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Refinements of the Weyl tensor classification in five dimensions

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Abstract
We refine the null alignment classification of the Weyl tensor of a five-dimensional spacetime. The paper focusses on the algebraically special alignment types N, III, II and D, while types I and G are briefly discussed. A first refinement is provided by the notion of spin type of the components of highest boost weight. Second, we analyze the Segre types of the Weyl operator acting on bivector space and examine the intersection with the spin type classification. We present a full treatment for types N and III, and illustrate the classification from different viewpoints (Segre type, rank, spin type) for types II and D, paying particular attention to possible nilpotence, which is a new feature of higher dimensions. We also point out other essential differences with the four-dimensional case. In passing, we exemplify the refined classification by mentioning the special subtypes associated to certain important spacetimes, such as Myers-Perry black holes, black strings, Robinson-Trautman spacetimes and purely electric/magnetic type D spacetimes.
Keywords
SPIN TYPE, BIVECTOR, CLASSIFICATION, WEYL TENSOR, FIVE DIMENSIONAL SPACETIMES

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MLA
Coley, Alan et al. “Refinements of the Weyl Tensor Classification in Five Dimensions.” CLASSICAL AND QUANTUM GRAVITY 29.15 (2012): n. pag. Print.
APA
Coley, A., Hervik, S., Ortaggio, M., & Wylleman, L. (2012). Refinements of the Weyl tensor classification in five dimensions. CLASSICAL AND QUANTUM GRAVITY, 29(15).
Chicago author-date
Coley, Alan, S Hervik, Marcello Ortaggio, and Lode Wylleman. 2012. “Refinements of the Weyl Tensor Classification in Five Dimensions.” Classical and Quantum Gravity 29 (15).
Chicago author-date (all authors)
Coley, Alan, S Hervik, Marcello Ortaggio, and Lode Wylleman. 2012. “Refinements of the Weyl Tensor Classification in Five Dimensions.” Classical and Quantum Gravity 29 (15).
Vancouver
1.
Coley A, Hervik S, Ortaggio M, Wylleman L. Refinements of the Weyl tensor classification in five dimensions. CLASSICAL AND QUANTUM GRAVITY. 2012;29(15).
IEEE
[1]
A. Coley, S. Hervik, M. Ortaggio, and L. Wylleman, “Refinements of the Weyl tensor classification in five dimensions,” CLASSICAL AND QUANTUM GRAVITY, vol. 29, no. 15, 2012.
@article{5639317,
  abstract     = {We refine the null alignment classification of the Weyl tensor of a five-dimensional spacetime. The paper focusses on the algebraically special alignment types N, III, II and D, while types I and G are briefly discussed. A first refinement is provided by the notion of spin type of the components of highest boost weight. Second, we analyze the Segre types of the Weyl operator acting on bivector space and examine the intersection with the spin type classification. We present a full treatment for types N and III, and illustrate the classification from different viewpoints (Segre type, rank, spin type) for types II and D, paying particular attention to possible nilpotence, which is a new feature of higher dimensions. We also point out other essential differences with the four-dimensional case. In passing, we exemplify the refined classification by mentioning the special subtypes associated to certain important spacetimes, such as Myers-Perry black holes, black strings, Robinson-Trautman spacetimes and purely electric/magnetic type D spacetimes.},
  articleno    = {155016},
  author       = {Coley, Alan and Hervik, S and Ortaggio, Marcello and Wylleman, Lode},
  issn         = {0264-9381},
  journal      = {CLASSICAL AND QUANTUM GRAVITY},
  keywords     = {SPIN TYPE,BIVECTOR,CLASSIFICATION,WEYL TENSOR,FIVE DIMENSIONAL SPACETIMES},
  language     = {eng},
  number       = {15},
  pages        = {50},
  title        = {Refinements of the Weyl tensor classification in five dimensions},
  url          = {http://dx.doi.org/10.1088/0264-9381/29/15/155016},
  volume       = {29},
  year         = {2012},
}

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