We revisit the problem of gravity coupled to a background metric $\eta_{ \mu\nu}$, looking for ghost free interactions. It is known that elimination of the Boulware-Desewr ghost is equivalent to a certain Hessian condition on the interacting potential. We elaborate on this equation and provide a proof that dRGT potential is the unique interaction between the spacetime metric and a background field $\eta_{ \mu\nu}$ which is both Lorentz invariant and ghost free. Our approach is fully non-perturbative using only the ADM formulation of general relativity.
Categories: gr-qc