General Relativity and Gravitation

, Volume 16, Issue 3, pp 243–247 | Cite as

General relativity in a (2 + 1)-dimensional space-time

  • J. Richard GottIII
  • Mark Alpert
Research Articles


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.


Dust General Relativity Field Equation Differential Geometry Gravitational Wave 
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Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • J. Richard GottIII
    • 1
  • Mark Alpert
    • 1
  1. 1.Department of Astrophysical SciencesPrinceton UniversityUSA

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