Nonlinear electrodynamics, regular black holes and wormholes

Understand

We consider spherically symmetric configurations in general relativity, supported by nonlinear electromagnetic fields with gauge-invariant Lagrangians depending on the single invariant $f = F_{\mu\nu} F^{\mu\nu}$.

• Static black hole and solitonic solutions are briefly described, both with only an electric or magnetic charge and with both nonzero charges (the dyonic ones).
• It is stressed that only pure magnetic solutions can be completely nonsingular.
• For dyonic systems, apart from a general scheme of obtaining solutions in quadratures for an arbitrary Lagrangian function $L(f)$, an analytic solution is found for the truncated Born-Infeld theory (depending on the invariant $f$ only).