  We present the Riemann and Ricci tensors for a fully general non-twisting and
shear-free geometry in arbitrary dimension D. This includes both the
non-expanding Kundt and expanding Robinson-Trautman family of spacetimes. As an
interesting application of these explicit expressions we then integrate the
Einstein equations and prove a surprising fact that in any D the
Robinson-Trautman class does not admit solutions representing gyratonic
sources, i.e., matter field in the form of a null fluid (or particles
propagating with the speed of light) with an additional internal spin. Contrary
to the closely related Kundt class and pp-waves, the corresponding off-diagonal
metric components thus do not encode the angular momentum of some gyraton.
Instead, we demonstrate that in standard D=4 general relativity they directly
determine two independent amplitudes of the Robinson-Trautman exact
gravitational waves.
