Pseudo-Riemannian VSI spaces

Abstract

In this paper we consider pseudo-Riemannian spaces of arbitrary signature for which all of their polynomial curvature invariants vanish (VSI spaces). We discuss an algebraic classification of pseudo-Riemannian spaces in terms of the boost weight decomposition and define the ${\mathbf{S}}_i$- and $\mathbf{N}$-properties, and show that if the curvature tensors of the space possess the $\mathbf{N}$-property then it is a VSI space. We then use this result to construct a set of metrics that are VSI. All of the VSI spaces constructed possess a geodesic, expansion-free, shear-free, and twist-free null-congruence. We also discuss the related Walker metrics.

14 pages

References in corpus (6)

• Classification of the Weyl Tensor in Higher Dimensions and Applications
• Spacetimes characterized by their scalar curvature invariants
• Kundt Spacetimes
• Higher dimensional VSI spacetimes
• Spin coefficients for four-dimensional neutral metrics, and null geometry
• Twistor Theory and Differential Equations