发表机构
Charles University; Czech Academy of Sciences（查理大学; 捷克科学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用广义Kerr-Schild变换从真空种子构造高维爱因斯坦-麦克斯韦解，得到三类分支解，还给出带电Taub-NUT度量的六维推广，明确了陈-西蒙斯项在壳上恒为零的性质。
AI 中文摘要
我们沿类光测地线矢量场$\boldsymbol{k}$，通过广义Kerr-Schild变换从真空种子解构造高维爱因斯坦-麦克斯韦（-陈-西蒙斯）解。假设矢量势$\boldsymbol{A}$与$\boldsymbol{k}$对齐，且$\boldsymbol{k}$为满足“光学约束”的外尔对齐类光方向，由此得到三类不同的解分支：若$\boldsymbol{k}$膨胀且扭转，则其剪切必须为零，该分支包含某些带电Taub-NUT度量；若$\boldsymbol{k}$膨胀且无扭转，则分为两个子族——剪切为零时的Robinson-Trautman电磁真空解（具有非零麦克斯韦场），或剪切不为零且场为零的解；最后，$\boldsymbol{k}$不膨胀的情况归为已知Kundt解的一个子集。所有情形下，陈-西蒙斯项在壳上恒为零。此外，通过放宽$\boldsymbol{A}$的对齐假设，我们还得到带电Taub-NUT度量的六维推广，其场强的磁部分是两个不同凯勒2-形式的线性组合，这与此前已知的四维以上例子不同。
英文摘要
We explore the construction of higher-dimensional Einstein-Maxwell(-Chern-Simons) solutions from vacuum seeds by means of a generalized Kerr-Schild transformation along a geodesic null vector field $\mathbf{k}$. Assuming the vector potential $\mathbf{A}$ to be aligned with $\mathbf{k}$, and $\mathbf{k}$ to be a Weyl aligned null direction satisfying the ``optical constraint'', we arrive at three distinct branches of solutions. If $\mathbf{k}$ is expanding and twisting, then its shear must vanish -- this branch includes certain charged Taub-NUT metrics. If $\mathbf{k}$ is expanding and twistfree, one finds two subfamilies: Robinson-Trautman electrovac solutions with a non-null Maxwell field if the shear is zero, or shearing solutions with a null field. Finally, the case when $\mathbf{k}$ is non-expanding reduces to a subset of the known Kundt solutions. In all cases, the Chern-Simons term turns out to be identically zero on-shell. In passing, by relaxing the alignment assumption on $\mathbf{A}$, we also obtain a six-dimensional extension of a charged Taub-NUT metric for which the magnetic part of the field strength is a linear combination of two distinct Kähler 2-forms, as opposed to the previously known examples in more than four dimensions.
Comments37 pages
