Lattice universes in (2+1)-dimensional gravity

Lattice universes are spatially closed spacetimes of spherical topology in the large, containing masses or black holes arranged in the symmetry of a regular polygon or polytope. Exact solutions for such spacetimes are found in 2 + 1 dimensions for Einstein gravity with a non-positive cosmological constant. By means of a mapping that preserves the essential nature of geodesics, we establish analogies between the flat and the negative curvature cases. This map also allows treatment of point particles and black holes on a similar footing.