General polarization modes for the Rosen gravitational wave

TL;DR

This paper develops a comprehensive formalism to describe arbitrary polarization states of gravitational waves in the Rosen form, resolving discrepancies between Rosen and Brinkmann representations.

Contribution

It introduces a novel approach representing polarization states as trajectories in a hyperbolic plane within the Rosen metric framework.

Findings

Unified description of polarization states in Rosen form

Resolution of differences between Rosen and Brinkmann formalisms

Framework for analyzing complex polarization in gravitational waves

Abstract

Strong-field gravitational plane waves are often represented in either the Rosen or Brinkmann forms. While these two metric ansatze are related by a coordinate transformation, so that they should describe essentially the same physics, they rather puzzlingly seem to treat polarization states quite differently. Both ansatze deal equally well with + and X linear polarizations, but there is a qualitative difference in they way they deal with circular, elliptic, and more general polarization states. In this article we will develop a general formalism for dealing with arbitrary polarization states in the Rosen form of the gravitational wave metric, representing an arbitrary polarization by a trajectory in a suitably defined two dimensional hyperbolic plane.