General Relativity and Gravitation

, Volume 13, Issue 9, pp 817–828 | Cite as

Necessary and sufficient conditions for trivial solutions in supergravity

  • P. C. Aichelburg
  • H. K. Urbantke
Research Articles

Abstract

We determine the conditions necessary for a solution of the supergravity field equations with infinitesimal spin-3/2 field to be a pure gauge transformation of an Einstein vacuum field. The analysis depends on the Petrov classification of the curvature tensor and uses two-component spinor calculus. For general type I, the type II, and typeD, the necessary conditions found are also shown to be sufficient, and the explicit form of the gauge transformation can be given.

Keywords

Explicit Form Field Equation Differential Geometry Gauge Transformation General Type 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Freedman, D. Z., van Nieuwanhuizen, P., and Ferrara, S. (1976).Phys. Rev. D,13, 3214.Google Scholar
  2. 2.
    Deser, S., and Zumino, B. (1976).Phys. Lett.,62B, 335.Google Scholar
  3. 3.
    Aichelburg, P. C., and Dereli, T. (1978).Phys. Rev. D,18, 1754.Google Scholar
  4. 4.
    Cordero, P., and Teitelboim, C. (1978).Phys. Lett.,78B, 80.Google Scholar
  5. 5.
    Aichelburg, P. C. (1980).Phys. Lett.,91B, 382.Google Scholar
  6. 6.
    Penrose, R. (1960).Ann. Phys. (N.Y.),10, 171.Google Scholar
  7. 7.
    Pirani, F. A. E. (1965). InGeneral Relativity, Brandeis Summer Institute, ed. S. Deser (Prentice-Hall, Englewood Cliffs, New Jersey).Google Scholar
  8. 8.
    O'Raifeartaigh, L. (1975). “Lecture Notes on Supersymmetry,” Communication of the Dublin Institute for Advanced Studies, Ser. A, No. 22.Google Scholar
  9. 9.
    Urrutia, I. F. (1979).Phys. Lett.,89B, 52.Google Scholar
  10. 10.
    Güven, R. (1980).Phys. Rev. D22, 2327.Google Scholar
  11. 11.
    Aichelburg, P. C., and Güven, R. (1981). “Can Charged Black Holes have a Superhair?” Vienna Univ. preprint UWThPh-81-10; to appear inPhys. Rev. D. Google Scholar

Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • P. C. Aichelburg
    • 1
  • H. K. Urbantke
    • 1
  1. 1.Institut für Theoretische PhysikUniversität WienDeutschland

Personalised recommendations