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

TL;DR

This paper applies a topological method to derive the Hawking temperature of BTZ black holes, including charged, rotating, and massive gravity cases, highlighting the method's accuracy and necessary modifications for massive gravity.

Contribution

It extends the topological approach to compute Hawking temperatures for BTZ black holes in massive gravity, addressing the need for an integral constant.

Findings

Accurately derives Hawking temperature for charged rotating BTZ black holes.

Adapts the topological method to BTZ black holes in massive gravity.

Identifies the necessity of an integral constant in the massive gravity case.

Abstract

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