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<p>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.</p>

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

  • 期刊论文

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  • 发表日期：

    2025年8月8日

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  • J. C. M. Hughes,
  • F. V. Kusmartsev

摘要

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.