Topological Origin of Horizon Temperature via the Chern-Gauss-Bonnet Theorem
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909972890124288 |
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| author | Hughes, Jack C. M. Kusmartsev, Fedor V. |
| author_facet | Hughes, Jack C. M. Kusmartsev, Fedor V. |
| contents | This paper establishes a connection between the Hawking temperature of spacetime horizons and global topological invariants, specifically the Euler characteristic of Wick-rotated Euclidean spacetimes. This is demonstrated for both de Sitter and Schwarzschild, where the compactification of the near-horizon geometry allows for a direct application of the Chern-Gauss-Bonnet theorem. For de Sitter, a simple argument connects the Gibbon-Hawking temperature to the global thermal de Sitter temperature of the Bunch-Davies state. This establishes that spacetime thermodynamics are a consequence of the geometrical structure of spacetime itself, therefore suggesting a deep connection between global topology and semi-classical analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05814 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological Origin of Horizon Temperature via the Chern-Gauss-Bonnet Theorem Hughes, Jack C. M. Kusmartsev, Fedor V. General Relativity and Quantum Cosmology This paper establishes a connection between the Hawking temperature of spacetime horizons and global topological invariants, specifically the Euler characteristic of Wick-rotated Euclidean spacetimes. This is demonstrated for both de Sitter and Schwarzschild, where the compactification of the near-horizon geometry allows for a direct application of the Chern-Gauss-Bonnet theorem. For de Sitter, a simple argument connects the Gibbon-Hawking temperature to the global thermal de Sitter temperature of the Bunch-Davies state. This establishes that spacetime thermodynamics are a consequence of the geometrical structure of spacetime itself, therefore suggesting a deep connection between global topology and semi-classical analysis. |
| title | Topological Origin of Horizon Temperature via the Chern-Gauss-Bonnet Theorem |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2505.05814 |