Comment on "Fully covariant radiation force on a polarizable particle"

Recently Pieplow and Henkel (PH) (NJP $\mathbf{\text{15}}$ (2013) 023027) presented a new fully covariant theory of the Casimir friction force acting on small neutral particle moving parallel to flat surface. We compare results of this theory with results which follow from a fully relativistic theory of friction in plate-plate configurations in the limit when one plate is considered as sufficiently rarefied. We show that there is the agreement between these theories.