Non-Riemannian Geometry, Born-Infeld Models and Trace Free Gravitational Equations: Mathematical and Physical Consequences

DIEGO JULIO CIRILO

Future Relativity, Gravitation, Cosmology

Nova Science Publishers, Inc.

Año: 2023; p. 135 - 183

Non-Riemannian generalization of the standard Born-Infeld (BI) Lagrangian was recently introduced and analized from a theory of gravitation with dynamical torsion field [14]. The field equations derived from the simplest proposed action lead to a trace free gravitational equation (non-riemannian analog to the trace free equation (TFE) from [1], [2], [3]) and the field equations for the torsion respectively. In this theoretical context, the fundamental constants arise all from the same geometry through geometrical invariant quantities (as from the curvature R). Important results involving generation of primordial magnetic fields and the link with leptogenesis and baryogenesis that were presented are reviewed and explained. The physically admisible matter fields can be introduced in the model via the torsion vector hµ. Such fields include some dark matter candidates such as axion, right neutrinos and Majorana and moreover, physical observables as vorticity can be included in the same way. From a new wormhole soluton in a cosmological spacetime with torsion we also show that the primordial cosmic magnetic fields can originate from hµ with the axion field (that is contained in hµ) the responsible to control the dynamics and stability of the cosmicmagnetic field and the magnetogenesis itself. The analisys of Grand Unified Theories(GUT) in the context of this model indicates that the group manifold candidates are based in SO(10), SU(5) or some exceptional groups as E(6),E (7), etc. High energy astrophysical effects, as the magnetosphere structure of compact objects is reviewed in the same new theoretical context [73]. To this end we show that the new spherically symmetric solution, obtained in this theoretical framework before, physically represents a compact object of pseudoscalar fields (for example, axion field). The axially symmetric version of the Grad-Shafranov equation (GSE) is also derived in this context, and used to describe the magnetosphere dynamics of the obtained ”axion star”.The interplay between high-energy processes and the seed magnetic field with respect to the global structure of the magnetosphere is briefly discussed.