Sparling two-forms, the conformal factor and the gravitational energy density of the teleparallel equivalent of general relativity. (English) Zbl 0924.53058

Summary: It has been shown recently that within the framework of the teleparallel equivalent of general relativity (TEGR) it is possible to define the energy density of the gravitational field in a unique way [J. W. Maluf, J. Math. Phys. 35, 335-343 (1994; Zbl 0797.53067)]. The TEGR amounts to an alternative formulation of Einstein’s general relativity, not to an alternative gravity theory. The localizability of the gravitational energy has been investigated in a number of spacetimes with distinct topologies, and the outcome of these analyses agree with previously known results regarding the exact expression of the gravitational energy, and/or with the specific properties of the spacetime manifold.
In this article, we establish a relationship between the expression of the gravitational energy density of the TEGR and the Sparling two-forms, which are known to be closely connected with the gravitational energy. We will also show that our expression of energy yields the correct value of gravitational mass contained in the conformal factor of the metric field.


53Z05 Applications of differential geometry to physics
83C40 Gravitational energy and conservation laws; groups of motions
Full Text: DOI arXiv


[1] Brown, J. D., and York, J. W. Jr. (1993). Phys. Rev. D47, 1407.
[2] Maluf, J. W. (1996). Gen. Rel. Grav.28, 1361. · Zbl 0867.58033
[3] Maluf, J. W. (1994). J. Math. Phys.35, 335.
[4] Maluf, J. W. (1995). J. Math. Phys.36, 4242. · Zbl 0841.53060
[5] Maluf, J. W., Martins, E. F., and Kneip, A. (1996). J. Math. Phys.37, 6302. · Zbl 0865.53077
[6] Arnowitt, R., Deser, S., and Misner, C. W. (1962). In Gravitation: An Introduction to Current Research, L. Witten, ed. (Wiley, New York).
[7] Maluf, J. W. (1996). J. Math. Phys.37, 6293. · Zbl 0865.53076
[8] Faddeev, L. D. (1982). Sov. Phys. Usp.25, 130. · Zbl 0541.53023
[9] Schouten, J. A. (1989). Tensor Analysis for Physicists(2nd. ed., Dover, New York). · Zbl 0044.38302
[10] Sparling, G. A. (1984). ”Twistors, Spinors and the Einstein vacuum equations”, University of Pittsburgh preprint; Dubois-Violette, M., and Madore, J. (1987). Commun. Math. Phys.108, 213.
[11] Wallner, R., and Thirring, W. (1978). Rev. Bras. Fis. (Brazil)8, 686.
[12] Goldberg, J. N. (1988). Phys. Rev. D37, 2116.
[13] Lau, S. (1993). Class. Quantum Grav.10, 2379. · Zbl 0802.53045
[14] Brill, D. (1959). Ann. Phys. (NY)7, 466; Murchadha, N. O., and York, J. W., Jr. (1974). Phys. Rev. D10, 2345; York, J. W., Jr. (1980). In Essays in General Relativity, F. Tipler, ed. (Academic Press, New York).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.