Gravitational field of relativistic gyratons

The metric ansatz (1) 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 $\mathbf{A}$ created by a pointlike source. The second requires finding the electric potential $\Phi$ created by a pointlike 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 $u$ and substitute the obtained expressions in the metric ansatz. These solutions are generalizations of the gyraton metrics found in [V. P. Frolov and D. V. Fursaev, Phys. Rev. D 71, 104034 (2005).]. We discuss properties of the solutions for relativistic gyratons and consider special examples.