Gauge-invariant formulation for the gravitational wave equations

TL;DR

This paper develops a gauge-invariant framework for gravitational wave equations, deriving solutions across various theories and clarifying polarization modes, thereby unifying and extending previous analyses.

Contribution

It introduces a gauge-invariant formulation that systematically derives gravitational wave solutions and polarization modes in multiple theories, including general relativity and generalized metric theories.

Findings

Derived plane wave solutions in different theories

Identified polarization modes for each theory

Reproduced earlier results using the gauge-invariant approach

Abstract

A gauge-invariant formulation for the gravitational wave equations is presented. Using this approach, weak, plane wave solutions in a vacuum are derived in various theories. These include general relativity with two modes of polarization with helicity $\pm 2$, Yang's theory with three modes of polarization with helicity $\pm 2$ and $0$, and so-called "general metric theories" with six modes of polarization with helicity $\pm 2$, $\pm 1$, and two $0$'s. To identify the polarizations of gravitational waves, it is explicitly demonstrated how the gauge-invariant approach reproduces the earlier results.