| 1. |
- Andersson, Fredrik, et al.
(author)
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Existence of Lanczos potentials and superpotentials for the Weyl spinor/tensor
- 2001
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In: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 18:12, s. 2297-2304
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Journal article (peer-reviewed)abstract
- 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.
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| 2. |
- Andersson, Fredrik, et al.
(author)
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Local existence of symmetric spinor potentials for symmetric (3,1)-spinors in Einstein space-times
- 2001
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In: Journal of Geometry and Physics. - 0393-0440 .- 1879-1662. ; 37:4, s. 273-290
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Journal article (peer-reviewed)abstract
- We investigate the possibility of existence of a symmetric potential HABA'B'=H(AB)(A'B') for a symmetric (3,1)-spinor LABCA', e.g., a Lanczos potential of the Weyl spinor, as defined by the equation LABCA'=?(AB'H BC)A'B'. We prove that in all Einstein space-times such a symmetric potential HABA'B' exists. Potentials of this type have been found earlier in investigations of some very special spinors in restricted classes of space-times. A tensor version of this result is also given. We apply similar ideas and results by Illge to Maxwell's equations in a curved space-time. © 2001 Elsevier Science B.V.
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| 3. |
- Rani, Raffaele, et al.
(author)
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Killing tensors and conformai Killing tensors from conformal Killing vectors
- 2003
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In: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 20:11, s. 1929-1942
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Journal article (peer-reviewed)abstract
- Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition, we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate that it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors, and hence all the Killing tensors (which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors.
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