From Nonextremal to Extremal: Entropy of Reissner-Nordström and Kerr black holes Revisited
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| Format: | Preprint |
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2025
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| _version_ | 1866912387082223616 |
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| author | Fairoos, C. Singha, Chiranjeeb |
| author_facet | Fairoos, C. Singha, Chiranjeeb |
| contents | In this paper, we derive the entropy of Reissner-Nordström (RN) and Kerr black holes using the Hawking-Gibbons path integral method. We determine the periodicity of the Euclidean time coordinate using two approaches: first, by analyzing the near-horizon geometry, and second, by applying the Chern-Gauss-Bonnet (CGB) theorem. For non-extremal cases, both these methods yield a consistent and unique periodicity, which in turn leads to a well-defined expression for the entropy. In contrast, the extremal case exhibits a crucial difference. The absence of a conical structure in the near-horizon geometry implies that the periodicity of the Euclidean time is no longer uniquely fixed within the Hawking-Gibbons framework. The CGB theorem also fails to constrain the periodicity, as the corresponding Euler characteristic vanishes. As a result, the entropy cannot be uniquely determined using either method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_16309 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Nonextremal to Extremal: Entropy of Reissner-Nordström and Kerr black holes Revisited Fairoos, C. Singha, Chiranjeeb General Relativity and Quantum Cosmology In this paper, we derive the entropy of Reissner-Nordström (RN) and Kerr black holes using the Hawking-Gibbons path integral method. We determine the periodicity of the Euclidean time coordinate using two approaches: first, by analyzing the near-horizon geometry, and second, by applying the Chern-Gauss-Bonnet (CGB) theorem. For non-extremal cases, both these methods yield a consistent and unique periodicity, which in turn leads to a well-defined expression for the entropy. In contrast, the extremal case exhibits a crucial difference. The absence of a conical structure in the near-horizon geometry implies that the periodicity of the Euclidean time is no longer uniquely fixed within the Hawking-Gibbons framework. The CGB theorem also fails to constrain the periodicity, as the corresponding Euler characteristic vanishes. As a result, the entropy cannot be uniquely determined using either method. |
| title | From Nonextremal to Extremal: Entropy of Reissner-Nordström and Kerr black holes Revisited |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2505.16309 |