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Conserved matter superenergy currents for hypersurface orthogonal Killing vectors
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
2006 (English)In: Classical and Quantum Gravity, ISSN 0264-9381, Vol. 23, no 7, 2279-2290 p.Article in journal (Refereed) Published
Abstract [en]

We show that for hypersurface orthogonal Killing vectors the corresponding Chevreton superenergy currents will be conserved and proportional to the Killing vectors. This holds for four-dimensional Einstein–Maxwell spacetimes with an electromagnetic field that is source-free and inherits the symmetry of the spacetime. A similar result also holds for the trace of the Chevreton tensor. The corresponding Bel currents have previously been proven to be conserved and our result can be seen as giving further support to the concept of conserved mixed superenergy currents. The analogous case for a scalar field has also previously been proven to give conserved currents and we show, for completeness, that these currents also are proportional to the Killing vectors.

Place, publisher, year, edition, pages
2006. Vol. 23, no 7, 2279-2290 p.
Keyword [en]
Einstein-Maxwell, superenergy, conservation laws
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-12679DOI: 10.1088/0264-9381/23/7/005OAI: oai:DiVA.org:liu-12679DiVA: diva2:16836
Available from: 2007-10-24 Created: 2007-10-24 Last updated: 2009-05-12
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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