Exact vacuum solution of a (1+2)-dimensional Poincare gauge theory:: BTZ solution with torsion -: art. no. 124016

In the framework of (1+2)-dimensional Poincare gauge gravity, we start from the Lagrangian of the Mielke-Baekler model that depends on torsion and curvature and includes translational and Lorentzian Chern-Simons terms. We find a general stationary circularly symmetric vacuum solution of the field equations. We determine the properties of this solution, in particular its mass and its angular momentum. For vanishing torsion, we recover the BTZ solution. We also derive the general conformally flat vacuum solution with torsion. In this framework, we discuss Cartan's (3-dimensional) spiral staircase and find that it is not only a special case of our new vacuum solution, but can alternatively be understood as a solution of the 3-dimensional Einstein-Cartan theory with matter of constant pressure and constant torque.