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Nonsingular Black Holes in Palatini Extensions of General Relativity

We discuss static, spherically symmetric solutions with an electric field in a quadratic extension of general relativity formulated in the Palatini approach (assuming that metric and connection are independent fields). Unlike the usual metric formulation of this theory, the field equations are second-order and ghost-free. It is found that the resulting black holes present a central core whose area is proportional to the Planck area times the number of charges. Some of these solutions are nonsingular. In this case, the charge-to-mass ratio implies that the core matter density is independent of the specific amounts of charge and mass and of order the Planck density.