Algebraic computing in torsion theories of gravitation

Mathematics and Computers in Simulation

Volumn 42, Issue 4-6, 1996, Pages 739-748

  Fonseca Neto, Joel B ^a   Reboucas, M J ^b   MacCallum, M A H ^c  

^a FEDERAL UNIVERSITY OF PARAÍBA   (Brazil)

^b CENTRO BRASILEIRO DE PESQUISAS FÍSICAS   (Brazil)

^c QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

Computer algebra; Equivalence problem; Gravitation; Torsion theories

Indexed keywords

ALGEBRA; ALGORITHMS; COMPUTER SOFTWARE; EQUIVALENCE CLASSES; GRAVITATION; TENSORS; TORSIONAL STRESS;

ALGEBRAIC COMPUTING; CURVATURE TENSORS; EQUIVALENCE PROBLEM; RIEMANN-CARTAN SPACE TIMES; TORSION THEORY;

COMPUTATIONAL METHODS;

EID: 0030285761     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4754(96)00047-X     Document Type: Article

References (23)

1. M.A.H. MacCallum, Computer-aided classification of exact solutions in general relativity, in: R. Cianci, R. de Ritis, M. Francaviglia, G. Marmo, C. Rubano and P. Scudellaro, eds., General Relativity and Gravitational Physics (9th Italian Conference) (World Scientific, Singapore, 1991).
2. E. Schrüfer, F. Hehl and J.D. McCrea, Application of the REDUCE package EXCALC to Poincaré gauge field theory, Gen. Rel. Grav. 19 (1987) 197.
3. J.D. McCrea, REDUCE in general relativity and Poincaré gauge theory, in: M.J. Rebouças and W. L. Roque, eds., Algebraic Computing in General Relativity, Lecture Notes from the First Brazilian School on Computer Algebra, Vol. II (Oxford Univ. Press, Oxford, 1994).
4. J.B. Fonseca-Neto, M.J. Rebouças and A.F.F. Teixeira, The equivalence problem in torsion theories of gravitation, J. Math. Phys. 33 (1992) 2574.
5. I. Frick, SHEEP Manual, University of Stockholm, Institute of Theoretical Physics Tech. Report, 1979. Distributed with the SHEEP sources.
6. A. Karlhede, A review of the geometrical equivalence of metrics in general relativity, Gen. Rel. Grav. 12 (1980) 693.
7. J.E. Åman, Manual for CLASSI: Classification programs for geometries in general relativity, Institute of Theoretical Physics Technical Report, 1987. Third provisional edition. Distributed with the SHEEP sources.
8. J.E. Åman and A. Karlhede, A computer-aided complete classification of geometries in general relativity. First results, Phys. Lett. A 80 (1980) 229.
9. J. E. Åman and A. Karlhede, An algorithmic classification of geometries in general relativity, in: P.S. Wang, ed., Proc. 1981 ACM Symposium on Symbolic and Algebraic Computation - SYMSAC'81 (Association of Computing Machinery, New York, 1981).
10. M.A.H. MacCallum, Classifying metrics in theory and practice, in: V. de Sabbata and E. Schmutzer, eds., Unified Field Theory in More Than 4 Dimensions, Including Exact Solutions (World Scientific, Singapore, 1983).
11. M.A.H. MacCallum, Algebraic computing in general relativity, in: W.B. Bonnor, J.N. Islam and M.A.H. MacCallum, eds., Classical General Relativity (Cambridge Univ. Press, Cambridge, 1984).
12. I. Cohen, I. Frick and J.E. Åman, Algebraic computing in general relativity, in: B. Bertotti, A. Pascolini and F. de Felice, eds., General Relativity and Gravitation (Reidel, Dordrecht, 1984)
13. G.C. Joly and M.A.H. MacCallum, Computer-aided classification of the Ricci tensor in general relativity, Class. Quant. Grav. 7 (1990) 541.
14. M.A.H. MacCallum and J.E.F. Skea, SHEEP: A computer algebra system for general relativity, in: M.J. Rebouças and W.L. Roque, eds., Algebraic Computing in General Relativity, Lecture Notes from the First Brazilian School on Computer Algebra, Vol. II (Oxford Univ. Press, Oxford, 1994).
15. S. Jogia and J.B. Griffiths, A Newman-Penrose-type formalism for space-times with torsion, Gen. Rel. Grav. 12 (1980) 597.
16. J.E. Åman, R.A. d'Inverno, G.C. Joly and M.A.H. MacCallum, Quartic equations and algorithms for Riemann tensor classification, in: J. Fitch, ed., EUROSAM 84: Proceedings of the 1984 European Conference on Symbolic and Algebraic Manipulation, Lecture Notes in Computer Science, 174 (Springer, Berlin, 1984).
17. S. Kobayashi and K. Nomizu, Foundations of differential geometry, Vol. I (Interscience, New York, 1963).
18. J.B. Fonseca-Neto, M.A.H. MacCallum and M.J. Rebouças A practical procedure for the equivalence problem in torsion theories of gravitation (1996) in preparation.
19. J.B. Fonseca-Neto, M.A.H. MacCallum and M.J. Rebouças, Algebraically independent derivatives of curvature and torsion tensors in Riemann-Cartan space-times (1996) in preparation.
20. E. Cartan, Leçons sur la Géométrie des Éspaces de Riemann (Gauthier-Villars, Paris, 1951). Reprinted, Editions Jacques Gabay, Paris, 1988. English translation by J. Glazebrook (Math. Sci. Press, Brookline, 1983).
21. M.A.H. MacCallum and J.E. Åman, Algebraically independent n-th derivatives of the Riemann curvature spinor in general relativity, Class. Quant. Grav. 3 (1986) 1133.
22. Y.N. Obukhov, V.N. Ponomariev and V.V. Zhytnikov, Quadratic Poincaré gauge theory of gravity: A comparison with the general relativity theory, Gen. Rel. Grav. 21 (1989) 1107.
23. F.W. Hehl, P. von der Heyde, G.D. Kerlick and J.M. Nester, General relativity with spin and torsion: Foundations and prospects, Rev. Mod. Phys. 48 (1976) 393.