Similar articles

Abstract: In arbitrary Riemannian 4-spaces, continuity equations are constructed which could be interpreted as conservation laws for the energy and momentum of the gravitational field. Special attention is given to general relativity to obtain, of natural manner, the pseudotensors of Einstein, Landau-Lifshitz, Möller, Goldberg and Stachel, and also the conservation equations of Komar, Trautman, DuPlessis and Moss.

[1] Adler, R., Bazin, M., Schiffer, M., 1965. Introduction to General Relativity. McGraw-Hill, New York, p.75-78.

[2] Anderson, J.L., 1967. Principles of Relativity Physics. Academic Press, New York, p.80-85.

[3] Babak, S.V., Grishchuk, L.P., 2000. The energy-momentum tensor for the gravitational field. Phys. Rev., D61:024038.

[4] Bak, D., Cangemi, D., Jackiw, R., 1994. Energy-momentum conservation in gravity theories. Phys. Rev., D49:5173-5181.

[5] Byers, N., 1996a. E. Noether’s Discovery of the Deep Connection between Symmetries and Conservation Laws. Proc. Symp. Heritage Emmy Noether. Bar-Ilan Univ., Israel, p.40-51.

[6] Byers, N., 1996b. History of Original Ideas and Basic Discoveries in Particle Physics. Plenum, New York, p.945-964.

[7] Chang, C.C., Nester, J., Chen, C.M., 1999. Pseudotensors and quasilocal energy-momentum. Phys. Rev. Lett., 83:1897-1901.

[8] Davis, W.R., 1974. Studies in Numerical Analysis. Academic Press, London, p.29-64.

[9] Dirac, P.A.M., 1975. General Theory of Relativity. John Wiley, New York, p.61-62.

[10] Du Plessis, J.C., 1969. Tensorial concomitants and conservation laws. Tensor, 20:347-360.

[11] Einstein, A., 1916. Die grundlage der allgemeinen relativitätstheorie. Ann. der Physik, 49:769-822.

[12] Florides, P.S., 1962. Applications of Möller theory on energy and its localization in general relativity. Proc. Camb. Phil. Soc., 58:102-109.

[13] Goldberg, J.N., 1958. Conservation laws in general relativity. Phys. Rev., 111:315-320.

[14] Kimberling, C.H., 1972. Emmy Noether. Am. Math. Mon., 79(2):136-149.

[15] Komar, A., 1959. Covariant conservation laws in general relativity. Phys. Rev., 113(3):934-936.

[16] Lanczos, C., 1969. Mathematical Methods in Solid State Physics and Superfluid Theory. Oliver & Boyd, Edinburgh, p.1-45.

[17] Lanczos, C., 1970. The Variational Principles of Mechanics. Univ. Toronto Press, Toronto, p.384-401.

[18] Lanczos, C., 1973. Emmy Noether and calculus of variations. Bull. Inst. Math. Appl., 9:253-258.

[19] Landau, L.D., Lifshitz, E.M., 1955. The Classical Theory of Fields. Addison Wesley, Cambridge, p.426-435.

[20] Laurent, B.E., 1959. Note on Möller’s energy-momentum pseudotensor. Nuovo Cimento, 11:740-743.

[21] Lovelock, D., Rund, H., 1975. Tensors, Differential Forms and Variational Principles. John Wiley, New York, p.298-330.

[22] Misner, C.W., Thorne, K.S., Wheeler, J.A., 1973. Gravitation. W.H. Freeman, San Francisco, p.402-410.

[23] Möller, C., 1958. On the localization of the energy of a physical system in the general theory of relativity. Ann. Phys., 4(4):347-371.

[24] Moss, M.K., 1972. A Komar superpotential expression for the Trautman conservation law generator of general relativity. Lett. Nuovo Cim., 5:543-550.

[25] Noether, E., 1918. Invariante variationsprobleme. Nachr. Ges. Wiss. Göttingen, 2:235-257.

[26] Palmer, T.N., 1980. Gravitational energy-momentum: the Einstein pseudotensor reexamined. Gen. Rel. Grav., 12(2):149-154.

[27] Persides, S., 1979. Energy and momentum in general relativity. Gen. Rel. Grav., 10(7):609-622.

[28] Rund, H., 1966a. Variational problems involving combined tensor fields. Abhandl. Math. Sem., 29:243-262.

[29] Rund, H., 1966b. The Hamilton-Jacobi Theory in the Calculus of Variations. London, p.293-297.

[30] Rund, H., Lovelock, D., 1972. Variational principles in the general theory of relativity. Jber. Deutsch. Math. Verein, 74:1-65.

[31] Schild, A., 1967. Lectures on General Relativity. Vol. 8, Chapter 1. AMS, p.1-104.

[32] Shah, K.B., 1967. Energy of a charged particle in Möller’s tetrad theory. Proc. Camb. Phil. Soc., 63:1157-1160.

[33] Stachel, J., 1977. A variational principle giving gravitational superpotentials, the affine connection, Riemann tensor, and Einstein field equations. Gen. Rel. Grav., 8(8):705-715.

[34] Synge, J.L., 1967. A new pseudotensor with vanishing divergence. Nature, 215:102.

[35] Synge, J.L., 1976. Relativity: The General Theory. North-Holland, Amsterdam, p.270-273.

[36] Trautman, A., 1962. Gravitation: An Introduction to Current Research. Wiley, New York, p.169-198.

[37] Trautman, A., 1964. Lectures on General Relativity— Brandeis Summer. Chapter 7. Prentice-Hall, New Jersey.

[38] Trautman, A., 1967. Noether equations and conservation laws. Commun. Math. Phys., 6(4):248-261.

[39] Weyl, H., 1935. Emmy Noether. Scripta Math., 3(3):201-220.

[40] Wigner, E., 1967. Symmetries and Reflections. Indiana Univ. Press, Indiana, USA, p.10-15.