标题： 二极 Kerr-Schild 假设 显示英文标题

标题： The dyonic Kerr-Schild ansatz

摘要： 我们开发了Kerr-Schild假设的几何扩展，该扩展在统一框架中结合了麦克斯韦场的电和磁部分，而无需采用对偶旋转。 我们首先观察到，已知的纯电解满足麦克斯韦方程，这是由于Kerr-Schild零流形遵循闭合条件。 从相关的局部精确性性质出发，我们构建了一个与流形自然关联的一形式，作为某种Poincaré对偶化的结果。 这使我们提出了一个在Kerr-Schild假设内几何驱动的二极矢量势，定义为沿流形的电贡献和与对偶化一形式对齐的磁贡献的叠加。 然后我们表明，对于静态且轴对称的Kerr-Schild假设，电真空圆周性定理不仅唯一地约束了度规的标量轮廓，还约束了与规范场的电-磁分解相关的那些项。 该形式化方法提供了二极Kerr-Newman解的清晰推导，并自然扩展到(A)dS情况，突显了Kerr-Schild设定中几何与物质之间的内在相互作用。 显示英文摘要

摘要： We develop a geometric extension of the Kerr-Schild ansatz that incorporates both electric and magnetic sectors of the Maxwell field in a unified framework, without resorting to duality rotations. We start observing that the known purely electric solution satisfies Maxwell's equations due to a closedness condition obeyed by the Kerr-Schild null congruence. From the associated local exactness property, we construct a new one-form naturally linked to the congruence as a sort of Poincar\'e dualization. This leads us to propose a geometrically motivated dyonic vector potential within the Kerr-Schild ansatz, defined as a superposition of an electric contribution along the congruence and a magnetic one that aligns to the dualized one-form. We then show that for a stationary and axisymmetric Kerr-Schild ansatz, the electrovac circularity theorem uniquely constrains not only the scalar profile of the metric, but also those associated to the electric-magnetic splitting of the gauge field. The resulting formalism provides a transparent derivation of the dyonic Kerr-Newman solution and extends naturally to the (A)dS case, highlighting the intrinsic interplay between geometry and matter in a Kerr-Schild setting.