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New electromagnetic conservation laws
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.
Departamento de Física Teórica, Universidad del País Vasco, Bilbao, Spain.
2003 (English)In: Classical and Quantum Gravity, ISSN 0264-9381, Vol. 20, no 13, 2663-2668 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2003. Vol. 20, no 13, 2663-2668 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-12678DOI: 10.1088/0264-9381/20/13/313OAI: oai:DiVA.org:liu-12678DiVA: diva2:16835
Available from: 2007-10-24 Created: 2007-10-24 Last updated: 2009-04-28
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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Bergqvist, GöranEriksson, Ingemar

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