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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Published in | arXiv.org |
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Main Authors | , |
Format | Paper |
Language | English |
Published |
Ithaca
Cornell University Library, arXiv.org
14.04.1999
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Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 2331-8422 |
DOI: | 10.48550/arxiv.9904031 |