Towards complete integrability of two dimensional Poincaré gauge gravity

E. W. Mielke, F. Gronwald, Y. N. Obukhov, R. Tresguerres, F. W. Hehl

Published 1993-04-10Version 1

It is shown that gravity on the line can be described by the two dimensional (2D) Hilbert-Einstein Lagrangian supplemented by a kinetic term for the coframe and a translational {\it boundary} term. The resulting model is equivalent to a Yang-Mills theory of local {\it translations} and frozen Lorentz gauge degrees. We will show that this restricted Poincar\'e gauge model in 2 dimensions is completely integrable. {\it Exact} wave, charged black hole, and `dilaton' solutions are then readily found. In vacuum, the integrability of the {\it general} 2D Poincar\'e gauge theory is formally proved along the same line of reasoning.