Unified theories metrics and primordial magnetic fields in Riemann–Cartan spacetime

Abstract

Several spacetime metrics in teleparallel geometry of Einstein like unified field theory (UFT) are presented. Cosmic magnetic fields are obtained in terms of the early universe torsion and other stages of the universe. For example, in one of the metrics, integration of the 2-form torsion 0-component is written in terms of magnetic flux, from Faraday’s induced equation. These ideas were obtained from a recent paper we published [Class. Quantum Grav. (2015)] on non-stationary teleparallel metrics, where at coherent length of [Formula: see text] a magnetic field of [Formula: see text] is obtained. At early universe, a torsion of [Formula: see text] leads us to a magnetic field of the order of [Formula: see text] which is weaker than the Bierman battery effect magnetic field of the order of [Formula: see text]. Hence this new metric indicates that unifield theory metrics a la Schrödinger may be used to obtain primordial magnetic fields. Other tests of this metric led to the nowadays magnetic field of [Formula: see text] from the torsion at present universe (at the laboratory using dual maser obtained by Kostelecky et al. [Phys. Rev. Lett.]) of [Formula: see text]. Cartan torsion has been frequently associated to topological defects in crystals or in pseudo-magnetic torsional fields. In this paper, we discuss how from teleparallel gravity one may obtain a theory of electromagnetism from metrics in spacetime. Topological defects given by Letelier [Class. Quantum Grav. 12 (1995) 1133] and Tod [Class. Quantum Grav. 11(5) (1994)] metrics can also be associated with pseudo-magnetic fields. Electromagnetism is geometrized via a bimetric theory of gravity where one metric is responsible for Ampere’s law and the other by the Faraday induction equation which gives rise to dynamo equation.