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Lattice universes in (2 + 1)-dimensional gravity

Dieter R Brill

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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.


PACS

04.20.Jb Exact solutions

04.70.Bw Classical black holes

98.80.Es Observational cosmology (including Hubble constant, distance scale, cosmological constant, early Universe, etc)

MSC

83C57 Black holes

83C15 Exact solutions

83F05 Cosmology

Subjects

Gravitation and cosmology

Astrophysics and astroparticles

Dates

Issue 3 (7 February 2004)

Received 9 September 2003

Published 9 January 2004



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