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

2025/05/09 by Hughes, Jack C. M., Kusmartsev, Fedor V. · 3 citations
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2505.05814

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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Cited by

• Thermodynamics of black and white holes in ensemble of Planckons
• Black hole thermodynamics and topology
• From Nonextremal to Extremal: Entropy of Reissner-Nordström and Kerr black holes Revisited

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• The Hawking Temperature of Anti-de Sitter Black Holes: Topology and Phase Transitions
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• Black hole in de Sitter space