Non-Linear Gravitational Lagrangians

"Alternative gravitational theories" based on Lagrangian densities that depend in a nonlinear way on the Ricci tensor of a metric are considered. It is shown that, provided certain weak regularity conditions are met, any such theory is equivalent, from the Hamiltonian point of view, to the standard Einstein theory for a new metric (which, roughly speaking, coincides with the momentum canonically conjugated to the original metric), interacting with external matterfields whose nature depends on the original Lagrangian density.