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arXiv · 2610.23916

Horizon-Boundary Localization of the Hawking Temperature in a Weak AdS/CFT Extension

Wen-Xiang Chen·M. Zeeshan Gul
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Abstract

We establish a conditional boundary-localization statement for the Hawking temperature. For a static, Euclideanizable black hole with a non-degenerate horizon, the temperature is determined entirely by the first non-vanishing near-horizon data. This result is obtained consistently through three approaches: removal of the Euclidean conical defect, the horizon boundary term in the two-dimensional Gauss-Bonnet theorem, and a complex residue calculation. In asymptotically anti-de Sitter spacetime, the Euclidean time periodicity selected at the horizon extends to the conformal boundary, so the boundary conformal field theory inherits the same thermal period up to time normalization. This provides only a weak, temperature-sector extension of the AdS/CFT framework and does not imply a full duality. For dynamical spherical spacetimes, the Hamilton-Jacobi analysis selects the trapping or apparent horizon as the local thermal boundary, whereas a separated event horizon is generally not associated with the relevant pole. Vaidya and charged-Vaidya examples support this boundary-selection picture and reduce to the standard stationary result when the horizons coincide. The construction is further checked using anti-de Sitter black holes, numerical contour calculations, limiting cases, and an extremal counterexample. The result concerns where the Hawking temperature is localized and does not replace the quantum-field-theoretic mechanism of Hawking radiation.

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Wen-Xiang Chen, M. Zeeshan Gul. 2026-10-03. Horizon-Boundary Localization of the Hawking Temperature in a Weak AdS/CFT Extension. https://arxiv.org/abs/2610.23916

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