  Many studies have been carried out in the literature to evaluate the number
of polarization modes of gravitational waves in modified theories, in
particular in $f(R)$ theories. In the latter ones, besides the usual two
transverse-traceless tensor modes present in general relativity, there are two
additional scalar ones: a massive longitudinal mode and a massless transverse
mode (the so-called breathing mode). This last mode has often been overlooked
in the literature, due to the assumption that the application of the Lorenz
gauge implies transverse-traceless wave solutions. We however show that this is
in general not possible and, in particular, that the traceless condition cannot
be imposed due to the fact that we no longer have a Minkowski background
metric. Our findings are in agreement with the results found using the
Newman-Penrose formalism, and thus clarify the inconsistencies found so far in
the literature.
