  The metric ansatz is used to describe the gravitational field of a beam-pulse
of spinning radiation (gyraton) in an arbitrary number of spacetime dimensions
D. First we demonstrate that this metric belongs to the class of metrics for
which all scalar invariants constructed from the curvature and its covariant
derivatives vanish. Next, it is shown that the vacuum Einstein equations reduce
to two linear problems in (D-2)-dimensional Euclidean space. The first is to
find the static magnetic potential created by a point-like source. The second
requires finding the electric potential created by a point-like source
surrounded by given distribution of the electric charge. To obtain a generic
gyraton-type solution of the vacuum Einstein equations it is sufficient to
allow the coefficients in the corresponding harmonic decompositions of
solutions of the linear problems to depend arbitrarily on retarded time and
substitute the obtained expressions in the metric ansatz. We discuss properties
of the solutions for relativistic gyratons and consider special examples.
