Zel'dovich states with very small mass and charge in nonlinear electrodynamics coupled to gravity

TL;DR

This paper demonstrates the existence of weakly singular, finite-mass configurations in nonlinear electrodynamics coupled with gravity, resembling classical elementary particles with small charge and mass concentrated in a finite core.

Contribution

It introduces a new class of weakly singular solutions in nonlinear electrodynamics coupled to gravity with finite mass and small charge, resembling elementary particles.

Findings

Finite proper mass despite energy density divergences

Charge and mass can be made arbitrarily small

Configurations have a finite core with almost zero surface area

Abstract

It is shown that in non-linear electrodynamics (in particular, Born-Infeld one) in the framework of general relativity there exist "weakly singular" configurations such that (i) the proper mass M is finite in spite of divergences of the energy density, (ii) the electric charge q and Schwarzschild mass m ~ q can be made as small as one likes, (iv) all field and energy distributions are concentrated in the core region. This region has an almost zero surface area but a finite longitudinal size L=2M. Such configurations can be viewed as a new version of a classical analogue of an elementary particle.