Regular electrically charged structures in Nonlinear Electrodynamics coupled to General Relativity

TL;DR

This paper demonstrates the existence of regular, electrically charged, spherically symmetric solutions in nonlinear electrodynamics coupled with gravity, featuring a de Sitter core and stable photon propagation, avoiding singularities.

Contribution

It provides a new exact analytic solution with a de Sitter center, analyzing energy conditions, Lagrangian cusp issues, and photon propagation in the effective geometry.

Findings

Regular solutions have a de Sitter core with maximal energy density.

Photon world lines in the effective geometry never terminate, indicating no singularities.

A new exact solution illustrating these properties is presented.

Abstract

We address the question of existence of regular spherically symmetric electrically charged solutions in Nonlinear Electrodynamics coupled to General Relativity. Stress-energy tensor of the electromagnetic field has the algebraic structure $T_0^0=T_1^1$. In this case the Weak Energy Condition leads to the de Sitter asymptotic at approaching a regular center. In de Sitter center of an electrically charged NED structure, electric field, geometry and stress-energy tensor are regular without Maxwell limit which is replaced by de Sitter limit: energy density of a field is maximal and gives an effective cut-off on self-energy density, produced by NED coupled to gravity and related to cosmological constant $\Lambda$. Regular electric solutions satisfying WEC, suffer from one cusp in the Lagrangian ${\cal L}(F)$, which creates the problem in an effective geometry whose geodesics are world lines of NED photons. We investigate propagation of photons and show that their world lines never terminate which suggests absence of singularities in the effective geometry. To illustrate these results we present the new exact analytic spherically symmetric electric solution with the de Sitter center.