On massive spin-2 in the Fradkin-Vasiliev formalism. II. General massive case

In this work we apply the Fradkin-Vasiliev formalism based on the frame-like gauge invariant description of the massive and massless spin 2 to the construction of the cubic interactions vertices for massive spin 2 self-interaction as well as its gravitational interaction. In the first case we show that the vertex can be reduced (by field redefinitions) to the set of the trivially gauge invariant terms. There are four such terms which are not equivalent on-shell and do not contain more than four derivatives. Moreover, one their particular combination reproduces the minimal (with no more than two derivatives) vertex. As for the gravitational vertex, we show that due to the presence of the massless spin 2 there exist two abelian vertices (besides the three trivially gauge invariant ones) which are not equivalent to any trivially gauge invariant terms and can not be removed by field redefinitions. Moreover, their existence appears to be crucial for the possibility to reproduce the minimal two derivatives vertex.