Full Text:   <2985>

CLC number: O186.12

On-line Access: 

Received: 2006-12-07

Revision Accepted: 2007-01-04

Crosschecked: 0000-00-00

Cited: 0

Clicked: 4966

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.4 P.665-668


Conservation laws for energy and momentum in curved spaces


Affiliation(s):  Section of Postgraduate Studies and Research, Superior School of Mechanical and Electrical Engineering, National Polytechnic Institute, CP 07738, Mexico; more

Corresponding email(s):   jlopezb@ipn.mx

Key Words:  Noether theorem, Lagrangians in curved spaces, Energy and momentum in Riemannian spaces, Rund-Lovelock identities

LÓPEZ-BONILLA J., MORALES J., OVANDO G.. Conservation laws for energy and momentum in curved spaces[J]. Journal of Zhejiang University Science A, 2007, 8(4): 665-668.

@article{title="Conservation laws for energy and momentum in curved spaces",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Conservation laws for energy and momentum in curved spaces
%J Journal of Zhejiang University SCIENCE A
%V 8
%N 4
%P 665-668
%@ 1673-565X
%D 2007
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2007.A0665

T1 - Conservation laws for energy and momentum in curved spaces
A1 - LÓ
J0 - Journal of Zhejiang University Science A
VL - 8
IS - 4
SP - 665
EP - 668
%@ 1673-565X
Y1 - 2007
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2007.A0665

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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[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.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE