VSI_i spacetimes and the epsilon-property

TL;DR

This paper studies special Lorentzian spacetimes with vanishing curvature invariants, distinguishing between VSI and related classes, and demonstrates how their curvature components can be made arbitrarily small through examples.

Contribution

It clarifies the differences between VSI and related spacetimes, analyzing their curvature properties and the epsilon-property in Lorentzian geometry.

Findings

VSI spacetimes have all curvature invariants vanish.

Components of the Riemann tensor and derivatives can be made arbitrarily small.

Examples illustrate the epsilon-property in these spacetimes.

Abstract

We investigate Lorentzian spacetimes where all zeroth and first order curvature invariants vanish and discuss how this class differs from the one where all curvature invariants vanish (VSI). We show that for VSI spacetimes all components of the Riemann tensor and its derivatives up to some fixed order can be made arbitrarily small. We discuss this in more detail by way of examples.