Geometry of a centrosymmetric electric charge

Abstract

The gravitational description given for an electric charge qn the basis of exact solution of the Einstein-Maxwell equations eliminates Coulomb divergence. The internal pulsating semiconfined world formed by neutral dust is smoothly joined with parallel Reissner-Nordstrem vacuum worlds via two static bottlenecks. The charge, rest mass, and electric field are expressed in terms of the space curvatures. The internal and external parameters of the maximon, electron, and the universe form a power series.

Throats as macroparticles on the basis of spherically symmetric solutions to the Einstein-Maxwell equations

“…(22), for positive values of the 4-curvature of radial spheres it is necessary that R > R f . This condition can always be satisfied in the solutions under study [7], which indicates that in such worlds, formed by dust and electromagnetic fields, the Coulomb divergence, i.e., the singularity R = 0 in the field of a point charge, which is present in Minkowski space, is removed. However, in the Tolman and Friedmann worlds [1], to which our solution passes over if the electromagnetic field is absent (R f = 0), as well as in the Reissner-Nordstr¨om space describing a vacuum world of a point charge e with mass m 0 , to which our solution passes over in the absence of matter (F = 0), this singularity is present.…”

“…The idea that the gravitational interaction, i.e., space-time curvature can be significant either in the mega-world at the scale of the Universe or in the micro-world, at critically small lengths (at the Planck scale), can be put to doubt due to the universal nature of gravity: any matter possessing stress-energy curves the space-time, and this curvature is equivalent to a gravitational field [1][2][3][4][5][6][7].…”

“…To set up the problem and to obtain the simplest results, in this paper we will present and use the solutions of the Einstein-Maxwell equations for a spherically symmetric space-time formed by neutral dustlike (without pressure and temperature) matter, the electromagnetic field and its sources-electric charges distributed with a certain density in a compact domain [3,6,7].…”

“…Moreover, GR is a geometrizing theory: all physical quantities, after solving the equations, can be expressed in terms of the space-time curvatures, i.e., the Riemann-Christoffel tensor R μνλρ and the metric tensor g μν [7]. For example, the energy densities of dust and the electromagnetic field, ε s and ε f , the total mass m(r), and the charge Q(r):…”

“…If one glues this inner world with the outer Reissner-Nordstr¨om vacuum world through these static throats, then, from the viewpoint of external observers, one throat will be perceived as, say, an electron (Q 0 < 0), and the other one as a positron (Q 0 > 0), having the rest mass m h = ε gh /c 2 , which is also a first integral of the GR equations [7].…”