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

Abstract

The Dirac lagrangian is minimally coupled to the most general R +T + T2-type lagrangian in (1+2)-dimensions. The field equations are obtained from the total lagrangian by a variational principle. The space-time torsion is calculated algebraically in terms of the Dirac condensate plus coupling coefficients. A family of circularly symmetric rotating exact solutions which is asymptotically AdS3 is obtained. Finally BTZ-like solutions are discussed.