Gravitational field of a spinning radiation beam-pulse in higher dimensions

TL;DR

This paper derives the gravitational field of a spinning radiation beam-pulse in higher dimensions, providing both linear and exact solutions, and explores effects on particles and light in four dimensions.

Contribution

It presents the first exact solution for the gravitational field of a polarized radiation beam in arbitrary higher dimensions, extending previous linear approximations.

Findings

Exact solution for higher-dimensional gravitational field of a spinning beam-pulse.

Demonstration that the field can be obtained via boosted Lense-Thirring metric.

Analysis of effects on test particles and light in 4D spacetime.

Abstract

We study the gravitational field of a spinning radiation beam-pulse in a higher dimensional spacetime. We derive first the stress-energy tensor for such a beam in a flat spacetime and find the gravitational field generated by it in the linear approximation. We demonstrate that this gravitational field can also be obtained by boosting the Lense-Thirring metric in the limit when the velocity of the boosted source is close to the velocity of light. We then find an exact solution of the Einstein equations describing the gravitational field of a polarized radiation beam-pulse in a space-time with arbitrary number of dimensions. In a $D-$dimensional spacetime this solution contains $[D/2]$ arbitrary functions of one variable (retarded time $u$), where $[d]$ is the integer part of $d$. For the special case of a 4-dimensional spacetime we study effects produced by such a relativistic spinning beam on the motion of test particles and light.