Higher dimensional VSI spacetimes

TL;DR

This paper classifies and explicitly describes higher-dimensional VSI Lorentzian spacetimes, highlighting their geometric properties, special subclasses, and relevance to supergravity and superstring theories.

Contribution

It provides explicit metric forms for higher-dimensional VSI spacetimes and characterizes those with covariantly constant null vectors, linking them to known models in supergravity.

Findings

All VSI spacetimes are in the higher dimensional Kundt class.

Ricci type N VSI spacetimes include higher dimensional pp-waves and gyratons.

VSI spacetimes with covariantly constant null vectors are of Ricci type III and Weyl type III.

Abstract

We present the explicit metric forms for higher dimensional vanishing scalar invariant (VSI) Lorentzian spacetimes. We note that all of the VSI spacetimes belong to the higher dimensional Kundt class. We determine all of the VSI spacetimes which admit a covariantly constant null vector, and we note that in general in higher dimensions these spacetimes are of Ricci type III and Weyl type III. The Ricci type N subclass is related to the chiral null models and includes the relativistic gyratons and the higher dimensional pp-wave spacetimes. The spacetimes under investigation are of particular interest since they are solutions of supergravity or superstring theory.