AI 中文总结
本文提出一种基于合流Heun Wronskian的谱方法，统一求解弱磁化Ernst--Schwarzschild时空中标量场的拟正规模与拟束缚态，并与现有基准一致。
AI 中文摘要
我们研究了弱磁化Ernst--Schwarzschild时空中无质量标量场的拟正规模与拟束缚态谱。在分离的$O(B_0^2)$阶区域内，Klein--Gordon方程约化为径向合流Heun方程。我们直接从规范的合流Heun递推关系及其正则到非正则连接极限构造了端点选择的谱Wronskian。拟正规模与拟束缚态随后分别作为同一解析谱函数在辐射叶与束缚叶上的零点获得，从而在分离弱场问题中对这两个谱扇区提供了统一处理。所得的QNM与QBS频率与文献中可用的独立弱场Ernst及有质量Schwarzschild基准一致。我们进一步表明，对于代表性情形，由本文考察的局部Heun级数终止关系所选择的频率不满足端点选择的拟束缚态条件。因此，该构造为弱场Ernst问题中的辐射态与束缚态提供了直接的从视界到无穷远的谱条件。
英文摘要
We study the quasinormal-mode and quasibound-state spectra of a massless scalar field in weakly magnetized Ernst--Schwarzschild spacetime. In the separated $O(B_0^2)$ regime, the Klein--Gordon equation reduces to a radial confluent-Heun equation. We construct an endpoint-selected spectral Wronskian directly from the canonical confluent-Heun recurrence and its regular-to-irregular connection limit. Quasinormal modes and quasibound states are then obtained as zeros of the same analytic spectral function on the radiative and bound sheets, respectively, providing a unified treatment of the two spectral sectors within the separated weak-field problem. The resulting QNM and QBS frequencies agree with independent weak-field Ernst and massive-Schwarzschild benchmarks available in the literature. We further show, for representative cases, that the frequencies selected by the local Heun-series termination relation examined here do not satisfy the endpoint-selected quasibound-state condition. The construction therefore provides a direct horizon-to-infinity spectral condition for both radiative and bound states within the weak-field Ernst problem.
Comments10 pages
