General relativity in a (2 + 1)-dimensional space-time |
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Authors: | J. Richard Gott III Mark Alpert |
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Affiliation: | (1) Department of Astrophysical Sciences, Princeton University, USA |
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Abstract: | General relativity is formulated for a (2+1)-dimensional space-time. Solutions to the vacuum field equations are locally flat. There are no gravitational waves and no Newtonian attraction between masses. The geometry around a point mass is a cone (locally flat) where the angle deficit at the apex is proportional to the mass. A uniform density planet has a spherical cap interior and a conical exterior solution. A convex polyhedron represents a closed universe with point masses at its vertices and approximates a static spherical universe of uniform density dust. |
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