Continuous coordinates for all impulsive pp - waves

TL;DR

This paper introduces a new continuous coordinate system for impulsive gravitational pp-waves that simplifies the metric and is better suited for analyzing particle trajectories.

Contribution

The authors develop a continuous, synchronous, and transverse coordinate system for impulsive pp-waves, improving the analysis of particle motion in these spacetimes.

Findings

Metric becomes explicitly continuous in the new coordinates

Coordinate system is more suitable for studying particle trajectories

Simplifies mathematical treatment of impulsive pp-waves

Abstract

We present a coordinate system for a general impulsive gravitational pp - wave in vacuum in which the metric is explicitly continuous, synchronous and "transverse". Also, it is more appropriate for investigation of particle motions.