General Relativity and Gravitation

, Volume 23, Issue 6, pp 623–639 | Cite as

Exact solutions inU4 gravity. I. The ansatz for self double dual curvature

  • R. P. Wallner
Research Articles


We investigate the energy-momentum and spin field equations of gravity theory on a Riemann-Cartan space-time (including metric and torsion,U4-manifold). The structure of the rather complicated nonlinear differential equations of second order is made considerably easier to survey by decomposing curvature into its self and anti-self double dual parts. This leads to an obvious ansatz for the self double dual curvature, whereby the field equations are reduced to Einstein's equations with cosmological term. To solve the double dual ansatz, we choose proper variables adopted to its double duality, and perform a (3+1)-decomposition of exterior calculus. We examine these equations further on a Kerr background with cosmological constant for the Riemannian geometry.


Differential Equation Exact Solution Field Equation Cosmological Constant Differential Geometry 
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  1. 1.
    Schouten, J. A. (1954).Ricci-Calculus (Springer-Verlag, Berlin).Google Scholar
  2. 2.
    Bishop, R. L., Crittenden, R. J. (1964).Geometry of Manifolds (Academic, New York).Google Scholar
  3. 3.
    Wallner, R. P. (1982).Acta Phys. Austr.,54, 165.Google Scholar
  4. 4.
    Wallner, R. P. (1980).Gen. Rel. Grav.,12, 719.Google Scholar
  5. 5.
    Kramer, D., Stephani, H., MacCallum, M., and Herlt, B. (1980).Exact Solutions of Einstein's Field Equations (Cambridge University Press, Cambridge).Google Scholar
  6. 6.
    Wallner, R. P. (1987). “Forms in Field Theory”. Lectures given at the Institute of Theoretical Physics, University of Cologne.Google Scholar
  7. 7.
    Wallner, R. P. (1982). Ph.D. thesis, University of Vienna.Google Scholar
  8. 8.
    Mielke, E. W., and Wallner, R. P. (1988).Nuovo Cimento,101B, 607;102B, 555(E).Google Scholar
  9. 9.
    Wallner, R. P. (1985).Gen. Rel. Grav.,17, 1081.Google Scholar
  10. 10.
    Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973).Gravitation (W. H. Freeman, San Francisco).Google Scholar
  11. 11.
    Hobert, S. (1989). Diploma thesis, University of Cologne.Google Scholar
  12. 12.
    Wallner, R. P. (1990). “On Exact Solutions inU 4-Gravity. II. The General Case”, in preparation.Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • R. P. Wallner
    • 1
  1. 1.Institute for Theoretical PhysicsUniversity of CologneKöln 41Germany

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