Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-06-03
Phys.Rev.D63:044005,2001
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
6 pages, Latex2e. One more theorem, some comments and two references have been added. Final journal version
Scientific paper
10.1103/PhysRevD.63.044005
It is shown that general relativity coupled to nonlinear electrodynamics (NED) with the Lagrangian $L(F)$, $F = F_mn F^mn$ having a correct weak field limit, leads to nontrivial static, 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 $F \to \infty$. Properties and examples of such solutions, which include magnetic black holes and soliton-like 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 $FP$ duality) is used as a tool for this comparison.
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