Araujo, Marcelo E.; Dray, Tevian; Skea, James E. F. Finding isometry groups in theory and practice. (English) Zbl 0765.53001 Gen. Relativ. Gravitation 24, No. 5, 477-500 (1992). Summary: An algorithm is given for determining the isometry group of an arbitrary spacetime (in four dimensions). Numerous examples are given and the partial implementation of this algorithm using the symbolic manipulation packages CLASSI is discussed. MSC: 53-04 Software, source code, etc. for problems pertaining to differential geometry 53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics 68W30 Symbolic computation and algebraic computation Keywords:algorithm; symbolic manipulation package; isometry group; spacetime PDFBibTeX XMLCite \textit{M. E. Araujo} et al., Gen. Relativ. Gravitation 24, No. 5, 477--500 (1992; Zbl 0765.53001) Full Text: DOI References: [1] Karlhede, A., and MacCallum, M. A. H. (1982).Gen. Rel. Grav. 14, 673. [2] Cartan, E. (1946).Leçons sur la Géométrie des Espaces de Riemann (Gauthier-Villars, Paris). · Zbl 0060.38101 [3] Brans, C. H. (1965).J. Math. Phys. 6, 94. · Zbl 0125.21204 · doi:10.1063/1.1704268 [4] Karlhede, A. (1980).Gen. Rel. Grav. 12, 693. · Zbl 0455.53023 · doi:10.1007/BF00771861 [5] Kobayashi, S., and Nomizu, K. (1963).Foundations of Differential Geometry (John Wiley and Sons, New York), vol. 1. · Zbl 0119.37502 [6] Spivak, M. (1979).A Comprehensive Introduction to Differential Geometry (2nd. ed., Publish or Perish, Houston) vol 2. · Zbl 0439.53003 [7] Karlhede, A. (1979). ?A Review of the Equivalence Problem?, University of Stockholm preprint, Appendices 2 and 3. This paper was later published without the appendices as Ref. 4. [8] MacCallum, M. A. H., and Skea, J. E. F. (1991). InAlgebraic Computing in General Relativity. Lecture Notes from the First Brazilian School on Computer Algebra, M. J. Rebouças and W. L. Roque, eds. (Oxford University Press, Oxford), vol. 2, to appear. [9] Schmidt, B. (1968). Dissertation, Universität Hamburg. [10] Kramer, D., Stephani, H., MacCallum, M. A. H., and Herlt, E. (1980).Exact Solutions of Einstein’s Field Equations (Cambridge University Press, Cambridge). · Zbl 0449.53018 [11] MacCallum, M. A. H. (1980). ?On Enumerating the Real Four Dimensional Lie Algebras?, Queen Mary College preprint. [12] Kruchkovich, G. I. (1954).Usp. Matem. Nauk SSSR, 9, part 1(59), 3; Petrov, A. Z. (1969).Einstein Spaces (Pergamon, Oxford); Bratzlavsky, F. (1959).Sur les algèbres et les groupes de Lie résolubles de dimension trois et quatre. Memoire de Licence, Université Libre de Bruxelles; Mubarakzyanov, G. M. (1963).Izv. Vyss. Uch. Zav. Mat. 1(32), 114;3(34), 99;4(35), 104; Patera, J., Sharp, R. T., Winternitz, P., and Zassenhaus, H. (1976).J. Math. Phys. 17, 986. [13] Gott III, J. R. (1985).Astrophys. J. 288, 422. · doi:10.1086/162808 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.