Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-10-09
Class.Quant.Grav. 19 (2002) 967-984
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
19 pages, no figures. Language and minor changes. Published version
Scientific paper
10.1088/0264-9381/19/5/309
Two essential properties of energy-momentum tensors T_{\mu\nu} are their positivity and conservation. This is mathematically formalized by, respectively, an energy condition, as the dominant energy condition, and the vanishing of their divergence \nabla^\mu T_{\mu\nu}=0. The classical Bel and Bel-Robinson superenergy tensors, generated from the Riemann and Weyl tensors, respectively, are rank-4 tensors. But they share these two properties with energy momentum tensors: the Dominant Property (DP) and the divergence-free property in the absence of sources (vacuum). Senovilla defined a universal algebraic construction which generates a basic superenergy tensor T{A} from any arbitrary tensor A. In this construction the seed tensor A is structured as an r-fold multivector, which can always be done. The most important feature of the basic superenergy tensors is that they satisfy automatically the DP, independently of the generating tensor A. In a previous paper we presented a more compact definition of T{A} using the r-fold Clifford algebra. This form for the superenergy tensors allowed to obtain an easy proof of the DP valid for any dimension. In this paper we include this proof. We explain which new elements appear when we consider the tensor T{A} generated by a non-degree-defined r-fold multivector A and how orthogonal Lorentz transformations and bilinear observables of spinor fields are included as particular cases of superenergy tensors. We find some sufficient conditions for the seed tensor A, which guarantee that the generated tensor T{A} is divergence-free. These sufficient conditions are satisfied by some physical fields, which are presented as examples.
Parra Josep M.
Pozo Jose M.
No associations
LandOfFree
Positivity and conservation of superenergy tensors does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Positivity and conservation of superenergy tensors, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Positivity and conservation of superenergy tensors will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-396364