Generalized interaction in multigravity

We consider a general approach to describing the interaction in multigravity models in a $D$-dimensional space–time. We present various possibilities for generalizing the invariant volume. We derive the most general form of the interaction potential, which becomes a Pauli–Fierz-type model in the bigravity case. Analyzing this model in detail in the $(3{+}1)$-expansion formalism and also requiring the absence of ghosts leads to this bigravity model being completely equivalent to the Pauli–Fierz model. We thus in a concrete example show that introducing an interaction between metrics is equivalent to introducing the graviton mass.