# Polarizations of gravitational waves in $f(R)$ gravity

## TL;DR

This paper clarifies that in $f(R)$ gravity, gravitational waves exhibit only three polarization modes, with the massive scalar mode being a mixture of longitudinal and transverse breathing polarizations, challenging previous classification methods.

## Contribution

It demonstrates that $f(R)$ gravity supports only three gravitational wave polarizations and highlights limitations of the Newman-Penrose classification for massive modes.

## Key findings

- Only three polarizations exist in $f(R)$ gravity.
- The massive scalar mode combines longitudinal and breathing polarizations.
- Newman-Penrose classification does not apply to massive modes.

## Abstract

We point out that there are only three polarizations for gravitational waves in $f(R)$ gravity, and the polarization due to the massive scalar mode is a mix of the pure longitudinal and transverse breathing polarization. The classification of the six polarizations by the Newman-Penrose quantities is based on weak, plane and null gravitational waves, so it is not applicable to the massive mode.