Towards complete integrability of two dimensional Poincar\'e gauge gravity
High Energy Physics - Theory
2009-10-22 v1 General Relativity and Quantum Cosmology
Abstract
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.
Cite
@article{arxiv.hep-th/9304043,
title = {Towards complete integrability of two dimensional Poincar\'e gauge gravity},
author = {E. W. Mielke and F. Gronwald and Y. N. Obukhov and R. Tresguerres and F. W. Hehl},
journal= {arXiv preprint arXiv:hep-th/9304043},
year = {2009}
}
Comments
35 pages, report Cologne-thp-1993-H6