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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.

MSC:
53Z05 Applications of differential geometry to physics
83C40 Gravitational energy and conservation laws; groups of motions
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References:
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