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A Study of Relativistic Gyratons

In this paper, we present a study of relativistic gyratons. We sum- marize general properties of the gyratons propagating in asymptotically flat and asymptotically AdS spacetimes. We discuss scalar invariants constructed from the curvature and its covariant derivatives and the reduction of Einstein equations to two linear problems in (D − 2)-dimensional Euclidean space. Then, in particular, we study the four dimensional example of the gyraton metric in AdS spacetime geometrically in more detail. We show that the gyraton metric is of algebraical type III or more special. Introduction The history of studies of gravitational fields of beams and pulses of light is quite long. In 1934 (Tolman, 1934) obtained solutions for the gravitational field of beams of radiation and pulses of light in the linear approximation. The exact solutions of the non-linear Einstein equations were found by (Peres, 1959, 1960) and (Bonnor, 1969). These solutions belong to the pp-wave class and reduce to Aichelburg- Sexl metric (Aichelburg, 1971) when we consider the infinitely small cross-section of the beam and the delta-type distribution of the light-pulse in time. Furthermore, (Bonnor, 1970) generalized these 4-dimensional solutions to the case the matter of beam (null fluid) is charged or spinning. Recently, (Frolov and Fursaev, 2005) and (Frolov, Israel and Zelnikov, 2005) found higher dimensional generalization of previous solutions to the case where the beam of radiation carries angular momentum. The solution describes a pulsed beam of radiation with negligible radius of cross-section, finite duration in time and with finite both energy E and angular momentum J. The ultra-relativistic source with these characteristics is called a gyraton. Typical example of a gyraton is a pulse of circular polarized light or a modulated beam of ultrarela- tivistic particles with spin. The gravitational field of the gyraton is determined by a number of arbitrary functions of the retarded time u. They describe profiles of the energy density and angular momenta distributions of the gyraton. The gyratons propagating in asymptotically flat D-dimensional spacetime