Abstract
Non linear gravitational actions obtained generalizing the tensor scalar density √−det∥gαβ∥ along the line of the Born infeld actions are studied. The requirements that the theory reduces to Einstein-Hilbert action for small curvature, be free of spin two ghosts and free of Coulomb like Schwarschild singularity, selects one Effective lagrangian whose dynamics is dictated by the tensors gµν and Rµνρ∼ (not Rµν or the scalar R).
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