Vacuum Plane Waves; Cartan Invariants and physical interpretation

TL;DR

This paper uses Cartan invariants to classify vacuum plane wave spacetimes, linking their invariant structure to physical effects like geodesic deviation, and explores specific subclasses such as polarized and circularly polarized waves.

Contribution

It provides an invariant classification of vacuum plane wave spacetimes and relates Cartan scalars to their physical interpretation, including notable subclasses.

Findings

Invariant classification of plane wave spacetimes

Relation of Cartan scalars to geodesic deviation

Analysis of polarized and circularly polarized waves

Abstract

As an application of the Cartan invariants obtained using the Karlhede algorithm, we study a simple subclass of the PP-wave spacetimes, the gravitational plane waves. We provide an invariant classification of these spacetimes and then study a few notable subcases: the linearly polarized plane waves, the weak-field circularly polarized waves, and another class of plane waves found by imposing conditions on the set of invariants. As we study these spacetimes we relate the invariant structure (i.e., Cartan scalars) to the physical description of these spacetimes using the geodesic deviation equations relative to timelike geodesic observers.