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Spinors, Clifford algebras and superenergy tensors
Mälardalen University, Department of Mathematics and Physics.
2004 (English)Doctoral thesis, comprehensive summary (Other scientific)
Place, publisher, year, edition, pages
2004. , 60 p.
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 10
National Category
Mathematics
Research subject
Matematik/tillämpad matematik
Identifiers
URN: urn:nbn:se:mdh:diva-60ISBN: 91-88834-76-X (print)OAI: oai:DiVA.org:mdh-60DiVA: diva2:121187
Public defence
2004-12-17, Gamma, Rosenhill, Västerås, 10:15
Opponent
Supervisors
Available from: 2005-11-24 Created: 2005-11-24
List of papers
1. Unique characterization of the Bel-Robinson tensor
Open this publication in new window or tab >>Unique characterization of the Bel-Robinson tensor
2004 (English)In: Classical and Quantum Graviry, ISSN 0264-9381, Vol. 21, no 14, 3499-3503 p.Article in journal (Refereed) Published
Abstract [en]

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.

National Category
Mathematical Analysis
Identifiers
urn:nbn:se:mdh:diva-4196 (URN)10.1088/0264-9381/21/14/012 (DOI)000223146300014 ()2-s2.0-3242662638 (Scopus ID)
Available from: 2005-11-24 Created: 2005-11-24 Last updated: 2015-07-09Bibliographically approved
2. Algebraic and differential Rainich conditions for symmetric trace-free tensors of higher rank
Open this publication in new window or tab >>Algebraic and differential Rainich conditions for symmetric trace-free tensors of higher rank
2005 (English)In: Proceedings of the Royal Society of London, ISSN 0035-9017, Vol. 461, no 2059, 2181-2195 p.Article in journal (Refereed) Published
Abstract [en]

We present a study of Rainich-like conditions for symmetric and trace-free tensors T. For arbitrary even rank we find a necessary and sufficient differential condition for a tensor to satisfy the source-free field equation. For rank 4, in a generic case, we combine these conditions with previously obtained algebraic conditions to gain a complete set of algebraic and differential conditions on T for it to be a superenergy tensor of a Weyl candidate tensor, satisfying the Bianchi vacuum equations. By a result of Bell and Szekeres, this implies that in vacuum, generically, T must be the Bel-Robinson tensor of the spacetime. For the rank 3 case, we derive a complete set of necessary algebraic and differential conditions for T to be the superenergy tensor of a massless spin-3/2 field, satisfying the source-free field equation.

National Category
Mathematics
Identifiers
urn:nbn:se:mdh:diva-4197 (URN)10.1098/rspa.2004.1411 (DOI)000230675100013 ()2-s2.0-33748860346 (Scopus ID)
Available from: 2005-11-24 Created: 2005-11-24 Last updated: 2016-01-15Bibliographically approved
3. New construction of casual tensors
Open this publication in new window or tab >>New construction of casual tensors
2004 (English)In: Advances in Applied Clifford Algebras, ISSN 0188-7009, Vol. 14, no 2, 191-205 p.Article in journal (Refereed) Published
Abstract [en]

We study the problem of constructing tensors satisfying the dominant property, a generalization of the dominant energy condition T ab u a v b ≥ 0 for all future directed causal vectors u, v. The construction is done on the paravector subspace of the r-fold Euclidean Clifford algebra ⊗rCℓp and is a generalization of the representation of superenergy tensors with complex 2-spinors. Especially, as with 2-spinors, we are able to construct causal tensors of arbitrary rank, contrary to earlier constructions using tensors or the r-fold Lorentzian Clifford algebra ⊗rCℓp,1 that only produce causal tensors of even rank. An advantage of the construction in ⊗rCℓp is that several algebraic properties become trivial due to the Euclidean norm on it.

National Category
Mathematics
Identifiers
urn:nbn:se:mdh:diva-4198 (URN)10.1007/s00006-004-0012-6 (DOI)
Available from: 2005-11-24 Created: 2005-11-24 Last updated: 2013-02-06Bibliographically approved
4. Generalized spinor representation of superenergy tensors
Open this publication in new window or tab >>Generalized spinor representation of superenergy tensors
(English)Manuscript (Other academic)
National Category
Other Engineering and Technologies
Identifiers
urn:nbn:se:mdh:diva-4199 (URN)
Available from: 2005-11-24 Created: 2005-11-24 Last updated: 2017-02-22Bibliographically approved

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