Abstract
Covariant conservation laws in the Palatini formalism are derived. The result indicates that the gravitational part of conserved charges in general relativity should be calculated from a combination of Komar's strongly conserved current and the Einstein tensor. This implies that the set of complete diffeomorphism charges of a gravitating system consisting of scalar matter is described by Komar's vector density, and that the identification of gravitational energy and momentum reduces to two choices: a choice of relative weights of the contributions resulting from Komar's current and from the Einstein tensor, and a choice of preferred vector fields in space-time. A proposal is made which yields energy and momentum as scalars under diffeomorphisms and as a Lorentz vector in tangent space. Furthermore, the result can be used to identify covariant conservation laws holding separately for the matter contributions to diffeomorphism charges.
Similar content being viewed by others
References
Bergmann, P. G. (1958).Physical Review,112, 287.
Carmeli, M., Leibowitz, E., and Nissani, N. (1990).SL(2, ℂ)Gauge Theory and Conservation Laws, World Scientific, Singapore.
De Felice, F., and Clarke, C. J. S. (1990).Relativity on Curved Manifolds, Cambridge University Press, Cambridge.
Dick, R. (1991). Topological aspects of chiral fields in two dimensions and superstring vertices, preprint LMU-TPW 91-01; to appear inFortschritte der Physik.
Fletcher, J. G. (1960).Reviews of Modern Physics,32, 65.
Komar, A. (1959).Physical Review,113, 934.
Kovacs, D. (1985).General Relativity and Gravitation,17, 927.
Misner, C. W., Thorne, K. S., and Wheeler, J. A. (1973).Gravitation, Freeman, San Francisco.
Mizkjewitsch, N. (1958).Annalen der Physik,1, 319.
Møller, C. (1958).Annals of Physics,4, 347.
Møller, C. (1972).The Theory of Relativity, 2nd ed., Oxford University Press, Oxford.
Murphy, G. L. (1990).International Journal of Theoretical Physics,29, 1003.
Nissani, N., and Leibowitz, E. (1988).Physics Letters A,126, 447.
Nissani, N., and Leibowitz, E. (1989).International Journal of Theoretical Physics,28, 235.
Nissani, N., and Leibowitz, E. (1991).International Journal of Theoretical Physics,30, 837.
Schmutzer, E. (1961).Zeitschrift für Naturforschung,16a, 825.
Schmutzer, E. (1968).Relativistische Physik, Akademische Verlagsgesellschaft Geest & Portig K. G., Leipzig.
Trautman, A. (1962). InGravitation: An Introduction to Current Research (L. Witten, ed.), Wiley, New York, Chapter 5.
Wald, R. M. (1984).General Relativity, University of Chicago Press, Chicago.
Weinberg, S. (1972).Gravitation and Cosmology, Wiley, New York.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dick, R. Covariant conservation laws from the palatini formalism. Int J Theor Phys 32, 109–119 (1993). https://doi.org/10.1007/BF00674399
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00674399