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

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.