2 General Robinson – Trautman and Kundt geometries and Einstein ’ s equations for aligned gyratonic matter

In our previous paper [Phys. Rev. D 89 (2014) 124029], cited as [1], we attempted to find Robinson–Trautman-type solutions of Einstein’s equations representing gyratonic sources (matter field in the form of an aligned null fluid, or particles propagating with the speed of light, with an additional internal spin). Unfortunately, by making a mistake in our calculations, we came to the wrong conclusion that such solutions do not exist. We are now correcting this mistake. In fact, this allows us to explicitly find a new large family of gyratonic solutions in the Robinson–Trautman class of spacetimes in any dimension greater than (or equal to) three. Gyratons thus exist in all twist-free and shear-free geometries, that is both in the expanding Robinson–Trautman and in the non-expanding Kundt classes of spacetimes. We derive, summarize and compare explicit canonical metrics for all such spacetimes in arbitrary dimension. PACS class: 04.20.Jb, 04.30.–w, 04.50.–h, 04.40.Nr