Born-Infeld-type electrodynamics and magnetic black holes

We investigate a Born-Infeld-type model of nonlinear electrodynamics, possessing three parameters, coupled with general relativity. As a particular case Born-Infeld electrodynamics is reproduced. There is no singularity of the electric field at the center of point-like charged particles and self-energy of charges is finite in this model. The magnetized black hole is studied and solutions are obtained. We find the asymptotic of the metric and mass functions at r→∞ and r→0, and corrections to the Reissner-Nordström solution. Thermodynamics of black holes is investigated. We calculate the Hawking temperature of black holes and show that black holes are stable and there are no phase transitions in the model under consideration.