发表机构
Shanghai Business School; Shanghai Normal University（上海商学院; 上海师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文基于双参数微扰框架推导有质量阴影半径公式，并构造连分数Padé近似，实现对黑洞度规参数的模型无关高精度重建。
AI 中文摘要
基于一个双参数微扰框架，我们推导了有质量粒子球半径和有质量阴影半径的微扰公式，其中以极端黑洞作为微扰背景。采用极端黑洞作为微扰背景使得能量依赖的扫描能够探测更强的引力区域。利用这些公式，我们对几种非标准黑洞的有质量阴影进行了微扰分析，并获得了极端黑洞光子球附近的展开表达式。研究发现，尽管各模型对能量参数 $\epsilon$ 的依赖相同，但与偏差参数 $\delta$ 相关的系数差异显著，这可用于区分不同的黑洞模型。此外，我们构造了一个连分数形式的二点Padé近似，该近似在整个参数范围内对黑洞的有质量阴影半径实现了全局精确近似。数值测试表明，基于该近似的相对误差足够小，为模型无关的度规参数重建提供了可靠基础。
英文摘要
Based on a two-parameter perturbative framework, we derive perturbative formulae for the radii of massive particle spheres and massive shadow radii, where an extremal black hole is employed as the perturbative background. Adopting extremal black holes as the perturbative background enables energy-dependent scans to probe stronger gravitational regimes. Using these formulae, we perform perturbative analyses of the massive shadows for several non-standard black holes, and obtain the expansion expressions near the photon sphere of the extremal black hole. It is found that, although the dependence on the energy parameter $ε$ is the same across models, the coefficients associated with the deviation parameter $δ$ differ significantly, which can serve to distinguish among different black hole models. Furthermore, we construct a two-point Padé approximant in the form of a continued fraction which achieves a globally accurate approximation for the massive shadow radius of the black hole over the entire parameter range. Numerical tests show that the relative errors based on this approximant are small enough to provide a reliable foundation for model-independent reconstruction of metric parameters.
Comments15 pages, 3 figures, references added
