Nonsingular black holes in quadratic Palatini gravity

We find that if general relativity is modified at the Planck scale by a Ricci-squared term, electrically charged black holes may be nonsingular. These objects concentrate their mass in a microscopic sphere of radius $r_{mathrm{core}}approx N_{q}^{1/2}l_{mathrm{P}}/3$ , where l _P is the Planck length and N _q is the number of electric charges. The singularity is avoided if the mass of the object satisfies the condition $M_{0}^{2}approx m_{mathrm{P}}^{2} alpha_{mathrm{em}}^{3/2} N_{q}^{3}/2$ , where m _P is the Planck mass and α _em is the fine-structure constant. For astrophysical black holes this amount of charge is so small that their external horizon almost coincides with their Schwarzschild radius. We work within a first-order (Palatini) approach.