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

Abstract

We address the question of correct description of Lagrange dynamics for regular electrically charged structures in nonlinear electrodynamics coupled to gravity. Regular spherically symmetric configuration satisfying the weak energy condition has obligatory de Sitter center in which the electric field vanishes while the energy density of electromagnetic vacuum achieves its maximal value. The Maxwell weak field limitLF→Fasr→∞requires vanishing electric field at infinity. A field invariantFevolves between two minus zero in the center and at infinity which makes a LagrangianLFwith nonequal asymptotic limits inevitably branching. We formulate the appropriate nonuniform variational problem including the proper boundary conditions and present the example of the spherically symmetric Lagrangian describing electrically charged structure with the regular center.

Basic Generic Properties of Regular Rotating Black Holes and Solitons

“…This problem is solved by the correct description of the Lagrange dynamics for regular electrically charged structures by the nonuniform variational problem with proper internal boundary conditions on the surface where the invariant has the minimum [38]. The nonuniform variational problem is described by the action…”

Regular rotating electrically charged structures in nonlinear electrodynamics minimally coupled to gravity

“…22 The question of correct description of NED-GR regular electrically charged structures by the Lagrange dynamics is considered in Ref. 23. Regular spherical solutions satisfying (3) are described by the metric…”

“…In the axially symmetric case non-zero field components are F 01 , F 02 , F 13 , F 23 . In geometry (9) they are related by F 31 = a sin 2 θF 10 ; aF 23 = (r 2 + a 2 )F 02 .…”

Mass, Spacetime Symmetry, de Sitter Vacuum, and the Higgs Mechanism

“…where R is the scalar curvature, and F µν = ∂ µ A ν − ∂ ν A µ is the electromagnetic field. The gauge-invariant electromagnetic Lagrangian L(F) is an arbitrary function of the field invariant F. The Lagrangian L(F) and its derivative L F = dL(F)/dF must have the Maxwell limits in the weak field region (details and subtleties of the Lagrange dynamics for regular electrically charged structures have been analyzed in [68]). The source-free dynamic field equations for electromagnetic field read…”