Entanglement Entropy of a Non-Minimally Coupled Self-Interacting Scalar across a Schwarzschild Horizon at $\mathcal{O}(α)$
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908979286769664 |
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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 |