# A New Twist on the Geometry of Gravitational Plane Waves

## TL;DR

This paper investigates the geometry of twisted null geodesic congruences in gravitational plane wave spacetimes, deriving new metrics, analyzing symmetries, and exploring implications for quantum field theory, string theory, and gravitational wave detection.

## Contribution

It introduces a generalized Rosen metric for gravitational plane waves, analyzes their symmetry algebra, and evaluates the van Vleck-Morette determinant for twisted congruences.

## Key findings

- Derived a generalized Rosen metric for plane waves
- Analyzed the isometry algebra of homogeneous plane waves
- Evaluated the van Vleck-Morette determinant for twisted congruences

## Abstract

The geometry of twisted null geodesic congruences in gravitational plane wave spacetimes is explored, with special focus on homogeneous plane waves. The role of twist in the relation of the Rosen coordinates adapted to a null congruence with the fundamental Brinkmann coordinates is explained and a generalised form of the Rosen metric describing a gravitational plane wave is derived. The Killing vectors and isometry algebra of homogeneous plane waves (HPWs) are described in both Brinkmann and twisted Rosen form and used to demonstrate the coset space structure of HPWs. The van Vleck-Morette determinant for twisted congruences is evaluated in both Brinkmann and Rosen descriptions. The twisted null congruences of the Ozsvath-Schucking,`anti-Mach' plane wave are investigated in detail. These developments provide the necessary geometric toolkit for future investigations of the role of twist in loop effects in quantum field theory in curved spacetime, where gravitational plane waves arise generically as Penrose limits; in string theory, where they are important as string backgrounds; and potentially in the detection of gravitational waves in astronomy.