Gravitational field of relativistic gyratons

TL;DR

This paper develops a metric ansatz to describe the gravitational field of relativistic gyratons in any spacetime dimension, reducing Einstein's equations to linear problems and exploring properties of these solutions.

Contribution

It introduces a new metric framework for gyratons in arbitrary dimensions, simplifying Einstein's equations to linear problems and enabling generic solution construction.

Findings

Scalar invariants of the metric vanish

Vacuum Einstein equations reduce to two linear problems

Solutions depend on retarded time and harmonic functions

Abstract

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.