On the algebraic classification of pseudo-Riemannian spaces

Abstract

We consider arbitrary-dimensional pseudo-Riemannian spaces of signature (k, k + m). We introduce a boost-weight decomposition and define a number of algebraic properties (e.g. the Si- and N-properties) and present a boost-weight decomposition to classify the Weyl tensors of arbitrary signature and discuss degenerate algebraic types (e.g. VSI spaces). We consider the four dimensional neutral signature space as an illustration.