Charging higher-dimensional spacetimes with a generalized Kerr-Schild transformation

Abstract

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.