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arXiv · 2505.05814

Topological Origin of Horizon Temperature via the Chern-Gauss-Bonnet Theorem

Jack C. M. Hughes·Fedor V. Kusmartsev
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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 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.

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Jack C. M. Hughes, Fedor V. Kusmartsev. 2025-05-09. Topological Origin of Horizon Temperature via the Chern-Gauss-Bonnet Theorem. https://doi.org/10.1134/s0021364025607602

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