Nonlinear gravitational waves and their polarization

TL;DR

This paper analyzes a specific class of nonlinear gravitational waves with light-like Killing fields, deriving their polarization and energy properties, and demonstrating their nonlinear superposition behavior.

Contribution

It introduces a new class of nonlinear gravitational waves invariant under a non-Abelian Lie algebra with light-like commutator, providing explicit polarization and energy calculations.

Findings

Explicit polarization states derived

Energy of the waves explicitly calculated

Nonlinear superposition laws demonstrated

Abstract

Vacuum gravitational fields invariant for a non Abelian Lie algebra generated by two Killing fields whose commutator is light-like are analyzed. It is shown that they represent nonlinear gravitational waves obeying to two nonlinear superposition laws. The energy and the polarization of this family of waves are explicitely evaluated.