. 12375053, by the Sichuan Science and Technology Program under Grant No. 2023NSFSC1347, by the Sichuan Youth Science and Technology Innovation Research Team under Grant No. 21CXTD0038, and by the Doctoral Research Initiation Project of China West Normal University under Grant No. 21E028.
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Wu, D., Gu, SY., Zhu, XD. et al. Topological classes of thermodynamics of the static multi-charge AdS black holes in gauged supergravities: novel temperature-dependent thermodynamic topological phase transition. J. High Energ. Phys. 2024, 213 (2024). https://doi.org/10.1007/JHEP06(2024)213
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DOI: https://doi.org/10.1007/JHEP06(2024)213