Towards complete integrability of two dimensional Poincar\'e gauge gravity

TL;DR

This paper demonstrates that two-dimensional Poincaré gauge gravity can be fully integrated, providing exact solutions like wave and black hole configurations, and establishes the formal integrability of the general theory.

Contribution

It shows the complete integrability of 2D Poincaré gauge gravity and derives exact solutions, advancing understanding of lower-dimensional gravitational models.

Findings

Exact wave solutions found

Charged black hole solutions derived

Formal proof of integrability for general 2D Poincaré gauge theory

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.