Einstein–Cartan–Heisenberg theory of gravity with dynamical torsion

Abstract

On the basis of an algebraic relation between torsion and a classical spinor field a new interpretation of Einstein–Cartan gravity interacting with a classical spinor field is proposed. In this approach the spinor field becomes an auxiliary field and the dynamical equation for this field (the Heisenberg equation) is a dynamical, gravitational equation for torsion. The simplest version of this theory is examined where the metric degrees of freedom are frozen and only torsion plays a role. A spherically symmetric solution of this theory is examined. This solution can be interpreted, in the spirit of Wheeler's ideas of “charge without charge” and “mass without mass”, as a geometrical model for an uncharged particle with spin (“spin without spin”).