On gravitational interactions for massive higher spins in $\mathrm{AdS_3}$

In this paper we investigate gravitational interactions of massive higher spin fields in three dimensional AdS space with arbitrary value of cosmological constant including flat Minkowski space. We use the frame-like gauge description for such massive fields adapted to the three-dimensional case. First, we carefully analyze the procedure of switching on gravitational interactions in the linear approximation in the example of a massive spin-3 field and then proceed with the generalization to the case of an arbitrary integer spin field. As a result we construct a cubic interaction vertex linear in a spin-2 field and quadratic in a higher spin field on the AdS3 background. As in the massless case the vertex does not contain any higher derivative corrections to the Lagrangian and/or gauge transformations. Thus, even after switching on gravitational interactions, one can freely consider any massless or partially massless limits as well as the flat one.