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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Gott, J.R., Alpert, M. General relativity in a (2 + 1)-dimensional space-time. Gen Relat Gravit 16, 243–247 (1984). https://doi.org/10.1007/BF00762539
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DOI: https://doi.org/10.1007/BF00762539