All spacetimes with vanishing curvature invariants

TL;DR

This paper classifies all Lorentzian spacetimes with zero curvature invariants, identifying a subclass within Kundt spacetimes and providing explicit metrics, with discussions on potential applications.

Contribution

It provides a complete characterization of Lorentzian spacetimes with vanishing curvature invariants, including explicit metrics and a subclass within Kundt spacetimes.

Findings

Identification of all Lorentzian spacetimes with zero curvature invariants

Explicit metrics for the subclass of Kundt spacetimes

Discussion of potential applications of these spacetimes

Abstract

All Lorentzian spacetimes with vanishing invariants constructed from the Riemann tensor and its covariant derivatives are determined. A subclass of the Kundt spacetimes results and we display the corresponding metrics in local coordinates. Some potential applications of these spacetimes are discussed.