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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

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.

Keywords

Dust General Relativity Field Equation Differential Geometry Gravitational Wave 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Abbott, E. A. (1884).Flatland, sixth ed., with introduction by Banesh Hoffman, Dover, New York, 1952.Google Scholar
  2. 2.
    Dewdney, A. (1980). Sci.Am.,243 (1), 18–31.Google Scholar
  3. 3.
    Lovelock, D. (1971).J. Math. Phys.,12, 498.Google Scholar
  4. 4.
    Weinberg, S. (1972).Gravitation and Cosmology (Wiley and Sons, New York), pp. 144, and 155.Google Scholar
  5. 5.
    Figari, R., Hoegh-Krohn, R. and Nappi, C. (1975).Commun. Math. Phys.,44, 265.Google Scholar
  6. 6.
    Gibbons, G. W., and Hawking, S. W. (1977).Phys. Rev. D,15, 2738.Google Scholar
  7. 7.
    Ellis, G.F.R., and Schmidt, B. G. (1980).Gen. Rel Grav.,11, 915.Google Scholar
  8. 8.
    Hawking, S. W., and Ellis, G.F.R. (1973).The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge), pp. 162–163.Google Scholar

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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