AI 中文总结
本文研究双曲Toda方程解在弯曲3+1时空中作为无源电磁势的条件，通过Maxwell方程分类Killing纤维尺度与扭转，并给出球对称单位电荷单极子实例。
AI 中文摘要
双曲Toda方程的每个解确定了一个(2+1)维Einstein-Weyl空间上的经典阿贝尔单极子。我们确定其联络何时也是具有类空Killing场的弯曲洛伦兹3+1时空上的无源电磁势。在一般分支上，Maxwell方程通过Toda场的一个特征对允许的Killing纤维尺度和水平扭转进行分类。分离的Liouville分支给出纯磁场，其纤维几何更为自由。球对称解产生单位电荷的单极子，在收缩屏幕上具有守恒通量。这里的背景度规既非假设为Einstein也非自对偶。
英文摘要
Every solution of the hyperbolic Toda equation determines a classical Abelian monopole on a (2+1)-dimensional Einstein--Weyl space. We determine when its connection is also a source-free electromagnetic potential on a curved Lorentzian 3+1 spacetime with a spacelike Killing field. On the generic branch, Maxwell's equation classifies the admissible Killing-fibre scale and horizontal twist through one characteristic of the Toda field. A separated Liouville branch gives purely magnetic fields with considerably freer fibre geometry. The round spherical solution yields a monopole of unit charge with conserved flux on a contracting screen. The background metric here is neither assumed to be Einstein nor self-dual.
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