Regular magnetic black holes and monopoles from nonlinear electrodynamics

It is shown that general relativity coupled to nonlinear electrodynamics (NED) with the Lagrangian L (F), F=F_F^ having a correct weak field limit, leads to nontrivial spherically symmetric solutions with a globally regular metric if and only if the electric charge is zero and L (F) tends to a finite limit as F. The properties and examples of such solutions, which include magnetic black holes and solitonlike objects (monopoles), are discussed. Magnetic solutions are compared with their electric counterparts. A duality between solutions of different theories specified in two alternative formulations of NED (called the FP duality) is used as a tool for this comparison.