  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.
