Self-gravitating stringlike configurations from nonlinear electodynamics

TL;DR

This paper explores static, cylindrically symmetric solitonic string-like solutions in general relativity coupled with nonlinear electrodynamics, identifying conditions for regularity and asymptotic behavior based on field orientation and the form of the nonlinear Lagrangian.

Contribution

It provides a detailed analysis of conditions under which regular, solitonic string-like solutions can exist in nonlinear electrodynamics coupled to gravity, including explicit solutions and asymptotic behaviors.

Findings

Regular axis impossible for R-fields with nonzero electric charge.

Solitonic solutions only for purely magnetic R-fields and purely electric A-fields.

Explicit example of a solution with  = const d a0sqrt{F}.

Abstract

We consider static, cylindrically symmetric configurations in general relativity coupled to nonlinear electrodynamics (NED) with an arbitrary gauge-invariant Lagrangian of the form $L_{em}= \Phi(F)$, $F =F_{mn}F^{mn}$. We study electric and magnetic fields with three possible orientations: radial (R), longitudinal (L) and azimuthal (A), and try to find solitonic stringlike solutions, having a regular axis and a flat metric at large $r$, with a possible angular defect. Assuming the function $\Phi(F)$ to be regular at small $F$, it is shown that a regular axis is impossible in R-fields if there is a nonzero effective electric charge and in A-fields if there is a nonzero effective electric current along the axis. Solitonic solutions are only possible for purely magnetic R-fields and purely electric A-fields, in cases when $\Phi(F)$ tends to a finite limit at large $F$. For both R- and A-fields, the desired large $r$ asymptotic is only possible with a non- Maxwell behaviour of $\Phi(F)$ at small $F$. For L-fields, solutions with a regular axis are easily obtained (and can be found by quadratures) whereas a desired large $r$ asymptotic is only possible in an exceptional solution; the latter gives rise to solitonic configurations in case $\Phi(F) = \const \cdot \sqrt{F}$. We give an explicit example of such a solution.