Chaotic motion in pp-wave spacetimes

TL;DR

This paper demonstrates chaotic behavior in geodesics within non-homogeneous vacuum pp-wave spacetimes, revealing fractal boundaries between different asymptotic outcomes, marking a novel example of chaos in exact radiative solutions.

Contribution

It provides the first rigorous analytic and numerical evidence of chaos in exact radiative spacetimes, specifically in non-homogeneous vacuum pp-wave solutions.

Findings

Chaotic geodesic behavior demonstrated in specific pp-wave solutions

Identification of fractal structure in outcome boundaries

First example of chaos in exact radiative spacetime solutions

Abstract

We investigate geodesics in non-homogeneous vacuum pp-wave solutions and demonstrate their chaotic behavior by rigorous analytic and numerical methods. For the particular class of solutions considered, distinct "outcomes" (channels to infinity) are identified, and it is shown that the boundary between different outcomes has a fractal structure. This seems to be the first example of chaos in exact radiative spacetimes.