Towards rotating 2-2-holes

Static 2-2-hole solutions of quadratic gravity have been investigated to be a possible horizonless replacement for black holes as the endpoint of gravitational collapse. Realistically such objects will form with spin, but rotating 2-2-hole solutions are currently not known. We take some steps here to explore the existence and properties of such solutions. We employ an expansion of the field equations where the expansion parameter is inversely related to the size of the object. This expansion parameter appears explicitly in the trial metrics, and we are able to find solutions of the leading order field equations. These vacuum solutions are candidates to describe most of the interior of a rotating 2-2-hole.