The Dirac field and the possible origin of gravity

TL;DR

This paper proposes that the Dirac field's spin connection, including an axial field, can explain the origin of gravity and the formation of compact objects, linking quantum fields to spacetime curvature.

Contribution

It introduces a mechanism where the axial field from the Dirac spin connection leads to stable compact objects and derives Einstein's equations from this framework.

Findings

The axial field causes auto-localization of the Dirac field into compact objects.

Stability conditions of these objects lead to Einstein's field equations.

Long-distance effects of the axial field mimic Newtonian gravity.

Abstract

The spin connections of the Dirac field have three ingredients that are connected with the Ricci rotations, the Maxwell field, and an axial field which minimally interacts with the axial current. I demonstrate that the axial field provides an effective mechanism of auto-localization of the Dirac field into compact objects. The condition that these objects are stable (the energy-momentum is self-adjoint) leads to Einstein's field equations. The Dirac field with its spin connection seem to be a natural material carrier of the space-time continuum in which compact objects are moving along geodesic lines. The long distance effect of the axial field is indistinguishable from Newton's gravity, which reveals the microscopic nature of gravity and the origin of the gravitational mass.