General Relativity and Gravitation

, Volume 5, Issue 2, pp 183–200 | Cite as

Conservation equations and equations of motion in the null formalism

  • Joshua N. Goldberg
Research Articles


The object of this paper is to relate three equations in the Newman-Penrose system of equations to the conservation laws and, hence, to the equations of motion. To do so, the corresponding result is first obtained using the Einstein equations in a null coordinate system. The Newman-Penrose equations are then analyzed. They are separated into hypersurface, propagation, supplementary, and conservation equations. When all field equations except the three conservation equations have been appropriately satisfied, the desired result follows.


Coordinate System Field Equation Differential Geometry Conservation Equation Einstein Equation 
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  1. 1.
    Newman, E.T. and Posadas, R. (1969).Phys. Rev. Lett.,22, 1196.Google Scholar
  2. 2.
    Newman, E.T. and Posadas, R. (1969).Phys. Rev.,187, 1784.Google Scholar
  3. 3.
    Newman, E.T. and Young, R. (1970).J. Math. Phys.,11, 3154.Google Scholar
  4. 4.
    Newman, E.T. and Posadas, R. (1971).J. Math. Phys.,12, 2319.Google Scholar
  5. 5.
    Lind, R. W., Mesmer, J. and Newman, E.T.J. Math. Phys., (to appear). ‘Gravitational Radiation Reaction’.Google Scholar
  6. 6.
    Lind, R. W., Mesmer, J. and Newman, E. T.J. Math. Phys., (to appear). Equations of Motion for the Sources of Asymptotically Flat Spaces.Google Scholar
  7. 7.
    Goldberg, J.N. (1971). ‘Equations of Motion in General Relativity’, inRelativity and Gravitation, (eds. Kuper, C. and Peres, A.), (Gordon and Breach Science Publishers, New York).Google Scholar
  8. 8.
    Bondi, H., van der Burg, M. and Metzner, A. (1962).Proc. Roy. Soc.,A269, 21.Google Scholar
  9. 9.
    Sachs, R.K. (1962).Proc. Roy. Soc.,A270, 103.Google Scholar
  10. 10.
    Newman, E.T. and Penrose, R. (1962).J. Math. Phys.,3, 566.Google Scholar
  11. 11.
    Newman, E.T. and Unti, T. (1962).J. Math. Phys.,3, 891.Google Scholar
  12. 12.
    Tamburino, L. and Winicour, J. (1966).Phys. Rev.,150, 1039.Google Scholar
  13. 13.
    Papapetrou, A. (1970).Ann. Inst. Henri Poincaré,13, 271.Google Scholar
  14. 14.
    Papapetrou, A. (1971).C. R. Acad. Sci., Paris,A272, 1537.Google Scholar
  15. 15.
    Papapetrou, A. (1971).C. R. Aaad. Sci., Paris,A272, 1613.Google Scholar
  16. 16.
    Herrera, L.A. and Papapetrou, A. (1971).C. R. Acad. Sci., Paris,A272, 1756.Google Scholar
  17. 17.
    Silaban, P. (1971).Null Tetrad Formulation of the Equations of Motion in General Relativity, (Dissertation, Syracuse University).Google Scholar
  18. 18.
    Goldberg, J.N. (1958).Phys. Rev.,111, 315.Google Scholar
  19. 19.
    Komar, A. (1959).Phys. Rev.,113, 934.Google Scholar
  20. 20.
    Goldberg, J.N. (1962). ‘Conservation Laws and Equations of Motion’ inLes Théories Relativiste de la Gravitation, (eds. Lichnerowicz, A. and Tonnelat, M.A.), (Centre National de la Recherche Scientifique, Paris).Google Scholar
  21. 21.
    Sachs, R.K. (1962).Phys. Rev.,128, 2851.Google Scholar
  22. 22.
    Coddington, E. and Levinson, N. (1955).Theory of Ordinary Differential Equations, (McGraw-Hill Book Publishers, Inc., New York).Google Scholar

Copyright information

© Plenum Publishing Company Limited 1974

Authors and Affiliations

  • Joshua N. Goldberg
    • 1
  1. 1.Department of PhysicsSyracuse UniversitySyracuse

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