Classification of charged solutions from general shearfree vacuum seeds

Determine the charged counterparts of all higher-dimensional vacuum spacetimes admitting a geodesic, expanding, twisting, shearfree null direction satisfying the stated alignment and optical conditions, without imposing the additional condition that the Weyl type be I(a) or more special.

Background

The charging proposition establishes that an expanding, twisting Einstein background can be charged through the aligned generalized Kerr–Schild transformation only in even dimensions and only when the relevant null direction is shearfree.

The paper gives a complete construction after imposing the stronger Weyl-type I(a) condition, because the necessary vacuum seeds are then known and coincide with higher-dimensional Taub–NUT metrics. The broader class of shearfree seeds, without that additional curvature restriction, remains unavailable; consequently, the charged solutions generated from those seeds cannot be explicitly determined.