# Differential invariants of Kundt waves

## TL;DR

This paper investigates scalar differential invariants for Kundt wave spacetimes, addressing their equivalence problem and comparing invariant computations with the Cartan-Karlhede algorithm.

## Contribution

It provides a finite representation of the algebra of invariants for Kundt waves and analyzes their behavior in vacuum cases, advancing the understanding of spacetime equivalence.

## Key findings

- Finite algebra of invariants for generic Kundt waves
- Distinct behavior of invariants in vacuum Kundt waves
- Comparison with Cartan-Karlhede invariants

## Abstract

Kundt waves belong to the class of spacetimes which are not distinguished by their scalar curvature invariants. We address the equivalence problem for the metrics in this class via scalar differential invariants with respect to the equivalence pseudo-group of the problem. We compute and finitely represent the algebra of those on the generic stratum and also specify the behavior for vacuum Kundt waves. The results are then compared to the invariants computed by the Cartan-Karlhede algorithm.