2 research outputs found
Towards complete integrability of two dimensional Poincar\'e gauge gravity
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.Comment: 35 pages, report Cologne-thp-1993-H
Geometric Interpretation and Classification of Global Solutions in Generalized Dilaton Gravity
Two dimensional gravity with torsion is proved to be equivalent to special
types of generalized 2d dilaton gravity. E.g. in one version, the dilaton field
is shown to be expressible by the extra scalar curvature, constructed for an
independent Lorentz connection corresponding to a nontrivial torsion.
Elimination of that dilaton field yields an equivalent torsionless theory,
nonpolynomial in curvature. These theories, although locally equivalent exhibit
quite different global properties of the general solution. We discuss the
example of a (torsionless) dilaton theory equivalent to the --model.
Each global solution of this model is shown to split into a set of global
solutions of generalized dilaton gravity. In contrast to the theory with
torsion the equivalent dilaton one exhibits solutions which are asymptotically
flat in special ranges of the parameters. In the simplest case of ordinary
dilaton gravity we clarify the well known problem of removing the Schwarzschild
singularity by a field redefinition.Comment: 21 pages, 6 Postscript figure