Bertotti-Robinson and Bonnor-Melvin universes in nonlinear electrodynamics

We review the status of Birkhoff's theorem in the presence of nonlinear electrodynamics (NLE) - extending the analysis to the case without asymptotic flatness. This leads to the Bertotti-Robinson-type (direct product) geometry with generally unequal radii for its $AdS_{2}$ and $S_{2}$ factors, determined by a given NLE model. As can be expected, such a geometry can also be recovered from a near-horizon limit of the corresponding extremal NLE charged black hole (if it exists). These extremal black holes are shown to be linearly stable for specific NLE models, unlike in the Maxwell-$\Lambda$ case where unequal radii also arise in near-horizon geometry. Regular particle-like models are constructed by replacing the interior of these black holes with corresponding Bertotti-Robinson-type geometry. We also revisit the NLE generalization of the Bonnor-Melvin universe, describing a regular axisymmetric configuration of magnetic field lines in gravito-magnetic equilibrium. Explicit examples are derived for the Maxwell, Born-Infeld, RegMax, and Frolov-Hayward theories of electrodynamics.