Magnetically charged black hole in framework of nonlinear electrodynamics model

A model of nonlinear electrodynamics is proposed and investigated in general relativity. We consider the magnetic black hole and find a regular solution which gives corrections into the Reissner-Nordstr\"{o}m solution. At $r\rightarrow\infty$ the asymptotic spacetime becomes flat. The magnetic mass of the black hole is calculated and the metric function is obtained. At some values of the model parameter there can be one, two or no horizons. Thermodynamics of black holes is studied and we calculate the Hawking temperature and heat capacity of black holes. It is demonstrated that there is a phase transition of second order. At some parameters of the model black holes are thermodynamically stable.