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.