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In this paper, we study the Hawking temperature of the BTZ black hole basedon the purely topological method proposed by Robson, Villari, and Biancalana(RVB) [Phys. Rev. D 99, 044042 (2019)]. The Hawking temperature of the chargedrotating BTZ black hole can be accurately derived by this topological method.We also calculate the Hawking temperature of the BTZ black hole in massivegravity. Because the metric function of the BTZ black hole in massive gravityhas a mass term, the corresponding Hawking temperature cannot be derived unlessan integral constant is added.

Topological approach to derive the global Hawking temperature of (massive) BTZ black hole