Super-energy tensor for space-times with vanishing scalar curvature

A four-index tensor is constructed with terms both quadratic in the Riemann tensor and linear in its second derivatives, which has zero divergence for space-times with vanishing scalar curvature. This tensor reduces in vacuum to the Bel-Robinson tensor. Furthermore, the completely timelike component...

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Bibliographic Details
Published inarXiv.org
Main Authors Bonilla, M A G, Sopuerta, C F
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 14.04.1999
Subjects
Curvature
Divergence
Gravitation
Gravitational fields
Gravitational waves
Mathematical analysis
Spacetime
Tensors
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Summary:A four-index tensor is constructed with terms both quadratic in the Riemann tensor and linear in its second derivatives, which has zero divergence for space-times with vanishing scalar curvature. This tensor reduces in vacuum to the Bel-Robinson tensor. Furthermore, the completely timelike component referred to any observer is positive, and zero if and only if the space-time is flat (excluding some unphysical space-times). We also show that this tensor is the unique that can be constructed with these properties. Such a tensor does not exist for general gravitational fields. Finally, we study this tensor in several examples: the Friedmann-Lema\^ıtre-Robertson-Walker space-times filled with radiation, the plane-fronted gravitational waves, and the Vaidya radiating metric.
ISSN:2331-8422
DOI:10.48550/arxiv.9904031