On the algebraic types of the Bel–Robinson tensor
TLDR
In this article, the Bel-Robinson tensor is analyzed as a linear map on the space of the traceless symmetric tensors and an algebraic classification that refines the usual Petrov-bel classification of the Weyl tensors is presented.Abstract:
The Bel–Robinson tensor is analyzed as a linear map on the space of the traceless symmetric tensors. This study leads to an algebraic classification that refines the usual Petrov–Bel classification of the Weyl tensor. The new classes correspond to degenerate type I space-times which have already been introduced in literature from another point of view. The Petrov–Bel types and the additional ones are intrinsically characterized in terms of the sole Bel–Robinson tensor, and an algorithm is proposed that enables the different classes to be distinguished. Results are presented that solve the problem of obtaining the Weyl tensor from the Bel–Robinson tensor in regular cases.read more
Citations
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On the Bel radiative gravitational fields
TL;DR: In this paper, the authors analyzed the intrinsic radiative gravitational fields defined by Bel and showed that the three radiative types, N, III and II, correspond with three different physical situations: pure radiation, asymptotic pure radiation and generic (non-pure, non-asymptotic) radiation.
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Obtaining the Weyl tensor from the Bel–Robinson tensor
TL;DR: The algebraic study of the Bel-Robinson tensor was initiated by Ferrando and Saez in this paper, where the canonical form of different algebraic types is obtained in terms of BelRobinson eigentensors.
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Cylindrical gravitational waves: C-energy, super-energy and associated dynamical effects
TL;DR: In this paper, the energy content of cylindrical gravitational wave spacetimes is analyzed by considering two local descriptions of energy associated with the gravitational field, namely those based on the C-energy and the Bel-Robinson super-energy tensor.
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Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor
TL;DR: In this paper, the algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its'superenergy' tensor.
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Poynting vector, super-Poynting vector, and principal observers in electromagnetism and general relativity
TL;DR: In this article, it was shown that the super-Poynting vector of the Weyl tensor can be replaced with a super-Petrov vector for any observer when the Petrov type is D, but only for a one-dimensional variety of observers when D is I.
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