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Conservation Laws on Riemann-Cartan and Lorentzian Spacetimes

  • Waldyr Alves RodriguesJr
  • Edmundo Capelas de Oliveira
Part of the Lecture Notes in Physics book series (LNP, volume 722)

Keywords

Conservation Laws Lagrangian Density Minkowski Spacetime Closed Universe Angular Momentum Conservation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Anderson, J. L., Principles of Relativity Physics, Academic Press, New York, 1967.Google Scholar
  2. 2.
    de Andrade, V. C., Guillen, L. C. T., and Pereira, J. G., Gravitational Energy-Momentum Density in Teleparallel Gravity, Phys. Rev. Lett. 84, 4533-4536 (2000).CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    Arnowitt, R., Deser, S. and Misner, C. W., The Dynamics of General Relativity, in Witten L. (ed.), Gravitation: An Introduction to Current Research, J. Willey, N. York, 1962. [gr-qc/0405109]Google Scholar
  4. 4.
    Benn, I. M., Conservation Laws in Arbitrary Space-times, Ann. Inst. H. Poincar, XXXVII, 67-91 (1982).MathSciNetGoogle Scholar
  5. 5.
    Bohzkov, Y., and Rodrigues, W. A. Jr., Mass and Energy in General Relativity, Gen. Rel. and Grav. 27, 813- 819 (1995).CrossRefADSGoogle Scholar
  6. 6.
    Bramson, B. D., Relativistic Angular Momentum for Asymptotically Flat Einstein-Maxwell Manifolds, Proc. R. Soc. London Ser. A 341, 463-469 (1975).zbMATHADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Dalton, K., Energy and Momentum in General Relativity , Gen. Rel. Grav. 21, 533-544 (1989).zbMATHCrossRefMathSciNetADSGoogle Scholar
  8. 8.
    Davis, W. R., Classical Fields, Particles and the Theory of Relativity, Gordon and Breach, New York, 1970.Google Scholar
  9. 9.
    Fernández, V. V, Moya, A. M., and Rodrigues, W. A. Jr., Covariant Derivatives on Minkowski Manifolds, in R. Ablamowicz and B. Fauser (eds.), Clifford Algebras and their Applications in Mathematical Physics (Ixtapa-Zihuatanejo, Mexico 1999), vol. 1, Algebra and Physics, Progress in Physics 18, pp 373-398, Birkhäuser, Boston, Basel and Berlin, 2000.Google Scholar
  10. 10.
    Feynman, R. P., Morinigo, F. B. and Wagner, W. G., (edited by Hatfield, B.), Feynman Lectures on Gravitation, Addison-Wesley Publ. Co., Reading, MA, 1995.Google Scholar
  11. 11.
    Geroch, R. Spinor Structure of Space-Times in General Relativity I, J. Math. Phys. 9, 1739-1744 (1968).zbMATHCrossRefMathSciNetADSGoogle Scholar
  12. 12.
    Geroch, R. Spinor Structure of Space-Times in General Relativity. II, J. Math. Phys. 11, 343-348 (1970).zbMATHCrossRefADSGoogle Scholar
  13. 13.
    Hawking, S. W. and Ellis, G. F. .R, The Large Scale Structure of Spacetime, Cambridge University Press, Cambridge, 1973.CrossRefGoogle Scholar
  14. 14.
    Hehl, F. W. and Datta, B. K., Nonlinear Spinor Equation and Asymmetric Connection in General Relativity, J. Math. Phys. 12, 798-808 (1967).MathSciNetGoogle Scholar
  15. 15.
    Lasenby, A., Doran, C. and Gull, S., Gravity, Gauge Theories and Geometric Algebras, Phil. Trans. R. Soc. 356, 487-582 (1998).zbMATHCrossRefADSMathSciNetGoogle Scholar
  16. 16.
    Logunov, A. A., Mestvirishvili, M. A., The Relativistic Theory of Gravitation, Mir Publ., Moscow, 1989.zbMATHGoogle Scholar
  17. 17.
    Logunov, A. A., Relativistic Theory of Gravity, Nova Science Publ., New York, 1999.Google Scholar
  18. 18.
    Maluf, J. W., Hamiltonian Formulation of the Teleparallel Description of General Relativity, J. Math. Phys. 35, 335-343 (1994).zbMATHCrossRefADSMathSciNetGoogle Scholar
  19. 19.
    Mo ller, C., Conservation Laws and Absolute Parallelism in General Relativity, Mat.-Fys. Skr. K. Danske Vid. Selsk 1, 1-50 (1961).Google Scholar
  20. 20.
    Misner, C. M., Thorne, K. S. and Wheeler,J. A., Gravitation, W.H. Freeman and Co. San Francesco, 1973.Google Scholar
  21. 21.
    Murchada, N. O., Total Energy Momentum in General Relativity, J. Math. Phys. 27, 2111-2118 (1986).CrossRefADSMathSciNetGoogle Scholar
  22. 22.
    Nakahara, M., Geometry, Topology and Physics, Institute of Physics Publ., Bristol and Philadelphia, 1990.zbMATHCrossRefGoogle Scholar
  23. 23.
    Penrose, R., The Road to Reality: A Complete Guide to the Laws of the Universe, Knopf Publ., N. York, 2005.zbMATHGoogle Scholar
  24. 24.
    Rodrigues, W.A. Jr., and Souza, Q. A. G., The Clifford Bundle and the Nature of the Gravitational Field, Found. of Phys. 23, 1465–1490 (1993).CrossRefADSGoogle Scholar
  25. 25.
    Rodrigues, W.A. Jr., da Rocha R., and Vaz, J. Jr., Hidden Consequence of Local Lorentz Invariance, Int. J. Geom. Meth. Mod. Phys. 2, 305-357 (2005). [math-ph/0501064]CrossRefADSGoogle Scholar
  26. 26.
    da Rocha, R., and Rodrigues, W.A. Jr., Diffeomorphism Invariance and Local Lorentz Invariance, in Anglés, P. (ed.), in publication in Proc. VII Int. Conf. Clifford Algebras and their Applications, Toulouse 2005, Birkhäuser, Basel, (2007). [math-ph/0510026]Google Scholar
  27. 27.
    Rodrigues, W. A., Jr., Souza, Q. A. G., and da Rocha, R., Conservation Laws on Riemann-Cartan, Lorentzian and Teleparallel Spacetimes. [math-ph/0605221]Google Scholar
  28. 28.
    Sachs, R. K., and Wu, H., General Relativity for Mathematicians, Springer-Verlag, New York, 1977.zbMATHGoogle Scholar
  29. 29.
    Schoen, R., and Yau, S. T., Proof of the Positive Mass Conjecture in General Relativity, Commun. Math. Phys. 65, 45-76 (1979).zbMATHCrossRefADSMathSciNetGoogle Scholar
  30. 30.
    Schoen, R., and Yau, S. T., Proof of the Positive Mass Theorem 2, Commun. Math. Phys. 79, 231-260 (1981).zbMATHCrossRefADSMathSciNetGoogle Scholar
  31. 31.
    Schwinger, J., Particles, Sources and Fields, vol. 1, Addison-Wesley Publ. Co., Reading, MA, 1970.Google Scholar
  32. 32.
    Sparling, G. A. J., Twistors, Spinors and the Einstein Vacuum Equations (unknown status), University of Pittsburg preprint (1982).Google Scholar
  33. 33.
    Szabados, L. B., Quasi-Local Energy-Momentum and Angular Momentum in GR: A Review Article, Living Reviews in Relativity. [http://www.livingreviews.org/lrr-2004-4]Google Scholar
  34. 34.
    Thirring, W., An Alternative Approach to the Theory of Gravitation, Ann. Phys. 16, 96-117 (1961).zbMATHCrossRefADSMathSciNetGoogle Scholar
  35. 35.
    Thirring, W. and Wallner, R., The Use of Exterior Forms in Einstein’s Gravitational Theory, Brazilian J. Phys. 8, 686-723 (1978).Google Scholar
  36. 36.
    Trautman, A., On the Einstein-Cartan Equations Part. 1, Bull Acad. Polon. Sci. (Sér. Sci. Math., Astr. et Phys.) 20, 185-190 (1972).MathSciNetGoogle Scholar
  37. 37.
    Trautman, A., On the Einstein-Cartan Equations Part. 2, Bull Acad. Polon. Sci. (Sér. Sci. Math., Astr. et Phys.) 20, 503-506 (1972).MathSciNetGoogle Scholar
  38. 38.
    Trautman, A., On the Einstein-Cartan Equations Part. 3, Bull Acad. Polon. Sci. (Sér. Sci. Math., Astr. et Phys.) 20, 895-896 (1972).Google Scholar
  39. 39.
    Trautman, A., On the Einstein-Cartan Equations Part. 4, Bull Acad. Polon. Sci. (Sér. Sci. Math., Astr. et Phys. ) 21, 345-346 (1973).MathSciNetGoogle Scholar
  40. 40.
    Vargas, J. G., and Torr, D. G., Conservation of Vector-Valued Forms and the Question of the Existence of Gravitational Energy-Momentum in General Relativity, Gen. Rel. Grav. 23, 713-732 (1991).zbMATHCrossRefMathSciNetADSGoogle Scholar
  41. 41.
    Wald, R., General Relativity, Univ. Chicago Press, Chicago, 1984.zbMATHGoogle Scholar
  42. 42.
    Weinberg, S., Photons and Gravitons in Perturbation Theory: Derivation of Maxwell’s and Einstein’s Equations, Phys. Rev. B 138, 988-1002 (1965).CrossRefADSMathSciNetGoogle Scholar
  43. 43.
    Weinberg, S., Gravitation and Cosmology, J. Wiley and Sons, Inc., New York, 1972.Google Scholar
  44. 44.
    Witten, E., A New Proof of the Positive Energy Theorem, Comm. Math. Phys. 80, 381-402 (1981).CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Waldyr Alves RodriguesJr
    • 1
  • Edmundo Capelas de Oliveira
    • 1
  1. 1.Universidade Estadual Campinas, Instituto de Matemática Estatística e Computação CientíficaCampinasBrasil

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