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

*O.B. Zaslavskii*^{1}

(1) Astronomical Institute of Kharkov V.N. Karazin National University, 35 Sumskaya St., Kharkov, 61022, Ukraine

### Abstract

It is shown that, in nonlinear (in particular, Born-Infeld) electrodynamics in the framework of general relativity, there exist "weakly singular" configurations such that (i) the proper mass *M* is finite despite divergences of the energy density, (ii) the electric charge *q* and the Schwarzschild mass *m* ~ *q* can be made as small as one likes, and (iii) 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* = 2*M*. Such configurations can be viewed as a new version of a classical analogue of an elementary particle.

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