Existence of Electrically Charged Structures with Regular Center in Nonlinear Electrodynamics Minimally Coupled to Gravity

Abstract EN

We address the question of correct description of Lagrangedynamics for regular electrically charged structures in nonlinearelectrodynamics coupled to gravity.

Regular spherically symmetricconfiguration satisfying the weak energy condition has obligatoryde Sitter center in which the electric field vanishes while theenergy density of electromagnetic vacuum achieves its maximalvalue.

The Maxwell weak field limit LF→F as r→∞ requires vanishing electric field at infinity.

A field invariant F evolves between two minus zero inthe center and at infinity which makes a Lagrangian LF with nonequal asymptotic limits inevitably branching.

Weformulate the appropriate nonuniform variational problemincluding the proper boundary conditions and present the exampleof the spherically symmetric Lagrangian describing electricallycharged structure with the regular center.