General Relativity and Gravitation

, Volume 19, Issue 8, pp 827–839 | Cite as

Gravitational field with toroidal topology

  • B. W. Stewart
  • Louis Witten
  • Demetrios Papadopoulos
Research Articles


The Weyl formalism for static, axially symmetric solutions to Einstein's equations is employed to examine solutions of Einstein's equations with toroidal topology. We investigate a particular family of solutions that contain the Schwarzschild, Curzon, Bach-Weyl, andγ metric (also known as the Zipoy-Voorhees metric) as special cases.


Differential Geometry Gravitational Field Symmetric Solution Weyl Formalism 
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  1. 1.
    Curzon, H. E. J. (1924).Proc. London Math. Soc.,23, 477.Google Scholar
  2. 2.
    Papadopoulos, Stewart, B., and Witten, L. (1981).Phys. Rev. D,24, 320.Google Scholar
  3. 3.
    Papadopoulos, D., and Witten, L. (1982).Phys. Rev. D,25, 1465.Google Scholar
  4. 4.
    Hawking, S. W. (1972).Commun. Math. Phys.,25, 152.Google Scholar
  5. 5.
    Hawking, S. W., and Ellis, B. F. R. (1973).The Large Scale Structure of Space-Time (Cambridge University Press, Massachusetts).Google Scholar
  6. 6.
    Thorne, K. S. (1975).J. Math. Phys.,16, 1860.Google Scholar
  7. 7.
    Bach, R., and Weyl, H. (1922).Math. Z.,13, 134.Google Scholar
  8. 8.
    Weyl, H. (1917).Ann. Phys.,54, 117.Google Scholar
  9. 9.
    Synge, J. L. (1960).Relativity: The General Theory (North-Holland, Amsterdam), 313–314.Google Scholar
  10. 10.
    Ernst, F. J. (1976).J. Math. Phys.,17, 1091.Google Scholar
  11. 11.
    Scott, S. M., and Szekeres, P. (1986).Gen. Rel. Grav.,18, 557.Google Scholar
  12. 12.
    Scott, S. M., and Szekeres, P. (1986).Gen. Rel. Grav.,18, 571.Google Scholar
  13. 13.
    Stewart, B. W., Papadopoulos, D., Witten, L., Berezdivin, R., and Herrera, L. (1982).Gen. Rel. Grav.,14, 97.Google Scholar
  14. 14.
    McCrea, J. D. (1976).J. Phys. A.,9, 697.Google Scholar

Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • B. W. Stewart
    • 1
  • Louis Witten
    • 2
  • Demetrios Papadopoulos
    • 3
  1. 1.Department of Mechanical and Industrial EngineeringUniversity of CincinnatiCincinnati
  2. 2.Department of PhysicsUniversity of CincinnatiCincinnati
  3. 3.Department of AstronomyUniversity of ThessalonikiThessalonikiGreece

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