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Lorentzian geometry; Newman-Penrose; Geroch-Held-Penrose; Weyl tensor; polynomial invariants; algebraically special spacetimes; quadratic gravity
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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