Null electromagnetic fields and relative CR embeddings

TL;DR

This paper explores the relationship between shear-free null rotating congruences and null electromagnetic fields using relative CR embeddings, providing negative and positive results and introducing new analytical techniques.

Contribution

It introduces novel methods based on relative CR embeddings to study null electromagnetic fields and shear-free congruences, answering longstanding questions in the field.

Findings

Negative answer to Penrose's question on shear-free null congruences

Existence of null electromagnetic fields aligned with given congruences

New techniques for analyzing null electromagnetic fields and congruences

Abstract

This paper applies the notion of relative CR embeddings to study two related questions. First, it answers negatively the question posed by Penrose whether every shear-free null rotating congruence is analytic. Second, it proves that given any shear-free null rotating congruence, there exists a null electromagnetic field which is null with respect to the given congruence. In the course of answering these questions, we introduce some new techniques for studying null electromagnetic fields and shear-free congruences in general based on the notion of a relative CR embedding.