  The principles of causality and unitarity are studied within rational
nonlinear electrodynamics proposed earlier. We investigate dyonic and
magnetized black holes and show that in the self-dual case, when the electric
charge equals the magnetic charge, corrections to Coulomb's law and
Reissner-Nordstr\"{o}m solutions are absent. In the case of the magnetic black
hole, the Hawking temperature, the heat capacity and the Helmholtz free energy
are calculated. It is shown that there are second-order phase transitions and
it was demonstrated that at some range of parameters the black holes are
stable.
