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We analyze the Hamiltonian structure of a general theory of bi-gravity wherethe interaction term is a scalar function of the form $ V(\mathcal{X}^{n}) $where $ \mathcal{X} $ may be $\sqrt{g^{-1}f} $ or $ g^{-1}f $. We givenecessary conditions for the interaction term of such a theory to be ghostfree. We give a precise constraint analysis of the bi-gravity theory of Hassan-Rosen and show that the additional constraint which omit the ghost is just onepossibility at the bifurcation point.

Hamiltonian structure of bi-gravity, problem of ghost and bifurcation