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Generalizations of gravitational Born-Infeld type Lagrangians are investigated. Phenomenological constraints (reduction to Einstein-Hilbert action for small curvature, spin-two ghost freedom, and absence of Coulomb-like Schwarschild singularity) select one effective Lagrangian whose dynamics is dictated by the tensors g_μν and R_μνρσ (not R_μν or the scalar R).
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D. Comelli (2005) studied this question.
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