Lattice Universes in 2+1-dimensional gravity
Dieter R. Brill
TL;DR
This paper derives exact solutions for lattice universes in 2+1-dimensional Einstein gravity with negative cosmological constant, revealing analogies between flat and curved cases and unifying point particles and black holes.
Contribution
It introduces a mapping that preserves geodesic properties, enabling unified treatment of particles and black holes in lattice universes with different curvatures.
Findings
Exact solutions for lattice universes in 2+1 dimensions
Established analogies between flat and curved cases
Unified treatment of particles and black holes
Abstract
Lattice universes are spatially closed space-times 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.
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