Towards complete integrability of two dimensional Poincar\'e gauge gravity
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 boundary term. The resulting model is equivalent to a Yang-Mills theory of local translations and frozen Lorentz gauge degrees. We will show that this restricted Poincar\'e gauge model in 2 dimensions is completely integrable. Exact wave, charged black hole, and `dilaton' solutions are then readily found. In vacuum, the integrability of the general 2D Poincar\'e gauge theory is formally proved along the same line of reasoning.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.