Abstract
In General Relativity, one has several traditional ways of interpreting the curvature of spacetime, expressed either through the curvature tensor or the sectional curvature function. This essay asks what happens if curvature is treated on a more primitive level, that is, if the curvature is prescribed, what information does one have about the metric and associated connection of space-time? It turns out that a surprising amount of information is available, not only about the metric and connection, but also, through Einstein's equations, about the algebraic structure of the energy-momentum tensor.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hawking, S. W., and Ellis, G. F. R. (1973).The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge.
Anderson, J. L. (1967).Principles of Relativity Physics. Academic Press, New York.
Kretchmann, E. (1917).Ann. Phys. (Leipzig),53, 575.
Synge, J. L., and Schild, A. (1949).Tensor Calculus. University of Toronto Press, Toronto.
Thorpe, J. A. (1969).J. Math. Phys.,10, 1.
Cormack, W. J., and Hall, G. S. (1979).Int. J. Theor. Phys.,18, 279.
Synge, J. L. (1960).Relativity: The General Theory. North-Holland, Amsterdam.
Pirani, F. A. E. (1956).Acta. Phys. Polon.,15, 389.
Eisenhart, L. P. (1966).Riemannian Geometry. Princeton University Press, Princeton, New Jersey.
Pirani, F. A. E. (1957).Phys. Rev.,105, 1089.
Hall, G. S., and McIntosh, C. B. G. (1983).Int. J. Theor. Phys.,22, 469.
McIntosh, C. B. G., and Halford, W. D. (1981).J. Phys. A.,14, 2331.
McIntosh, C. B. G., and Halford, W. D. (1982).J. Math. Phys.,23, 436.
Hall, G. S. (1983).Gen. Rel. Grav.,15, 581.
Ihrig, E. (1975).Int. J. Theor. Phys.,14, 23.
Hall. G. S. (1984).Gen. Rel. Grav. (to appear).
Ruh, B. (1982). Doctors der Mathematik dissertation, Eidgenoessischen Technischen Hochschule, Zurich.
Hall, G. S. (1982). In Proceedings of First International Arab Conference on Mathematics, Riyadh, Saudi Arabia. (to appear).
Collinson, C. D., and da Graça Lopes Rodrigues Vaz, E. (1982).Gen. Rel. Grav.,14, 5.
Kowalski, O. (1972).Math. Z.,125, 129.
Kulkarni, R. S. (1970).Ann. Math.,91, 311.
Hall, G. S. In preparation.
Tarig, N., and Tupper, B. O. J. (1977).Tensor,31, 42.
Hall, G. S. Submitted for publication.
Hall, G. S. (1976).J. Phys. A.,9, 541.
Author information
Authors and Affiliations
Additional information
This essay received an honorable mention from the Gravity Research Foundation for the year 1983-Ed.
Rights and permissions
About this article
Cite this article
Hall, G.S. The significance of curvature in general relativity. Gen Relat Gravit 16, 495–500 (1984). https://doi.org/10.1007/BF00762342
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00762342