Zel'dovich states with very small mass and charge in nonlinear electrodynamics coupled to gravity
(1) Astronomical Institute of Kharkov V.N. Karazin National University, 35 Sumskaya St., Kharkov, 61022, Ukraine
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 = 2M. Such configurations can be viewed as a new version of a classical analogue of an elementary particle.
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