2001•Annalen der PhysikOpen access

Some remarks on the Bel-Robinson tensor

Janusz Garecki

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Abstract

In this paper we present our point of view on the correct physical interpretation of the Bel-Robinson tensor within the framework of standard General Relativity (GR), i.e., within the framework of GR without supplementary elements like an arbitrary vector field, a distinguished tetrad field or a second metric. We show that this tensor arises as a consequence of the Bianchi identities and, in a natural manner, it is linked to the difference of the canonical gravitational energy-momentum as calculated in normal coordinates in a small vicinity of their origin P and in the origin P.

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In this paper we present our point of view on the correct physical interpretation of the Bel-Robinson tensor within the framework of standard General Relativity (GR), i.e., within the framework of GR without supplementary elements like an arbitrary vector field, a distinguished tetrad field or a second metric. We show that this tensor arises as a consequence of the Bianchi identities and, in a natural manner, it is linked to the difference of the canonical gravitational energy-momentum as calculated in normal coordinates in a small vicinity of their origin P and in the origin P.

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Available abstract

In this paper we present our point of view on the correct physical interpretation of the Bel-Robinson tensor within the framework of standard General Relativity (GR), i.e., within the framework of GR without supplementary elements like an arbitrary vector field, a distinguished tetrad field or a second metric. We show that this tensor arises as a consequence of the Bianchi identities and, in a natural manner, it is linked to the difference of the canonical gravitational energy-momentum as calculated in normal coordinates in a small vicinity of their origin P and in the origin P.

Key concepts: Metric tensor, Physics, Tensor (intrinsic definition), Stress–energy tensor, Mathematical physics, General relativity, Tensor field, Interpretation (philosophy)

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