Exact plane gravitational waves in the de Rham-Gabadadze-Tolley model of massive gravity

TL;DR

This paper demonstrates that the de Rham-Gabadadze-Tolley massive gravity model admits exact plane gravitational wave solutions governed by the Helmholtz equation, generalizing known solutions in general relativity.

Contribution

It provides the first exact plane wave solutions in the nonlinear massive gravity model, valid for arbitrary coefficients of higher-order terms.

Findings

Exact plane wave solutions exist in the dRGT model.

Waveforms satisfy the two-dimensional Helmholtz equation.

Solutions reduce to Aichelburg-Sexl metric in the massless limit.

Abstract

We show that the nonlinear massive gravity model of de Rham, Gabadadze, and Tolley admits exact plane gravitational wave solution whose waveform obeys the two-dimensional Helmholtz equation. The solution is valid for arbitrary values of the coefficients of the cubic and quartic terms. In the massless limit the solution reduces to the Aichelburg-Sexl metric in general relativity.