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.
Highlights
The Abraham-Lorentz concept of a finite size electron which makes the total energy of the electron Coulomb field finite [1] encountered the problem of preventing the electron from flying apart under the Coulomb repulsion
Theories based on assumptions about the charge distribution were compelled to introduce cohesive forces of nonelectromagnetic origin (Poincarestress), testifying that replacing a point charge with an extended one is impossible within the Maxwell electrodynamics since it demands introducing cohesive nonelectromagnetic forces [2]
We have proved the existence of spherically symmetric electrically charged structures with the regular center in nonlinear electrodynamics coupled to gravity
Summary
The Abraham-Lorentz concept of a finite size electron which makes the total energy of the electron Coulomb field finite [1] encountered the problem of preventing the electron from flying apart under the Coulomb repulsion. The mass of an object is the finite positive electromagnetic mass generically related to interior de Sitter vacuum and breaking of space-time symmetry from the de Sitter group in the origin [29, 34, 36, 42, 43] The price for such a promising road is unavoidable branching of a spherically symmetric Lagrangian for regular electrically charged NED-GR configurations. The generic feature of any regular electromagnetic spherically symmetric structure satisfying the weak energy condition is the de Sitter center where Lagrangian takes the value L = 2ρ(0) as r → 0 [36]. Appendix contains the detailed consideration concerning definition of the stress-energy tensor for an electromagnetic field
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
