Curvature invariants in type-III spacetimes

Abstract

The results of paper [1] are generalized for vacuum type-III solutions with, in general, a non-vanishing cosmological constant Lambda. It is shown that all curvature invariants containing derivatives of the Weyl tensor vanish if a type-III spacetime admits a non-expanding and non-twisting null geodesic congruence. A non-vanishing curvature invariant containing first derivatives of the Weyl tensor is found in the case of type-III spacetime with expansion or twist.