Isometries in higher dimensional CCNV spacetimes

TL;DR

This paper investigates higher-dimensional CCNV spacetimes, focusing on their symmetries and curvature invariants, and classifies those with additional isometries, especially in the context of constant curvature invariants.

Contribution

It provides a classification of CCNV spacetimes with extra isometries, including those with constant curvature invariants, expanding understanding of their geometric symmetries.

Findings

List of CCNV spacetimes with additional non-spacelike isometries

Characterization of CSI CCNV spacetimes with extra symmetries

Identification of spacetimes invariant under translations in v

Abstract

We study the class of higher-dimensional Kundt metrics admitting a covariantly constant null vector, known as CCNV spacetimes. We pay particular attention to those CCNV spacetimes with constant (polynomial) curvature invariants (CSI). We investigate the existence of an additional isometry in CCNV spacetimes, by studying the Killing equations for the general form of the CCNV metric. In particular, we list all CCNV spacetimes allowing an additional non-spacelike isometry for all values of the lightcone coordinate v, which are of interest due to the invariance of the metric under a translation in v. As an application we use our results to find all CSI CCNV spacetimes with an additional isometry as well as the subset of these spacetimes in which the isometry is non-spacelike for all values v.