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The Chevreton tensor and Einstein-Maxwell spacetimes conformal to Einstein spaces
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
2007 (English)In: Classical and Quantum Gravity, ISSN 0264-9381, Vol. 24, no 13, 3437-3455 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2007. Vol. 24, no 13, 3437-3455 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-12680DOI: 10.1088/0264-9381/24/13/018OAI: oai:DiVA.org:liu-12680DiVA: diva2:16837
Available from: 2007-10-24 Created: 2007-10-24 Last updated: 2009-04-23
In thesis
1. The Chevreton Superenergy Tensor in Einstein-Maxwell Spacetimes
Open this publication in new window or tab >>The Chevreton Superenergy Tensor in Einstein-Maxwell Spacetimes
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we investigate the superenergy tensor that was introduced by Chevreton in 1964 as an electromagnetic counterpart to the Bel-Robinson tensor for the gravitational feld.

We show that in Einstein-Maxwell spacetimes with a source-free electromagnetic feld, the Chevreton superenergy tensor has many interesting properties. It is a completely symmetric rank-4 tensor and it gives rise to conserved currents for orthogonally transitive 1- and 2-parameter isometry groups.

The trace of this tensor is divergence-free and it is related to the Bach tensor. We investigate the implications for when the trace vanishes and we are able to determine the full set of such spacetimes. We use this to treat the problem of Einstein{-Maxwell spacetimes that are conformally related to Einstein spaces and we find new exact solutions with this property.

Place, publisher, year, edition, pages
Matematiska institutionen, 2007
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1136
Keyword
Einstein-Maxwell, graviational energy, superenergy, Bel tensor, Chevreton tensor, conservation laws, Conformal Einstein space
National Category
Other Physics Topics
Identifiers
urn:nbn:se:liu:diva-10093 (URN)978-91-85895-76-2 (ISBN)
Public defence
2007-12-03, Planck, Fysik, Campus Valla, Linköpings universitet, Linköping, 13:15 (English)
Opponent
Supervisors
Available from: 2007-10-24 Created: 2007-10-24 Last updated: 2009-04-27

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