Test particle motion in a gravitational plane wave collision background

TL;DR

This paper analyzes the motion of test particles in complex gravitational wave collision backgrounds, using numerical methods and conserved quantities to understand geodesic behavior across different spacetime regions.

Contribution

It provides a detailed numerical analysis of geodesic motion in Ferrari-Ibanez colliding gravitational wave spacetimes, highlighting the use of Killing vectors and boundary matching techniques.

Findings

Geodesic equations reduced to first order systems

Numerical integration of particle trajectories

Matching of geodesics across spacetime boundaries

Abstract

Test particle geodesic motion is analysed in detail for the background spacetimes of the degenerate Ferrari-Ibanez colliding gravitational wave solutions. Killing vectors have been used to reduce the equations of motion to a first order system of differential equations which have been integrated numerically. The associated constants of the motion have also been used to match the geodesics as they cross over the boundary between the single plane wave and interaction zones.