  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.
