Extended Kerr—Schild spacetimes of any dimension

We study geometric and algebraic properties of extended Kerr-Schild space times(xKS), i.e. an extension of the Kerr-Schild(KS) ansatz where, in addition to the null KS vector, a spacelike vector field appears in the metric. In contrast to the KS case, it turns out that xKS space times with a geodetic KS vector are not necessarily algebraically special and we obtain, in general, only a necessary condition under which the KS vector is geodetic. However, it is shown that this condition becomes sufficient if we appropriately restrict the geometry of the null and spacelike vector fields. Examples of xKS space times belonging to the Kundt class and also expanding xKS space times, namely the CCLP black hole, are provided and briefly discussed. (paper)