Extremal limit of the regular charged black holes in nonlinear electrodynamics

Solutions of the coupled equations of general relativity and nonlinear electrodynamics with topology AdS₂×S² are constructed and studied both analytically and numerically. It is shown that the near horizon limit of the extreme nonlinear black hole corresponds to the solution expressible in terms of the Lambert special functions. It is explicitly demonstrated that for the formulation of the nonlinear theory considered in this paper the resulting solutions do not belong to the Bertotti-Robinson class unless electrodynamics is Maxwellian. The question of the boundary conditions is briefly discussed.