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.
@article{702907,
title = {Algebraic classification of the Weyl tensor: selected applications},
booktitle = {Applications of Mathematics 2012},
series = {GDML\_Books},
publisher = {Institute of Mathematics AS CR},
address = {Prague},
year = {2012},
pages = {214-223},
mrnumber = {MR3204413},
zbl = {1313.53029},
url = {http://dml.mathdoc.fr/item/702907}
}
Pravda, Vojtěch. Algebraic classification of the Weyl tensor: selected applications, dans Applications of Mathematics 2012, GDML_Books, (2012), pp. 214-223. http://gdmltest.u-ga.fr/item/702907/