Classical Physics


Stress-Energy Tensor Beyond the Belinfante and Rosenfeld Formula

Authors: Juan Ramón González Álvarez

The physical importance of the stress-energy tensor is twofold: at the one hand, it is a fundamental quantity appearing on the equations of mechanics; at the other hand, this tensor is the source of the gravitational field. Due to this importance, two different procedures have been developed to find this tensor for a given physical system. The first of the systematic procedures gives the canonical tensor, but this tensor is not usually symmetric and it is repaired, via the Belifante and Rosenfeld formula, to give the Hilbert tensor associated to the second procedure. After showing the physical deficiencies of the canonical and Hilbert tensors, we introduce a new and generalized tensor $\Theta^{\mu\nu}$ without such deficiencies. This $\Theta^{\mu\nu}$ is (i) symmetric, (ii) conserved, (iii) in agreement with the energy and momentum of a system of charges interacting via NILI potentials $\Lambda^\mu(R(t))$, and (\textbf{iv}) properly generalizes the Belifante and Rosenfeld formula, with the Hilbert tensor being a special case of $\Theta^{\mu\nu}$.

Comments: 7 Pages.

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[v1] 2012-07-01 05:45:25

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