静态球对称时空中有限距离弱引力透镜的参考再规范化曲率原始Gauss-Bonnet格式

我们发展了一种参考再规范化（无极光球）规范，用于静态、球对称时空中有限距离的Gauss-Bonnet引力透镜。该方法将用于降低Gauss-Bonnet曲率-面积积分的曲率原始量视为仅在加法常数（加法规范自由度）下定义的量。我们通过匹配外部区域中选定的参考光学几何（其中物理几何趋近于参考几何）来固定此规范，从而通过参考减法定义唯一的再规范化偏差原始量 $\mathcal{P}_e(r)$。 resulting master formula yields the Ishihara-Li finite-distance deflection angle without invoking any circular null orbit, while remaining fully compatible with orbit-normalized prescriptions whenever a suitable photon sphere exists (the two gauges differ only by a constant shift and give identical $\alpha$). In asymptotically flat settings the canonical reference is Minkowski, while in Kottler-type backgrounds the canonical reference is de Sitter within the static patch, making the operational fiducial explicit. We validate the method by reproducing Ishihara's finite-distance weak-deflection formulas for Schwarzschild, Reissner-Nordstr"om, and Kottler spacetimes, including the mixed $r_g\Lambda$ term in the Kottler case within the static-patch fiducial. We also present a demonstrative example in which orbit normalization is genuinely inapplicable because no circular null orbit exists in the physical optical region (the Janis-Newman-Winicour spacetime for $\gamma\le \tfrac12$). The result is a unified, geometrically transparent route to finite-distance lensing that preserves compatibility with orbit-normalized prescriptions whenever those apply.