Abstract
Algorithms for the symbolic computation of the NP spin coefficients and curvature components for a given null coframe based on the structural equations of Cartan and the complex vectorial formalism of Debever are described. The efficiency of the algorithms is compared theoretically and also empirically in a number of test cases using implementations in the computer algebra system Maple. The test results confirm the theoretical superiority of the algorithm based on Debever's formalism over the one based directly on Cartan's first structural equations for the computation of the spin coefficients both with respect to execution time and storage requirements. The algorithm for the computation of the curvature components based on Debever's formalism is generally superior to the one based on Cartan's second structural equations but the advantage is not as marked as for the spin coefficients.
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References
Cartan, E. (1963).Leçons sur la géométrie des espaces de Riemann (2nd. ed., Gauthier-Villars, Paris).
MacCallum, M. A. H. (1992). InProc. 4th Canadian Conference on General Relativity and Relativistic Astrophysics, G. Kunstatter, D. E. Vincent, J. G. Williams, eds. (World Scientific, Singapore).
Ernst, F. J. (1968). 7090 Subroutines: Exterior calculus, Proceedings of the Relativity Seminar PORS II-9, Illinois Institute of Technology.
Harrison, G. H. (1969),J. Comput. Phys. 4, 594.
Frick, I. (1977). “SHEEP—user's guide.” University of Stockholm Report 77-15.
Campbell, S. J., and Wainwright, J. (1977).Gen. Rel. Grav. 8, 987.
Barton, D., and Fitch, J. P. (1972).Rep. Prog. Phys. 35, 235.
Krasinski, A., and Perkowski, M. (1981).Gen. Rel. Grav. 13, 67.
Schrufer, E., Hehl, F. W., and McCrae, J. D. (1987).Gen. Rel. Grav. 19, 197.
Harper, J. F., and Dyer, C. C. (1986).The muTENSOR Reference Manual (Department of Astronomy, University of Toronto, Toronto, Ontario, Canada).
The Soft Warehouse (1983).MuMATH-83 Reference Manual (The Soft Warehouse, Honolulu).
Debever, R. (1964).Cah. Phys. 168–169, 303.
Cahen, M., Debever, R., and Defrise, L. (1967).J. Math. Mech. 16, 761.
Bichteler, K. (1964).Z. Physik 178, 488.
Hauser, I., and Malhiot, R. J. (1975).J. Math. Phys. 15, 816.
Plebański, J. F. (1974).Lecture Notes on Spinors, Tetrads and Forms (Centro de Investigacion y de Estudios Avanzados del IPN, Mexico).
Newman, E. T., and Penrose, R. (1962).J. Math. Phys. 3, 566.
Fee, G. J., and McLenaghan, R. G. (1977) InGeneral Relativity and Gravitation 8: Conference Abstracts (University of Waterloo, Waterloo, Ontario, Canada).
Char, B. W., Geddes, K. O., Gentleman, W. M., and Gonnet, G. H. (1983).Lecture Notes in Computer Science 162, 101.
Kramer, D., Stephani, H., MacCallum, M. A. H., and Herlt, E. (1980).Exact Solutions of Einstein's Field Equations (Cambridge University Press, Cambridge).
Helgason, S. (1962).Differential Geometry and Symmetric Spaces (Academic Press, New York).
Ehlers, J., and Kundt, W. (1962). InGravitation: An introduction to current research, L. Witten, ed. (Wiley, New York).
McLenaghan, R. G., and Leroy, J. (1972).Proc. Roy. Soc. Lond. A327, 229.
Griffiths, J. B. (1975).Proc. Cambridge Phil. Soc. 77, 559.
Ernst, F. J. (1977).Phys. Rev. 167, 1175.
Bondi, H., van den Burg, M. G. J., and Metzner, A. W. K. (1962).Proc. Roy. Soc. Lond. A269, 21.
Debever, R., McLenaghan, R. G., and Tariq, N. (1979).Gen. Rel. Grav. 10, 853.
Kerr, R. P. (1963).Phys. Rev. Lett. 11, 237.
Newman, E. T., et al. (1965).J. Math. Phys. 6, 918.
Carter, B. (1977).Phys. Rev. D 16, 3414.
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Allen, S., Fee, G.J., Kachura, A.T. et al. Comparison of algorithms for the symbolic computation of the NP spin coefficients and curvature components. Gen Relat Gravit 26, 21–40 (1994). https://doi.org/10.1007/BF02088206
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DOI: https://doi.org/10.1007/BF02088206