Charging Kerr-Schild spacetimes in higher dimensions

TL;DR

This paper classifies and constructs higher-dimensional charged Kerr-Schild spacetimes, revealing conditions for shear and twist, and identifying new solutions including charged black holes and Taub-NUT metrics, with implications for the KS double copy.

Contribution

It provides a complete classification of shearfree solutions and explores the properties of twisting solutions in higher-dimensional charged Kerr-Schild spacetimes.

Findings

Shear obstructs non-null fields in expanding Kerr-Schild spacetimes.

Complete family of shearfree solutions includes charged Schwarzschild-Tangherlini-like black holes.

Twisting solutions include higher-dimensional charged Taub-NUT metrics.

Abstract

We study higher dimensional charged Kerr-Schild (KS) spacetimes that can be constructed by a KS transformation of a vacuum solution with an arbitrary cosmological constant, and for which the vector potential is aligned with the KS vector $\mathbf{k}$. Focusing on the case of an expanding $\mathbf{k}$, we first characterize the presence of shear as an obstruction to non-null fields (thereby extending an early no-go result of Myers and Perry). We next obtain the complete family of shearfree solutions. In the twistfree case, they coincide with charged Schwarzschild-Tangherlini-like black holes. Solutions with a twisting $\mathbf{k}$ consist of a four-parameter family of higher dimensional charged Taub-NUT metrics with a base space of constant holomorphic sectional curvature. In passing, we identify the configurations for which the test-field limit gives rise to instances of the KS double copy. Finally, it is shown that null fields define a branch of twistfree but shearing solutions, exemplified by the product of a Vaidya-like radiating spacetime with an extra dimension.