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Topological origin of horizon temperature via the Chern–Gauss–Bonnet theorem
- Authors: Hughes J.C.1, Kusmartsev F.V1
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Affiliations:
- College of Engineering and Physical Sciences, Khalifa University
- Issue: Vol 122, No 3-4 (2025)
- Pages: 199-200
- Section: Articles
- URL: https://clinpractice.ru/0370-274X/article/view/693465
- DOI: https://doi.org/10.31857/S0370274X25080136
- EDN: https://elibrary.ru/FWSKBQ
- ID: 693465
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Abstract
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 of the Bunch–Davies state to the global thermal de Sitter temperature. 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.
About the authors
J. C.M Hughes
College of Engineering and Physical Sciences, Khalifa University
Email: jack.hughes.phys.14@gmail.com
Abu Dhabi, United Arab Emirates
F. V Kusmartsev
College of Engineering and Physical Sciences, Khalifa University
Email: fedor.kusmartsev@ku.ac.ae
Abu Dhabi, United Arab Emirates
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