Killing vectors in higher dimensional spacetimes with constant scalar curvature invariants

TL;DR

This paper investigates the existence and characteristics of non-spacelike Killing vectors in higher-dimensional Kundt spacetimes with constant scalar curvature invariants, focusing on their forms and conditions for covariant constancy.

Contribution

It provides explicit forms and constraints for non-spacelike Killing vectors in higher-dimensional CSI Kundt spacetimes, including conditions for covariant null vectors.

Findings

Identification of null and timelike Killing vectors in CSI Kundt spacetimes

Constraints on metric functions for non-spacelike isometries

Conditions for covariantly constant null vectors

Abstract

We study the existence of a non-spacelike isometry, \zeta, in higher dimensional Kundt spacetimes with constant scalar curvature invariants (CSI). We present the particular forms for the null or timelike Killing vectors and a set of constraints for the metric functions in each case. Within the class of N dimensional CSI Kundt spacetimes, admitting a non-spacelike isometry, we determine which of these can admit a covariantly constant null vector that also satisfy \zeta_{[a;b]} = 0.