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Conserved matter superenergy currents for orthogonally transitive Abelian G2 isometry groups
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 20, 4955-4968 p.Article in journal (Refereed) Published
Abstract [en]

In a previous paper we showed that the electromagnetic superenergy tensor, the Chevreton tensor, gives rise to a conserved current when there is a hypersurface orthogonal Killing vector present. In addition, the current is proportional to the Killing vector. The aim of this paper is to extend this result to the case where we have a two-parameter Abelian isometry group that acts orthogonally transitive on non-null surfaces. It is shown that for four-dimensional Einstein–Maxwell theory with a source-free electromagnetic field, the corresponding superenergy currents lie in the orbits of the group and are conserved. A similar result is also shown to hold for the trace of the Chevreton tensor and for the Bach tensor, and also in Einstein–Klein–Gordon theory for the superenergy of the scalar field. This links up well with the fact that the Bel tensor has these properties and it gives further support to the possibility of constructing conserved mixed currents between the gravitational field and the matter fields.

Place, publisher, year, edition, pages
2007. Vol. 24, no 20, 4955-4968 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-12681DOI: 10.1088/0264-9381/24/20/004OAI: oai:DiVA.org:liu-12681DiVA: diva2:16838
Available from: 2007-10-24 Created: 2007-10-24 Last updated: 2009-04-27
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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Eriksson, Ingemar

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