Introduction to Kundt spaces

TL;DR

This paper offers a pedagogical introduction to Kundt spaces, clarifying their properties and key concepts using geometric language, to serve as a clear reference in the mathematical literature.

Contribution

It provides a coherent, geometric overview of Kundt spaces, consolidating scattered information and emphasizing their fundamental properties and structures.

Findings

Clarification of key properties of Kundt spaces

Use of geometric language for better understanding

Focus on lightlike totally geodesic foliations

Abstract

This paper provides an introduction to Kundt spaces, clarifying several important properties, many of which are typically scattered across the mathematical literature or presented without explicit reference to Kundt terminology. While not exhaustive, our approach aims to offer a pedagogical introduction, using a more geometric language and focusing on key concepts directly related to these spaces, such as lightlike totally geodesic foliations.