AI 中文总结
该研究采用高性能代码，计算了五种正则黑洞外部的重整化标量真空极化，揭示了量子变形对极化的调控规律及近极端 regime的独特量子几何效应，结果在经典极限下与史瓦西黑洞一致。
AI 中文摘要
我们计算了Hartle–Hawking态下，静态球对称量子修正、有效且正则的黑洞族外部区域中，一个有质量、非最小耦合量子场的重整化标量真空极化⟨φ²⟩；该黑洞族包括Kazakov–Solodukhin量子变形黑洞、Zhang–Lewandowski–Ma–Yang的两种有效圈量子引力几何、Bonanno–Reuter的重整化群改进史瓦西黑洞以及Bardeen正则黑洞。我们采用扩展点分裂模式求和形式论，将其实现为高性能代码，并给出了真空极化在量子变形参数、场质量μ=mM和曲率耦合ξ的网格上的外部轮廓。这五种几何展现出定性不同的视界响应。在所有五种几何中，变形印记由背景里奇标量的符号通过与(ξ-1/6)ℛ线性相关的DeWitt–Schwinger曲率项调控，且在共形耦合时被强烈抑制，我们在量级和ξ依赖性上均验证了这一点。在具有内视界的两种几何的近极端 regime中，我们发现轻场质量下视界极化发生符号变化——在匹配温度的Reissner–Nordström黑洞中不存在该现象，且可被共形耦合消除——这一现象标志着一种真正的量子几何、德西特核驱动的 regime。所有结果在经典极限下均约化为史瓦西值，验证了计算的正确性。
英文摘要
We compute the renormalized scalar vacuum polarization $\langle ϕ^2 \rangle$ of a massive, non-minimally coupled quantum field in the Hartle--Hawking state exterior to a family of static, spherically symmetric quantum-corrected, effective and regular black holes: the Kazakov--Solodukhin quantum-deformed black hole, the two effective loop-quantum-gravity geometries of Zhang--Lewandowski--Ma--Yang, the renormalization-group improved Schwarzschild black hole of Bonanno--Reuter, and the Bardeen regular black hole. We adapt the extended point-splitting mode-sum formalism, implemented as a high-performance code, and present the exterior profile of the vacuum polarization over a grid of the quantum-deformation parameter, the field mass $μ=mM$ and the curvature coupling $ξ$. The five geometries display qualitatively distinct horizon responses. In all five geometries the deformation imprint is governed by the sign of the background Ricci scalar through the DeWitt--Schwinger curvature term linear in $(ξ-1/6)\mathcal{R}$, and is strongly suppressed at conformal coupling. We verify this both in magnitude and in the $ξ$-dependence. In the near-extremal regime of the two geometries with inner horizons we find a sign change of the horizon polarization at light field mass -- absent for Reissner--Nordström at matched temperature and removed by conformal coupling -- identifying a genuinely quantum-geometric, de-Sitter-core-driven regime. Every result reduces to the Schwarzschild value in the classical limit, validating the calculation.
Comments20 pages; 15 figures
