Topological classes of BTZ black holes
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909404450783232 |
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| author | Du, Yongbin Zhang, Xiangdong |
| author_facet | Du, Yongbin Zhang, Xiangdong |
| contents | In the recent paper [Phys. Rev. Lett. 129, 191101 (2022)], the black holes were viewed as topological thermodynamic defects by using the generalized off-shell free energy. Their work indicates that all black hole solutions in the pure Einstein-Maxwell gravity theory could be classified into three different topological classes for four and higher spacetime dimensions. In this paper, we investigate the topological number of BTZ black holes with different charges $(Q)$ and rotational $(J)$ parameters. By using generalized free energy and Duan's $ϕ$-mapping topological current theory, we interestingly found only two topological classes for BTZ spacetime. Particularly, for $Q=J=0$ BTZ black hole, there has only one zero point and therefore the total topological number is 1. While for rotating or charged cases, there are always two zero points and the global topological number is zero. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2302_11189 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topological classes of BTZ black holes Du, Yongbin Zhang, Xiangdong General Relativity and Quantum Cosmology In the recent paper [Phys. Rev. Lett. 129, 191101 (2022)], the black holes were viewed as topological thermodynamic defects by using the generalized off-shell free energy. Their work indicates that all black hole solutions in the pure Einstein-Maxwell gravity theory could be classified into three different topological classes for four and higher spacetime dimensions. In this paper, we investigate the topological number of BTZ black holes with different charges $(Q)$ and rotational $(J)$ parameters. By using generalized free energy and Duan's $ϕ$-mapping topological current theory, we interestingly found only two topological classes for BTZ spacetime. Particularly, for $Q=J=0$ BTZ black hole, there has only one zero point and therefore the total topological number is 1. While for rotating or charged cases, there are always two zero points and the global topological number is zero. |
| title | Topological classes of BTZ black holes |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2302.11189 |