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We analyze the Hamiltonian structure of a general theory of bi-gravity where the interaction term is a scalar function of the form V(Xn) where X may be g-1f- or g-1f. We give necessary conditions for the interaction term of such a theory to be ghost free. 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 one possibility at the bifurcation point.
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