Spacetimes with all scalar curvature invariants in terms of the Cosmological Constant

TL;DR

This paper characterizes spacetimes where all polynomial scalar invariants derived from the Riemann tensor and its derivatives vanish except for those related to the cosmological constant, providing explicit metric forms.

Contribution

It offers an invariant classification of such spacetimes and explicit metric solutions based solely on the cosmological constant.

Findings

Invariant characterization of the spacetimes

Explicit metric forms derived from the classification

Clarification of scalar invariants in relation to the cosmological constant

Abstract

In this letter we provide an invariant characterization for all spacetimes with all polynomial scalar invariants constructed from the Riemann tensor and its covariant derivatives vanishing except those zeroth order curvature invariants expressed as polynomials in $\Lambda$, the cosmological constant. Using this invariant description we provide explicit forms for the metric.