Einstein's theory in a three-dimensional spacetime

As a preparation for studying quantum models, we analyze unusual features of Einstein's theory of gravitation in a three-dimensional spacetime. In three dimensions, matter curves spacetime only locally and the gravitational field has no dynamical degrees of freedom. The standard correspondence of Einstein's theory with Newton's theory breaks down. A dust distribution moves without any geodesic deviation between the particles. The cosmological models and relativistic stars behave in a qualitatively different way from their Newtonian counterparts. These features are important for the correct understanding of mini-superspace models.