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Existence of Lanczos potentials and superpotentials for the Weyl spinor/tensor
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
2001 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 18, no 12, p. 2297-2304Article in journal (Refereed) Published
Abstract [en]

A new and concise proof of existence - emphasizing the very natural and simple structure - is given for the Lanczos spinor potential LABCA' of an arbitrary symmetric spinor WABCD defined by WABCD = 2?(AA' LBCD)A', this proof is easily translated into tensors in such a way that it is valid in four-dimensional spaces of any signature. In particular, this means that the Weyl spinor ?ABCD has Lanczos potentials in all spacetimes, and furthermore that the Weyl tensor has Lanczos potentials on all four-dimensional spaces, irrespective of signature. In addition, two superpotentials for WABCD are identified: the first TABCD (= T(ABC)D) is given by LABCA' = ?A'DTABCD, while the second HABA'B' (= H(AB)(A'B')) (which is restricted to Einstein spacetimes) is given by LABCA' = ? (AB' HBC)A'B'. The superpotential TABCD is used to describe the gauge freedom in the Lanczos potential.

Place, publisher, year, edition, pages
2001. Vol. 18, no 12, p. 2297-2304
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-47347DOI: 10.1088/0264-9381/18/12/304OAI: oai:DiVA.org:liu-47347DiVA, id: diva2:268243
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2022-03-16
In thesis
1. On Curvature-Free Connections and Other Properties of the Lanczos Spinar
Open this publication in new window or tab >>On Curvature-Free Connections and Other Properties of the Lanczos Spinar
2000 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis we study various properties of the Lanczos spinor. The results include an algebraic classification scheme for symmetric (3,1)-spinors, a link between Lanczos potentials of the Weyl spinor and the spin coefficients in certain classes of spacetimes, an existence proof for the Lanczos potential of a general Weyl candidate that is much simpler than those previously known and the existence of a symmetric potential HABA'B' of an arbitrary symmetric (3,1)-spinor LABCA' in Einstein spacetimes according tothe equation LABCA' = ∇(AB' HBC)A'B'. In addition we study a large subclass of algebraically special spacetimes and obtain necessary and sufficient conditions for a Lanczos potential of the Weyl spinor to define a metric, curvature-free connection; we also prove existence of such connections. This construction is analogous to a construction of quasi-local momentum in the Kerr spacetime by Bergqvist and Ludvigsen and we therefore obtain an analogue of the Nester-Witten 2-form in these spacetimes.

Place, publisher, year, edition, pages
Linköping: Linköping University, 2000. p. 18
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 633
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:liu:diva-183660 (URN)9172197250 (ISBN)
Public defence
2000-05-31, BL32, hus B, bv, ingång 23, Linköpings Universitet, Linköping, 13:15
Opponent
Note

All or some of the partial works included in the dissertation are not registered in DIVA and therefore not linked in this post.

Available from: 2022-03-16 Created: 2022-03-16 Last updated: 2022-03-16Bibliographically approved

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Andersson, Fredrik

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