Regular magnetic black holes and monopoles from nonlinear electrodynamics

It is shown that general relativity coupled to nonlinear electrodynamics (NED) with the Lagrangian $L(F),$ ${F=F}_{\ensuremath{\mu}\ensuremath{\nu}}{F}^{\ensuremath{\mu}\ensuremath{\nu}}$ 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 $\stackrel{\ensuremath{\rightarrow}}{F}\ensuremath{\infty}.$ 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 $\mathrm{FP}$ duality) is used as a tool for this comparison.

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