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

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 three-dimensional anti-de Sitter is obtained. Finally, Banados-Teitelboim- Zanelli-like solutions are discussed. © 2012 American Physical Society