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VOLUME 122 (2025) | ISSUE 4 | PAGE 199
Topological origin of horizon temperature via the Chern-Gauss-Bonnet theorem
DOI: 10.31857/S0370274X25080136
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.