| 1. |
- Bergqvist, Göran, et al.
(författare)
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Algebraic Rainich theory and antisymmetrization in higher dimensions
- 2002
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 19:12, s. 3341-3355
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Tidskriftsartikel (refereegranskat)abstract
- The classical Rainich(-Misner-Wheeler) theory gives necessary and sufficient conditions on an energy-momentum tensor T to be that of a Maxwell field (a 2-form) in four dimensions. Via Einstein's equations, these conditions can be expressed in terms of the Ricci tensor, thus providing conditions for a spacetime geometry to be an Einstein-Maxwell spacetime. One of the conditions is that T2 is proportional to the metric, and it has previously been shown in arbitrary dimension that any tensor satisfying this condition is a superenergy tensor of a simple p-form. Here we examine algebraic Rainich conditions for general p-forms in higher dimensions and their relations to identities by antisymmetrization. Using antisymmetrization techniques we find new identities for superenergy tensors of these general (non-simple) forms, and we also prove in some cases the converse: that the identities are sufficient to determine the form. As an example we obtain the complete generalization of the classical Rainich theory to five dimensions.
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| 2. |
- Bergqvist, Göran, et al.
(författare)
-
New electromagnetic conservation laws
- 2003
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 20:13, s. 2663-2668
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Tidskriftsartikel (refereegranskat)abstract
- The Chevreton superenergy tensor was introduced in 1964 as a counterpart, for electromagnetic fields, of the well-known Bel–Robinson tensor of the gravitational field. We here prove the unnoticed facts that, in the absence of electromagnetic currents, Chevreton's tensor (i) is completely symmetric, and (ii) has a trace-free divergence if the Einstein–Maxwell equations hold. It follows that the trace of the Chevreton tensor is a rank-2, symmetric, trace-free, conserved tensor, which is different from the energy–momentum tensor, and nonetheless can be constructed for any test Maxwell field or any Einstein–Maxwell spacetime.
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| 3. |
- Bergqvist, Göran, et al.
(författare)
-
The Chevreton tensor and Einstein-Maxwell spacetimes conformal to Einstein spaces
- 2007
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Ingår i: Classical and Quantum Gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 24:13, s. 3437-3455
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we characterize the source-free Einstein–Maxwell spacetimes which have a trace-free Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure radiation type and that it restricts the spacetimes to Petrov type N or O. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein–Maxwell spacetimes with a zero cosmological constant that have a vanishing Bach tensor. Among these spacetimes we then look for those which are conformal to Einstein spaces. We find that the electromagnetic field and the Weyl tensor must be aligned, and in the case that the electromagnetic field is null, the spacetime must be conformally Ricci-flat and all such solutions are known. In the non-null case, since the general solution is not known on a closed form, we settle by giving the integrability conditions in the general case, but we do give new explicit examples of Einstein–Maxwell spacetimes that are conformal to Einstein spaces, and we also find examples where the vanishing of the Bach tensor does not imply that the spacetime is conformal to a C-space. The non-aligned Einstein–Maxwell spacetimes with vanishing Bach tensor are conformally C-spaces, but none of them are conformal to Einstein spaces.
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| 4. |
- Bergqvist, Göran, 1963-, et al.
(författare)
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Unique characterization of the Bel-Robinson tensor
- 2004
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 21:14, s. 3499-3503
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Tidskriftsartikel (refereegranskat)abstract
- We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors.
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