General polarization modes for the Rosen gravitational wave

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.

V1: 12 pages, no figures. V2: still 12 pages, reformatted. Minor technical edits, discussion of Riemann tensor added, two references added, no significant physics changes. This version accepted for publication in Classical and Quantum Gravity