发表机构
Silesian University in Opava; Universidade Federal do ABC (UFABC)（奥帕瓦西里西亚大学; ABC联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种自动半解析WKB方法，用于计算有效势极小值支持的准束缚态和俘获模，结合Padé重求和与Gamow隧穿近似，在多种致密天体场景中验证了准确性与实用性。
AI 中文摘要
我们发展了一种高度自动化的半解析方法，用于计算由有效势局部极小值支持的弱阻尼准束缚态和俘获模。频率的实部通过任意高阶局部WKB展开和Padé重求和获得，而指数小的虚部则利用Gamow近似估计穿过一个或两个势垒的隧穿效应。由于局部量子化仅需势在其极小值处的导数，该方法可轻易应用于非有理有效势以及不同的致密天体几何。我们提供了一个实现该过程的Mathematica笔记本。与Schwarzschild和Kerr黑洞周围有质量标量场的连分数和直接数值结果以及均匀密度恒星的轴向俘获模的比较表明，该方法在超辐射区之外能给出准确的实频率和有用的衰减率估计。
英文摘要
We develop a largely automatic semi-analytic method for calculating weakly damped quasi-bound states and trapped modes supported by a local minimum of an effective potential. The real part of the frequency is obtained from an arbitrarily high-order local WKB expansion and Padé resummation, while the exponentially small imaginary part is estimated using the Gamow approximation for tunnelling through one or two potential barriers. Because the local quantization requires only derivatives of the potential at its minimum, the method applies readily to non-rational effective potentials and to different compact-object geometries. We provide a Mathematica notebook implementing the procedure. Comparisons with continued-fraction and direct numerical results for massive scalar fields around Schwarzschild and Kerr black holes and for axial trapped modes of a uniform-density star show that the method yields accurate real frequencies and useful estimates of decay rates outside the superradiant regime.
Comments11 pages, 2 figures, 1 ancillary Mathematica notebook
