Differential invariants of Kundt spacetimes

TL;DR

This paper develops a method to generate rational differential invariants for Kundt spacetimes, aiding in their classification and equivalence analysis, especially in three and four dimensions.

Contribution

It provides explicit generators for the algebra of invariants of Kundt spacetimes, connecting to existing equivalence problem approaches.

Findings

Generated algebra of invariants for general and degenerate Kundt spacetimes.

Connected invariant theory to Lorentzian metric equivalence approaches.

Focused analysis on three- and four-dimensional cases.

Abstract

We find generators for the algebra of rational differential invariants for general and degenerate Kundt spacetimes and relate this to other approaches to the equivalence problem for Lorentzian metrics. Special attention is given to dimensions three and four.