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Non-self-dual nonlinear gravitons

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Abstract

Penrose has given a twistor description of all self-dual complex Riemannian space-times. We modify his construction to characterize all complex Riemannian space-times and all complex teleparallel space-times. This construction may be useful in finding non-self-dual solutions to the gravitational field equations (Einstein's or otherwise) without or with sources. It may also lead to a nonperturbative method for computing path integrals. Whereas Penrose shows that a self-dual space-time may be specified by a deformation of projective twistor space (the set of α planes in complex Minkowski space), we find that a Riemannian or teleparallel space-time may be described by a deformation of projective ambitwistor space (the set of null geodesics in complex Minkowski space).

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References

  1. Penrose, R. (1976).Gen. Rel. Grav.,7, 171–176.

    Google Scholar 

  2. Penrose, R. (1976).Gen. Rel. Grav.,7, 31–52.

    Google Scholar 

  3. Curtis, W. D., Lerner, D. E., and Miller, F. R. (1979).Gen. Rel. Grav.,10, 557–565.

    Google Scholar 

  4. Ward, R. (1978).Proc. R. Soc. London Ser. A,363, 289–295.

    Google Scholar 

  5. Gibbons, G. W., and Hawking, S. W. (1977).Phys. Rev. D,15, 2752–2756.

    Google Scholar 

  6. Hehl, F., Nitsch, J., and von der Heyde, P. (1980). In Held, A. (ed.),General Relativity and Gravitation, Vol. 1 (Plenum Press, New York), pp. 329–355.

    Google Scholar 

  7. Isenberg, J., Yasskin, P. B., and Green, P. S. (1978).Phys. Lett.,78B, 462–464; Isenberg, J., and Yasskin, P. B. (1979). In Lerner, D. E., and Sommers, P. D. (eds.)Complex Manifold Techniques in Theoretical Physics, (Pitman, London), pp. 180–206.

    Google Scholar 

  8. Witten, E. (1978).Phys. Lett.,77B, 394–398.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of California, 94720, Berkeley, California

    Philip B. Yasskin & James A. Isenberg

Authors
  1. Philip B. Yasskin
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  2. James A. Isenberg
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Additional information

This essay received Fifth Award from the Gravity Research Foundation for the year 1981-Ed.

Research supported in part by DOE contract DOE AM 03-76SF00034.

Chaim Weizmann fellow.

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Yasskin, P.B., Isenberg, J.A. Non-self-dual nonlinear gravitons. Gen Relat Gravit 14, 621–627 (1982). https://doi.org/10.1007/BF00761453

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