Refinements of the Weyl tensor classification in five dimensions
arXiv:1203.1846 · doi:10.1088/0264-9381/29/15/155016
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 {\bf {N}}, {\bf {III}}, {\bf {II}} and {\bf {D}}, while types {\bf {I}} and {\bf {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 {\bf {N}} and {\bf {III}}, and illustrate the classification from different viewpoints (Segre type, rank, spin type) for types {\bf {II}} and {\bf {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 {\bf {D}} spacetimes.
44 pages
References in corpus (11)
- Bicycling Black Rings
- Black ring with two angular momenta
- Classification of the Weyl Tensor in Higher Dimensions and Applications
- Robinson-Trautman spacetimes in higher dimensions
- Generalization of the Geroch-Held-Penrose formalism to higher dimensions
- Type D Einstein spacetimes in higher dimensions
- Higher dimensional Kerr-Schild spacetimes
- Spinor classification of the Weyl tensor in five dimensions
- Complete classification of purely magnetic, non-rotating and non-accelerating perfect fluids
- Algebraic classification of five-dimensional spacetimes using scalar invariants
- An exhaustive classification of aligned Petrov type D purely magnetic perfect fluids