| 1. |
- Bergqvist, Göran, 1963-, et al.
(författare)
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Algebraic and differential Rainich conditions for symmetric trace-free tensors of higher rank
- 2005
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Ingår i: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences. - : The Royal Society. - 1364-5021 .- 1471-2946. ; 461:2059, s. 2181-2195
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 2. |
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| 3. |
- Bergqvist, Göran, 1963-
(författare)
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Causal tensors in Lorentzian geometry
- 2003
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Ingår i: Publications of the Spanish mathematical society. ; 5, s. 73-83
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Tidskriftsartikel (refereegranskat)
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| 4. |
- Bergqvist, Göran, 1963-
(författare)
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Exact probabilities for typical ranks of 2 × 2 × 2 and 3 × 3 × 2 tensors
- 2013
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Ingår i: Linear Algebra and its Applications. - : Elsevier. - 0024-3795 .- 1873-1856. ; 438:2, s. 663-667
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Tidskriftsartikel (refereegranskat)abstract
- We show that the probability to be of rank 2 for a 2×2×2 tensor with elements from a standard normal distribution is π/4, and that the probability to be of rank 3 for a 3×3×2 tensor is 1/2. In the proof results on the expected number of real generalized eigenvalues of random matrices are applied. For n×n×2 tensors with n≥4 we also present some new aspects of their rank.
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| 5. |
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| 6. |
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| 7. |
- Bergqvist, Göran, 1963-
(författare)
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Spinors and conformal curvature
- 2005
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Ingår i: Publications of the Spanish mathematical society.
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Tidskriftsartikel (refereegranskat)
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| 8. |
- Bergqvist, Göran, 1963-, et al.
(författare)
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Structure of conformal Lorentz transformations
- 2003
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Ingår i: Current Trends in Relativistic Astrophysics. - : Springer. - 3540019839 - 9783540019831 ; , s. 245-251
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- The present volume contains the expanded lectures of a meeting on relativistic astrophysics, the goal of which was to provide a modern introduction to specific aspects of the field for young researchers, as well as for nonspecialists from related areas. Particular emphasis is placed on the theory of black holes and evolution, relativistic stars and jet hydrodynamics, as well as the production and detection of gravitational waves. The book is complemented by further contributions and animation supplied on the accompanying CD-ROM.
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| 9. |
- Bergqvist, Göran, 1963-
(författare)
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The Penrose inequality and null hypersurfaces
- 2003
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Ingår i: Joint meeting of the American Mathematical Society and the Spanish Mathematical Society,2003.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)
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| 10. |
- Bergqvist, Göran, 1963-, et al.
(författare)
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Unique characterization of the Bel-Robinson tensor
- 2004
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Ingår i: Classical and quantum gravity. - : IOP Publishing. - 0264-9381 .- 1361-6382. ; 21:14, s. 3499-3503
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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