  Dyonic and magnetic black holes solutions with spherically symmetric
configurations in general relativity are obtained. Black holes possessing
electric and magnetic charges are studied where the source of the gravitational
field is electromagnetic fields obeying the arcsin-electrodynamics. We find
corrections to Coulomb's law and Reissner - Nordstr\"{o}m solutions. The
principles of causality and unitarity are investigated. We obtain the Hawking
temperature and it was shown that at some event horizons there are second-order
phase transitions.
