Algebraic classification of higher dimensional spacetimes based on null alignment

0387097 - MÚ 2013 RIV GB eng J - Journal Article
Ortaggio, Marcello - Pravda, Vojtěch - Pravdová, Alena
Algebraic classification of higher dimensional spacetimes based on null alignment.
Classical and Quantum Gravity. Roč. 30, č. 1 (2013), 013001. ISSN 0264-9381. E-ISSN 1361-6382
R&D Projects: GA ČR GAP203/10/0749
Institutional support: RVO:67985840
Keywords : spacetime topology * higher-dimensional gravity
Subject RIV: BA - General Mathematics
Impact factor: 3.103, year: 2013
http://iopscience.iop.org/0264-9381/30/1/013001/

We review recent developments and applications of the classification of the Weyl tensor in higher dimensional Lorentzian geometries. First, we discuss the general setup, i.e. main definitions and methods for the classification, some refinements and the generalized Newman–Penrose and Geroch–Held–Penrose formalisms. Next, we summarize general results, such as a partial extension of the Goldberg–Sachs theorem, characterization of spacetimes with vanishing (or constant) curvature invariants and the peeling behaviour in asymptotically flat spacetimes. Finally, we discuss certain invariantly defined families of metrics and their relation with the Weyl tensor classification, including Kundt and Robinson–Trautman spacetimes; the Kerr–Schild ansatz in a constant-curvature background; purely electric and purely magnetic spacetimes; direct and (some) warped products; and geometries with certain symmetries. To conclude, some applications to quadratic gravity are also overviewed.
Permanent Link: http://hdl.handle.net/11104/0217875