Abstract
This is the first of a series of papers on complex spaces and their use in complex relativity. The basic aim is to develop the theory of complex relativity but only insofar as it helps in obtaining, and understanding, real solutions of Einstein's vacuum equations as slices of complex solutions. In this first paper, specific aims of the whole series are first presented. The basic equations and key entities, which are used later, are presented. The basic relativistic language used is that of Newman and Penrose. Included is a discussion of a number of important properties which arise in the development of the basic equations and key concepts, these properties being mainly ones which are not apparent in standard real formulations.
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References
Newman, E. T., and Penrose, R. (1962).J. Math. Phys.,3, 566.
Flaherty, E. J. (1980).General Relativity and Gravitation, Vol. 2, A. Held, ed. (Plenum Press, New York), p. 207.
Boyer, J. P., Finley, J. D., and Plebański, J. F. (1980).General Relativity and Gravitation, Vol. 2, A. Held, ed. (Plenum Press, New York), p. 241.
Penrose, R., and Ward, R. S. (1980).General Relativity and Gravitation, Vol. 2, A. Held, ed. (Plenum Press, New York), p. 283.
Ko, M., Ludvigsen, M., and Newman, E. T. (1981).Phys. Rep.,71, 51.
Kerr, R. P., and Schild, A. (1965).Proc. Symp. Appl. Math.,17, 199.
Plebański, J. F., and Robinson, I. (1977).Asymptotic Structure of Space-Time (Plenum Press, New York), p. 361.
Cohen, J. M., and Kegeles, L. S. (1975).Phys. Lett.,54A, 5.
Stewart, J. M. (1979).Proc. R. Soc. London Ser. A.,367, 527.
Tod, K. P. (1982).J. Math. Phys.,23, 1147.
Penrose, R. (1976).Gen. Rel. Grav.,7, 171.
Neugebauer, G. (1979).J. Phys. A: Math. Gen.,12, L67.
Ward, R. S. (1983).Gen. Rel. Grav.,15, 105.
Hall, G. S., Hickman, M. S., and McIntosh, C. B. G. (1984), Complex relativity and real solutions: II Classification of complex bivectors and metric classes,Gen. Rel. Grav., to appear.
Rózga, K. (1977).Rep. Math. Phys.,11, 197.
Kramer, D., Stephani, H., MacCallum, M., and Herlt, E. (1980).Exact Solutions of Einstein's Field Equations (VEB Deutscher Verlag der Wissenschaften, Berlin/Cambridge University Press, Cambridge).
Debever, R., McLenaghan, R. G., and Tariq, N. (1979).Gen. Rel. Grav.,10, 853.
Flaherty, E. J. (1976).Hermitian and KÄhlerian Geometry in Relativity (Springer-Verlag, Berlin).
Geroch, R., Held, A., and Penrose, R. (1973).J. Math. Phys.,14, 874.
Sachs, R. K., (1961).Proc. R. Soc. London Ser. A.,264, 309.
Robinson, I. (1982).Spacetime and Geometry (Univ. Texas Press, Austin, Texas), p. 26.
Przanowski, M., and Plebański, J. F. (1979).Acta. Phys. Polon.,B10, 485.
Plebanski, J. F., and Hacyan, S. (1975).J. Math. Phys.,16, 2403.
Przanowski, M., and Plebański, J. F. (1979).Acta Phys. Polon.,B10, 573.
Plebański, J. F. (1980). Private communication.
McIntosh, C. B. G., Foyster, J. F., and Lun, A. W-C. (1981).J. Math. Phys.,22, 2620.
Plebański, J. F., and Robinson, I. (1976).Phys. Rev. Lett.,37, 493.
Plebański, J. F., and Schild, A. (1976).Nuovo Cimento,35B, 35.
Hickman, M. S. (1983). Vacuum spacetimes from a complex viewpoint II: Quarter flat spaces, inContributed Papers of the Tenth International Conference on General Relativity and Gravitation, Padova, Bertotti, B., de Felice, F., and Pascolini, A., eds. (Consiglio Nazionale delle Ricerche, Roma), Vol. 1, p. 259.
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Mcintosh, C.B.G., Hickman, M.S. Complex relativity and real solutions. I: Introduction. Gen Relat Gravit 17, 111–132 (1985). https://doi.org/10.1007/BF00760525
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DOI: https://doi.org/10.1007/BF00760525