Abstract
In this note, an algorithm is presented for the symbolic calculation of certain algebraic invariants of the Weyl tensor which permits the determination of the Bel-Petrov types of a gravitational field. This algorithm, although more specialized than that of D'Inverno and Russell-Clark, requires neither the use of a special coordinate system nor the spin coefficient formalism. The algorithm has been implemented in FORMAC and is designed to complete the classification scheme proposed by Petrov in his book. An appendix contains examples illustrating the use of the algorithm.
- 1 Barton, D., and Fitch, J.P. General relativity and the application of algebraic manipulative systems. Comm. A CM 14, 8 (Aug 1971), 542-547. Google ScholarDigital Library
- 2 Bel, L. La radiation gravitationnelle. Th~se, Paris, 1960.Google Scholar
- 3 D'Inverno, R.A. Algebraic computing in general relativity. General Relativity and Gravitation 5 (1975), 567-598.Google ScholarCross Ref
- 4 D'Inverno and Russell-Clark, R. Classification of the Harrison metrics. J. Math. Physics 12 (1971), 1258-1263.Google ScholarCross Ref
- 5 Dubourdieu, J. Sur le groupes d'holonomie des espaces de Riemann h 4-dimensions (Cas d'un ds 2 einsteinian). Rend. Acc. Lincei (Roma), Ser. 6, 5 (1927), 409-415.Google Scholar
- 6 Harris, R.A. A computer investigation of exact solutions of the Einstein equations in general relativity. Ph.D. Th., New Mexico State U., Las Cruces, N. Mex., 1974. Google ScholarDigital Library
- 7 Harris, R.A., and Zund, J.D. A family of algebraically general exact solutions of Einstein's source-free field equations. Tensor, N. S. 29 (1975), 103-106.Google Scholar
- 8 Harris, R.A., and Zund, J.D. An investigation of Dubourdieu's list of spacetimes which admit holonomy groups. Submitted to J. Math. Physics.Google Scholar
- 9 Harrison, G.H. A compact method for symbolic computation of the Riemann tensor. Tech. Rep. 68-80, U. of Maryland, College Park, Md., 1968.Google Scholar
- 10 Kerr, R.P. Gravitational field of a spinning mass as an example of algebraically special metrics. Physical Rev. Letters 11 (1963), 237-238.Google ScholarCross Ref
- 11 Lichnerowicz, A. Thbories Relativistes de la Gravitation et de l'Electromagnbtisme. Masson et Cie, Paris, 1955.Google Scholar
- 12 Petrov, A.Z. Einstein Spaces. Pergamon Press, Oxford, 1969.Google Scholar
- 13 Zund, J.D. Algebraic invariants and the projective geometry of spinors, Annali di Mate. Pura ed Appl. Ser. IV 82 (1969), 381-412.Google Scholar
Index Terms
- An algorithm using symbolic techniques for the Bel-Petrov classification of gravitational fields
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