Nonsingular Dirac particles in spacetime with torsion

TL;DR

This paper demonstrates that Dirac fields in Einstein-Cartan gravity are inherently nonsingular, replacing singular structures with finite-sized particles, and suggests torsion prevents micro black hole formation at high energies.

Contribution

It shows Dirac fields cannot form singular surfaces in Einstein-Cartan gravity, replacing singularities with finite-sized particles and modifying models of the electron and black hole formation.

Findings

Dirac particles are nonsingular with a minimum size of the Cartan radius.

Torsion modifies the structure of the Dirac electron from a singular ring to a toroidal shape.

LHC cannot produce micro black holes if torsion and Einstein-Cartan theory are correct.

Abstract

We use the Papapetrou method of multipole expansion to show that a Dirac field in the Einstein-Cartan-Kibble-Sciama (ECKS) theory of gravity cannot form singular configurations concentrated on one- or two-dimensional surfaces in spacetime. Instead, such a field describes a nonsingular particle whose spatial dimension is at least on the order of its Cartan radius. In particular, torsion modifies Burinskii's model of the Dirac electron as a Kerr-Newman singular ring of the Compton size, by replacing the ring with a toroidal structure with the outer radius of the Compton size and the inner radius of the Cartan size. We conjecture that torsion produced by spin prevents the formation of singularities from matter composed of quarks and leptons. We expect that the Cartan radius of an electron, ~10^{-27} m, introduces an effective ultraviolet cutoff in quantum field theory for fermions in the ECKS spacetime. We also estimate a maximum density of matter to be on the order of the corresponding Cartan density, ~10^{51} kg m^{-3}, which gives a lower limit for black-hole masses ~10^{16} kg. This limit corresponds to energy ~10^{43} GeV which is 39 orders of magnitude larger than the maximum beam energy currently available at the LHC. Thus, if torsion exists and the ECKS theory of gravity is correct, the LHC cannot produce micro black holes.