Internal Structure of Wormholes—Geometric Images of Charged Particles in General Relativity

Abstract

Using an exact solution of the Einstein-Maxwell equations for a free electric field and dustlike matter, we study the internal structure of the wormhole-type space with two nonclosing static throats opening to two parallel vacuum spaces or to a single space. This geometry is considered as a particleantiparticle pair with two electric charges of opposite signs, ±e, and the rest mass m₀ (the total mass of the particle’s gravitational internal world) specified on the throats. These fundamental constants emerge while solving the Cauchy problem in the form of first integrals. Using the energy conservation law, we consider an irremovable rotation of the internal structure, and the projection of the corresponding angular momentum onto the rotation axis is identified with the z-projection of the charged particle’s spin. The Gaussian 2D curvature radius of the throat is identified with the particle’s radius; the z-projection of the magnetic moment and the gyromagnetic ratio have been found. The plausibility of this gravitational model is confirmed by the fact that the proton and electron spins, s = 1/2, turn out to be independent of the particle radius and of the relativistic mass of the rotating throat; also, there is a coincidence with great accuracy between the proton radius value calculated in this model, 0.8412 × 10⁻¹³ cm, and the one obtained in measurements of the Lamb shift in muonic hydrogen, 0.8409× 10⁻¹³ cm. The electron turns out to be also a structured particle, with a radius of 3.8617 × 10⁻¹¹ cm.