Gravitational model of the internal structure of proton, electron and neutron in general relativity theory

In this paper, from the point of view of general relativity, obstacles that prevent the use of gravitational and electromagnetic fields to create a model of elementary particles and atomic nuclei are discussed: the vanishing smallness of the gravitational interaction compared to the electromagnetic at microworld lengths; incomplete geometrizability of the electromagnetic field itself; its long-range nature compared with short-range nuclear forces; Coulomb repulsion of like-charged protons in the nucleus, which, it would seem natural, can not focus the nucleons and keep the nuclei in a compact state - all these phenomena receive a different interpretation in GTR, primarily because of the universality of the gravitational interaction, which plays the main role at any length - at microworld and macroworld. Based on the exact solution of the Einstein - Maxwell equations for a centrally symmetric free electromagnetic field and a dusty substance, gravitational models of a proton, electron and neutron are proposed in the form of pulsating unclosed wormholes with two static throats - oppositely charged electric charges that extend into two parallel asymptotically flat vacuum spaces. The neutron is represented as a double wormhole. The radii are calculated: proton - 0.8412 fm, electron - 386.17 fm and neutron - 1.0049 fm. The proton radius with an accuracy of 0.04% coincided with its experimental value of 0.8409 fm, obtained by measuring the Lamb shift on muonic hydrogen. The electron radius was 459 times the proton radius. But when a proton, scattered by an electron, penetrates into the center of the electron's wormhole with its wormhole, the radius of curvature of the neck of the latter decreases to the above neutron radius value due to the transfer of part of the relativistic energy of proton rotation and the energy of curved space, i.e. gravitational field.

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