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Recently Bandos, Lechner, Sorokin, and Townsend [Phys. Rev. D \textbf{102},121703 (2020)] proposed Modified Maxwell (ModMax) model of nonlinearduality-invariant conformal electrodynamics. Here, Generalized ModMax(GenModMax) model of nonlinear electrodynamics coupled to general relativity isstudied. The metric and mass functions, and their asymptotic as$r\rightarrow\infty$ and $r\rightarrow 0$ of a magnetic black hole areobtained. Corrections to the Reissner--Nordstr\"{o}m solution are found and weshow that for some model parameters the black hole is regular. The Hawkingtemperature and heat capacity of black holes are calculated and phasetransitions are investigated. We demonstrate that black holes are not stablefor certain model parameters.

Magnetic black holes with generalized ModMax model of nonlinear electrodynamics