General relativity in a (2 + 1)-dimensional space-time
- 381 Downloads
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.
KeywordsDust General Relativity Field Equation Differential Geometry Gravitational Wave
Unable to display preview. Download preview PDF.
- 1.Abbott, E. A. (1884).Flatland, sixth ed., with introduction by Banesh Hoffman, Dover, New York, 1952.Google Scholar
- 2.Dewdney, A. (1980). Sci.Am.,243 (1), 18–31.Google Scholar
- 3.Lovelock, D. (1971).J. Math. Phys.,12, 498.Google Scholar
- 4.Weinberg, S. (1972).Gravitation and Cosmology (Wiley and Sons, New York), pp. 144, and 155.Google Scholar
- 5.Figari, R., Hoegh-Krohn, R. and Nappi, C. (1975).Commun. Math. Phys.,44, 265.Google Scholar
- 6.Gibbons, G. W., and Hawking, S. W. (1977).Phys. Rev. D,15, 2738.Google Scholar
- 7.Ellis, G.F.R., and Schmidt, B. G. (1980).Gen. Rel Grav.,11, 915.Google Scholar
- 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