# Locally Homogeneous Kundt Triples and CSI Metrics

## TL;DR

This paper classifies all locally homogeneous CSI Kundt spacetimes of alignment type D, showing they form a fundamental subclass from which all other CSI Kundt metrics can be derived, advancing understanding of curvature invariants in Lorentzian geometry.

## Contribution

It provides an invariant classification of locally homogeneous CSI Kundt spacetimes of type D, establishing a foundation for constructing all other CSI Kundt metrics.

## Key findings

- Classified all locally homogeneous CSI Kundt spacetimes of type D.
- Demonstrated that all other CSI Kundt metrics can be constructed from these.
- Enhanced understanding of scalar polynomial invariants in Lorentzian geometry.

## Abstract

A pseudo-Riemannian manifold is called CSI if all scalar polynomial invariants constructed from the curvature tensor and its covariant derivatives are constant. In the Lorentzian case, the CSI spacetimes have been studied extensively due to their application to gravity theories. It is conjectured that a CSI spacetime is either locally homogeneous or belongs to the subclass of degenerate Kundt metrics. Independent of this conjecture, any CSI spacetime can be related to a particular locally homogeneous degenerate Kundt metric sharing the same scalar polynomial curvature invariants. In this paper we will invariantly classify the entire subclass of locally homogeneous CSI Kundt spacetimes which are of alignment type {\bf D} to all orders and show that any other CSI Kundt metric can be constructed from them.