# Propagation of Polar Gravitational Waves in f(R,T) Scenario

## TL;DR

This study explores how polar gravitational waves propagate in a modified gravity model, revealing their effects on matter distribution and velocity, and analyzing the influence of model parameters on wave amplitude.

## Contribution

It provides a detailed formulation and solution of gravitational wave propagation in the $R+2 T$ gravity model, extending understanding beyond general relativity.

## Key findings

- Polar gravitational waves affect matter distribution and velocity in the radiation era.
- Model parameters influence the amplitude of gravitational waves.
- Wave behavior is consistent with general relativity in certain limits.

## Abstract

This paper investigates the propagation of polar gravitational waves in the spatially flat FRW universe consisting of a perfect fluid in the scenario of $R+2\lambda T$ model of $f(R,T)$ gravity ($\lambda$ being the model parameter). The spatially flat universe model is perturbed via Regge-Wheeler perturbations inducing polar gravitational waves and the field equations are formulated for both unperturbed as well as perturbed spacetimes. We solve these field equations simultaneously for the perturbation parameters introduced in the metric, matter, and velocity in the radiation, as well as dark energy, dominated phases. It is found that the polar gravitational waves can produce changes in the background matter distribution as well as velocity components in the radiation era similar to general relativity case. Moreover, we have discussed the impact of model parameter on the amplitude of gravitational waves.