2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33894New type III and type N approximate solutions which are regular in the linear approximation are shown to exist. For that, we use complex transformations on self-dual Robinson-Trautman metrics rather then the classical approach. The regularity criterion is the boundedness and vanishing at infinity of a scalar obtained by saturating the Bel-Robinson tensor of the first approximation by a time-like vector which is constant with respect to the zeroth approximation.6 pages, no figuresGeneral Relativity and Quantum Cosmologytext