Gauge fields and particle-like formations associated with shear-free null congruences

TL;DR

This paper explores Maxwell fields linked to shear-free null geodesic congruences, revealing particle-like formations with quantized charge and dynamic behavior, constructed algebraically via the Kerr theorem.

Contribution

It introduces a novel algebraic method to generate singular Maxwell and Yang-Mills solutions associated with shear-free null congruences, highlighting particle-like structures with quantized charge.

Findings

Bounded singular loci behave as particle-like formations.

These formations possess self-quantized electric charge.

Solutions can be algebraically constructed using the Kerr theorem.

Abstract

We consider Maxwell fields associated with any shear-free null geodesic congruence on Minkowski or Riemannian background space-time. Bounded singular loci of these fields are treated as particle-like formations, possess "self-quantized" electric charge and undergo self-consistent time dynamics. Complicated singular solutions of Maxwell (as well as related complex Yang-Mills) equations can be obtained in a purely algebraic way using the Kerr theorem.