2+1 dimensional solution of Einstein Cartan equations

In this work a static solution of Einstein-Cartan (EC) equations in 2+1 dimensional space-time is given by considering classical spin-1/2 field as external source for torsion of the space-time. Here, the torsion tensor is obtained from metricity condition for the connection and the static spinor field is determined as the solution of Dirac equation in 2+1 spacetime with non-zero cosmological constant and torsion. The torsion itself is considered as a non-dynamical field.