General Relativity and Gravitation

, Volume 9, Issue 11, pp 987–997 | Cite as

Twistors and linearized Einstein theory on plane-fronted impulsive wave backgrounds

  • G. E. Curtis
Research Article

Abstract

The spinor form of linearized gravitation on a curved vacuum background is obtained from the Bianchi identities. There are no Buchdahl constraints to be satisfied, and for a flat background the approach reduces to the usual massless spin 2 theory. The equations are specialized to the plane-fronted impulsive gravitational wave backgrounds which include the ultrarelativistic limit of a moving black hole. Given a solution of the resulting system, it is possible to construct the metric perturbations up to gauge terms. It is shown that this linearized scheme is equivalent to the proposed twistor Hamiltonian formalism. As an example, colliding plane impulsive waves are considered, and the model compares well with the known exact solution. A discussion is given of the application of these methods to ultrarelativistic black-hole encounters.

Keywords

Black Hole Exact Solution Differential Geometry Gravitational Wave Bianchi Identity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Pirani, F. A. E. (1965). InBrandeis Lectures on General Relativity. (Prentice-Hall, New York).Google Scholar
  2. 2.
    Penrose, R. (1968).Int. J. Theor.Phys.,1, 61–99.Google Scholar
  3. 3.
    Penrose, R. (1972). InGeneral Relativity, Papers in Honour of J. L. Synge, edited by L. O'Raifeartaigh (Clarendon Press, Oxford).Google Scholar
  4. 4.
    Penrose, R. (1968). InBattelle Rencontres, edited by C. M. DeWitt and J. A. Wheeler (Benjamin, New York).Google Scholar
  5. 5.
    Penrose, R., and MacCallum, M. A. H. (1973).Phys. Rep.,6C, 243–315.Google Scholar
  6. 6.
    Aichelburg, P. C., and Sexl, R. U. (1971).Gen. Rel. Grav.,2, 303–312.Google Scholar
  7. 7.
    Curtis, G. E. (1975).Twistor Theory and the Collision of Plane-Fronted Impulsive Gravitational Waves. D.Phil. Thesis, Oxford University.Google Scholar
  8. 8.
    Newman, E. T., and Penrose, R. (1968).Proc. Roy. Soc. A,305, 175–204.Google Scholar
  9. 9.
    Penrose, R. (1963). In P. G. Bergmann's A.R.L. Tech. Docum. Rep. no. 63–56,Quantization of Generally Covariant Field Theories.Google Scholar
  10. 10.
    Stewart, J. M., and Walker, M. (1974).Proc. Roy. Soc. A,341, 49–74.Google Scholar
  11. 11.
    Newman, E. T., and Penrose, R. (1962).J. Math. Phys.,3, 566–578.Google Scholar
  12. 12.
    Bell, P., and Szekeres, P. (1973).Int. J. Theor. Phys.,6, 111–121.Google Scholar
  13. 13.
    Gel'fand, I. M., and Shilov, G. E. (1964).Generalized Functions, vol. 1. (Academic Press, New York).Google Scholar
  14. 14.
    Penrose, R. (1975). InQuantum Gravity, edited by C. J. Isham, R. Penrose, and D. W. Sciama (University Press, Oxford).Google Scholar
  15. 15.
    Khan, K. A., and Penrose, R. (1971).Nature,229, 185–186.Google Scholar
  16. 16.
    Szekeres, P. (1972).J. Math. Phys.,13, 286–294.Google Scholar
  17. 17.
    Erdélyi, A., Magnus, W., Oberhettinger, F., and Tricomi, F. G. (1953).Higher Transcendental functions, vol. 1 (McGraw-Hill, New York, Toronto, London).Google Scholar

Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • G. E. Curtis
    • 1
  1. 1.Department of MathematicsUniversity of YorkHeslingtonEngland

Personalised recommendations