Nonlinear electrodynamics and self-gravitating particle-like configurations

In the framework of Einstein's general relativity theory, the authors study regular static spherically symmetric solutions for the gravitational field coupled to a self-interacting matter represented by the vector field A_{mu}. They define the particle-like solutions (PLS) as stationary configurations with everywhere regular matter and metric which has an asymptotic Schwarzschild limit. The matter Lagrangian L is assumed to be an arbitrary function of four invariants, I=-F_{munu}F^{munu}, K={}^{*}F_{munu}F^{munu}, J=A_{mu}A^{mu}, widetilde{I}=F_{munu} F^{mulambda}A^{nu}A_{lambda}, where F_{munu}=partial_{mu}A_{nu}- partial_{nu}A_{mu} and ^{*} is the Hodge dual. The authors show that no PLS exists for any gauge-invariant nonlinear Lagrangians L=L(I,K), and no PLS with a nontrivial magnetic charge exists for an arbitrary Lagrangian L=L(I,K,J,widetilde{I}). The study of PLS with a regular center and a trivial magnetic charge reveals instability of such configurations (with respect to spherically symmetric perturbations) for all gauge non-invariant Lagrangians L=L(I,K,J,widetilde{I}). The existence and stability of the wormhole type PLS for certain Lagrangians is demonstrated.