Aichelburg-Sexl boost of an isolated source in general relativity

TL;DR

This paper investigates the Aichelburg--Sexl boost of an isolated gravitational source, focusing on the curvature tensor rather than the metric, and explores how different boost directions affect the resulting field.

Contribution

It extends the Aichelburg--Sexl boost analysis to the Weyl vacuum gravitational field of an isolated axially symmetric source, highlighting differences based on boost direction.

Findings

Transverse and parallel boosts yield significantly different results.

The curvature tensor approach provides new insights into ultra-relativistic limits.

The study offers detailed calculations for specific boost directions.

Abstract

A study of the Aichelburg--Sexl boost of the Schwarzschild field is described in which the emphasis is placed on the field (curvature tensor) with the metric playing a secondary role. This is motivated by a description of the Coulomb field of a charged particle viewed by an observer whose speed relative to the charge approaches the speed of light. Our approach is exemplified by carrying out an Aichelburg-- Sexl type boost on the Weyl vacuum gravitational field due to an isolated axially symmetric source. Detailed calculations of the boosts transverse and parallel to the symmetry axis are given and the results, which differ significantly, are discussed.