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Article

Pravda, Vojtěch
Algebraic classification of the Weyl tensor: selected applications. (English). In: Brandts, J., Chleboun, J., Korotov, S., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Applications of Mathematics 2012, In honor of the 60th birthday of Michal Křížek. Proceedings. Prague, May 2-5, 2012. Institute of Mathematics AS CR, Prague, 2012. pp. 214-223
MSC: 53A55, 53B30, 53B50, 83C20, 83C60, 83E99 | MR 3204413 | Zbl 1313.53029
Keywords:
Lorentzian geometry; Newman-Penrose; Geroch-Held-Penrose; Weyl tensor; polynomial invariants; algebraically special spacetimes; quadratic gravity
Summary:
Selected applications of the algebraic classification of tensors on Lorentzian manifolds of arbitrary dimension are discussed. We clarify some aspects of the relationship between invariants of tensors and their algebraic class, discuss generalization of Newman-Penrose and Geroch-Held-Penrose formalisms to arbitrary dimension and study an application of the algebraic classification to the case of quadratic gravity.
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