Entanglement Entropy of a Non-Minimally Coupled Self-Interacting Scalar across a Schwarzschild Horizon at $\mathcal{O}(α)$

Fuente: arXiv
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Autor principal: Manea, Florin
Formato: Preprint
Publicado: 2025
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author Manea, Florin
author_facet Manea, Florin
contents We compute the first-order correction in the quartic coupling $α$ to the entanglement entropy of a massive, non-minimally coupled scalar across the horizon of a four-dimensional Schwarzschild black hole, treating the non-minimal coupling $ξ$ as a free parameter. Combining the replica trick on the conical manifold $\mathcal{M}_n$ with heat-kernel methods in proper-time regularization, we obtain a closed-form expression for $δS^{(1)}(m,α,ξ)$. The bare correction exhibits a log-enhanced quadratic divergence $ε^{-2}\ln(m^2ε^2)$, arising from interference between bulk fluctuations and the distributional curvature at the tip; we show it is cancelled at $\mathcal{O}(α)$ by the bulk mass counterterm. The residual $m^2\ln(m^2ε^2)$ divergence renormalizes Newton's constant, preserving $S_{\mathrm{BH}} = \mathcal{A}_Σ/ 4 G_F$. The correction is proportional to $(1/6-ξ)$ and vanishes identically for conformal coupling.
format Preprint
id arxiv_https___arxiv_org_abs_2511_21504
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Entanglement Entropy of a Non-Minimally Coupled Self-Interacting Scalar across a Schwarzschild Horizon at $\mathcal{O}(α)$
Manea, Florin
General Relativity and Quantum Cosmology
High Energy Physics - Theory
Mathematical Physics
We compute the first-order correction in the quartic coupling $α$ to the entanglement entropy of a massive, non-minimally coupled scalar across the horizon of a four-dimensional Schwarzschild black hole, treating the non-minimal coupling $ξ$ as a free parameter. Combining the replica trick on the conical manifold $\mathcal{M}_n$ with heat-kernel methods in proper-time regularization, we obtain a closed-form expression for $δS^{(1)}(m,α,ξ)$. The bare correction exhibits a log-enhanced quadratic divergence $ε^{-2}\ln(m^2ε^2)$, arising from interference between bulk fluctuations and the distributional curvature at the tip; we show it is cancelled at $\mathcal{O}(α)$ by the bulk mass counterterm. The residual $m^2\ln(m^2ε^2)$ divergence renormalizes Newton's constant, preserving $S_{\mathrm{BH}} = \mathcal{A}_Σ/ 4 G_F$. The correction is proportional to $(1/6-ξ)$ and vanishes identically for conformal coupling.
title Entanglement Entropy of a Non-Minimally Coupled Self-Interacting Scalar across a Schwarzschild Horizon at $\mathcal{O}(α)$
topic General Relativity and Quantum Cosmology
High Energy Physics - Theory
Mathematical Physics
url https://arxiv.org/abs/2511.21504