Spinor coupling to the weak Poincare gauge theory of gravity in three dimensions

Abstract

Minimal coupling of a Dirac field to gravity with the most general non-propagating torsion is considered in (1+2)-dimensions. The field equations are obtained from a lagrangian by a variational principle. The space-time torsion is calculated algebraically in terms of a quadratic spinor condensate plus coupling coefficients. Firstly we give circularly symmetric rotating exact solutions that collapse to $AdS_3$ geometry in the absence of the Dirac condensate. Secondly we investigate a BTZ-like solution.