New solutions in pure gravity with degenerate tetrads
  In first order formulation of pure gravity, we find a new class of solutions to the equations of motion represented by degenerate four-geometries. These configurations are described by non- invertible tetrads with two zero eigenvalues and admit non-vanishing torsion. The homogeneous ones among these infinitely many degenerate solutions admit a geometric classification provided by the three fundamental geometries that a closed two-surface can accomodate, namely, E^2 , S^2 and H^2. 
Romesh K. Kaul and Sandipan Sengupta
gr-qc hep-th