Spacetime symmetry and mass of a lepton

Abstract

The Einstein equations admit the class of regular solutions generated by stress-energy tensors representing vacuum with the reduced symmetry as compared with the maximally symmetric de Sitter vacuum. In the spherically symmetric case they describe, in particular, gravitational vacuum solitons with the de Sitter center whose mass is related to the de Sitter vacuum trapped inside and smooth breaking of spacetime symmetry from the de Sitter group in the origin to the Poincaré group at infinity. In nonlinear electrodynamics coupled to gravity and satisfying the weak energy condition, an electrovacuum soliton has an obligatory de Sitter center where the electric field vanishes while the energy density of the electromagnetic vacuum achieves its maximal finite value which gives a natural cutoff on self-energy. By the Gürses–Gürsey algorithm based on the Trautman–Newman technique it is transformed into a spinning electrovacuum soliton asymptotically Kerr–Newman for a distant observer, with the gyromagnetic ratio g = 2. The de Sitter center becomes the de Sitter equatorial disk which has properties of a perfect conductor and ideal diamagnetic. The interior de Sitter vacuum disk displays superconducting behavior within a single spinning particle. This behavior is generic for the class of spinning electrovacuum solitons. The de Sitter vacuum supplies a particle with the finite electromagnetic mass related to breaking of spacetime symmetry.