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Algebraic computing in torsion theories of gravitation. (English) Zbl 1037.83500
Summary: A suite of computer algebra programs for tensor and spinor calculations in torsion theories of gravitation is presented. Modules for the algebraic classification of curvature tensors in Riemann-Cartan space-times are discussed. The basic theoretical results and an algorithm for the equivalence problem for Riemann-Cartan space-times are presented.

MSC:
83-04 Software, source code, etc. for problems pertaining to relativity and gravitational theory
68W30 Symbolic computation and algebraic computation
Software:
SHEEP
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[1] Maccallum, M. A. H.: Computer-aided classification of exact solutions in general relativity. 9th italian conference (1991)
[2] Schrüfer, E.; Hehl, F.; Mccrea, J. D.: Application of the reduce package excalc to Poincaré gauge field theory. Gen. rel. Grav. 19, 197 (1987) · Zbl 0604.53030
[3] Mccrea, J. D.: Reduce in general relativity and Poincaré gauge theory. Lecture notes from the first Brazilian school on computer algebra (1994) · Zbl 0829.53058
[4] Fonseca-Neto, J. B.; Rebouças, M. J.; Teixeira, A. F. F.: The equivalence problem in torsion theories of gravitation. J. math. Phys. 33, 2574 (1992) · Zbl 0773.53042
[5] I. Frick, sheep Manual, University of Stockholm, Institute of Theoretical Physics Tech. Report, 1979. Distributed with the sheep sources.
[6] Karlhede, A.: A review of the geometrical equivalence of metrics in general relativity. Gen. rel. Grav. 12, 693 (1980) · Zbl 0455.53023
[7] åman, J. E.: Manual for classi: classification programs for geometries in general relativity. Institute of theoretical physics technical report (1987)
[8] åman, J. E.; Karlhede, A.: A computer-aided complete classification of geometries in general relativity. First results. Phys. lett. A 80, 229 (1980)
[9] åman, J. E.; Karlhede, A.: An algorithmic classification of geometries in general relativity. Proc. 1981 ACM symposium on symbolic and algebraic computation–SYMSAS’81 (1981) · Zbl 0507.68022
[10] Maccallum, M. A. H.: Classifying metrics in theory and practice. Unified field theory in more than 4 dimensions, including exact solutions (1983)
[11] Maccallum, M. A. H.: Algebraic computing in general relativity. Classical general relativity (1984) · Zbl 0571.53051
[12] Cohen, I.; Frick, I.; åman, J. E.: Algebraic computing in general relativity. General relativity and gravitation (1984)
[13] Joly, G. C.; Maccallum, M. A. H.: Computer-aided classification of the Ricci tensor in general relativity. Class. quant. Grav. 7, 541 (1990) · Zbl 0693.53032
[14] Maccallum, M. A. H.; Skea, J. E. F.: Sheep: A computer algebra system for general relativity. Lecture notes from the first Brazilian school on computer algebra (1994) · Zbl 0829.53057
[15] Jogia, S.; Griffiths, J. B.: A Newman-Penrose-type formalism for space-times with torsion. Gen. rel. Grav. 12, 597 (1980) · Zbl 0454.53022
[16] åman, J. E.; D’inverno, R. A.; Joly, G. C.; Maccallum, M. A. H.: Quartic equations and algorithms for Riemann tensor classification. Lecture notes in computer science 174 (1984) · Zbl 0583.68013
[17] Kobayashi, S.; Nomizu, K.: Foundations of differential geometry. (1963) · Zbl 0119.37502
[18] Fonseca-Neto, J. B.; Maccallum, M. A. H.; Rebouças, M. J.: A practical procedure for the equivalence problem in torsion theories of gravitation. (1996) · Zbl 1037.83500
[19] Fonseca-Neto, J. B.; Maccallum, M. A. H.; Rebouças, M. J.: Algebraically independent derivatives of curvature and torsion tensors in Riemann-Cartan space-times. (1996)
[20] Cartan, E.: Leçons sur la géométrie des éspaces de Riemann. (1951) · Zbl 0044.18401
[21] Maccallum, M. A. H.; åman, J. E.: Algebraically independent n-th derivatives of the Riemann curvature spinor in general relativity. Class. quant. Grav. 3, 1133 (1986) · Zbl 0603.53036
[22] Obukhov, Y. N.; Ponomariev, V. N.; Zhytnikov, V. V.: Quadratic Poincaré gauge theory of gravity: A comparison with the general relativity theory. Gen. rel. Grav. 21, 1107 (1989) · Zbl 0679.53069
[23] Hehl, F. W.; Von Der Heyde, P.; Kerlick, G. D.; Nester, J. M.: General relativity with spin and torsion: foundations and prospects. Rev. mod. Phys. 48, 393 (1976) · Zbl 1371.83017
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