Lorentzian spacetimes with constant curvature invariants in four dimensions

TL;DR

This paper classifies four-dimensional Lorentzian spacetimes with constant curvature invariants, showing they are either locally homogeneous or belong to a special class called Kundt-$CSI$ spacetimes, with implications for their geometric properties.

Contribution

It proves a classification theorem for 4D $CSI$ spacetimes, identifying conditions under which they are locally homogeneous or Kundt-$CSI$, advancing understanding of their geometric structure.

Findings

$CSI$ spacetimes are either locally homogeneous or Kundt-$CSI$.

Kundt-$CSI$ spacetimes have specific curvature tensor properties.

Discussion of applications including $ ext{I}$-symmetric and degenerate Kundt $CSI$ spacetimes.

Abstract

In this paper we investigate four dimensional Lorentzian spacetimes with constant curvature invariants ($CSI$ spacetimes). We prove that if a four dimensional spacetime is $CSI$, then either the spacetime is locally homogeneous or the spacetime is a Kundt spacetime for which there exists a frame such that the positive boost weight components of all curvature tensors vanish and the boost weight zero components are all constant. We discuss some of the properties of the Kundt-$CSI$ spacetimes and their applications. In particular, we discuss $\mathcal{I}$-symmetric spaces and degenerate Kundt $CSI$ spacetimes.