2007/10/31 by A. A. Coley, A. Coley · 4 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/25/3/033001
published as Class.Quant.Grav.25:033001,2008 · Topical Review for Classical and Quantum Gravity. Final published version
openalex publication_date 2008/01/14 · arxiv created 2008/01/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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 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.