Causality of Massive Spin 2 Field in External Gravity

We investigate the structure of equations of motion and lagrangian constraints in the most general theory of massive spin 2 field interacting with external gravitational field. We demonstrate how consistency with the flat spacetime limit can be achieved if the external gravity fulfills vacuum Einstein equations with arbitrary cosmological constant and show that in this case there exists one-parameter family of theories describing the massive spin 2 field. These theories describe causal propagation of the correct number of degrees of freedom. For a specific value of the parameter a gauge invariance with a vector parameter appears, we interpret this value as massless limit of the theory. Another specific value of the parameter produces gauge invariance with a scalar parameter and this cannot be interpreted as a consistent massive or massless theory.