Complete classification of charged strictly type-I GKS solutions

Construct the most general family of charged generalized Kerr–Schild solutions when the expanding, twisting Weyl-aligned null direction has strictly Weyl type I, rather than type I(a) or more special, by determining the corresponding complete class of vacuum seed spacetimes.

Background

The paper studies charging procedures for higher-dimensional Einstein vacuum spacetimes using a generalized Kerr–Schild transformation with an aligned vector potential. In the expanding and twisting branch, the field equations force the null direction to be shearfree and restrict the spacetime dimension to be even.

For Weyl type I(a) or more special, the authors obtain the complete charged family by using the known classification of appropriate vacuum seeds, which yields higher-dimensional Taub–NUT geometries. They explicitly state that this classification is unavailable for the strictly type-I case, so the corresponding most general charged family cannot presently be constructed. The unresolved issue is therefore both the classification of the relevant vacuum seeds and the resulting charged solutions.