A Coley 2008 Class. Quantum Grav. 25 033001 doi:10.1088/0264-9381/25/3/033001
Classification of the Weyl tensor in higher dimensions and applications
REVIEW ARTICLEA Coley
Show affiliationsTOPICAL REVIEW
We review the theory of alignment in Lorentzian geometry and apply it to the algebraic classification of the Weyl tensor in higher dimensions. This classification reduces to the well-known Petrov classification of the Weyl tensor in four dimensions. We discuss the algebraic classification of a number of known higher dimensional spacetimes. There are many applications of the Weyl classification scheme, especially when used in conjunction with the higher dimensional frame formalism that has been developed in order to generalize the four-dimensional Newman–Penrose formalism. For example, we discuss higher dimensional generalizations of the Goldberg–Sachs theorem and the peeling theorem. We also discuss the higher dimensional Lorentzian spacetimes with vanishing scalar curvature invariants and constant scalar curvature invariants, which are of interest since they are solutions of supergravity theory.
- PACS
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04.50.-h Higher-dimensional gravity and other theories of gravity
- MSC
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83E15 Kaluza-Klein and other higher-dimensional theories
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
- Subjects
- Dates
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Issue 3 (7 February 2008)
Received 21 September 2007, in final form 19 November 2007
Published 14 January 2008
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Classification of the Weyl tensor in higher dimensions and applications
A Coley 2008 Class. Quantum Grav. 25 033001
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