Helical Symmetry in Linear Systems

TL;DR

This paper explores solutions to the scalar wave and Maxwell's equations on Minkowski space with helical symmetry, analyzing their existence, asymptotic behavior, and specific symmetries of Newman--Penrose scalars.

Contribution

It demonstrates the existence of solutions with helical symmetry and analyzes their asymptotic properties and symmetries, extending understanding of wave behavior in symmetric spacetimes.

Findings

Existence of local and global solutions with helical symmetry

Specific symmetry properties of Newman--Penrose scalars

Generalized peeling properties of solutions

Abstract

We investigate properties of solutions of the scalar wave equation and Maxwell's equations on Minkowski space with helical symmetry. Existence of local and global solutions with this symmetry is demonstrated with and without sources. The asymptotic properties of the solutions are analyzed. We show that the Newman--Penrose retarded and advanced scalars exhibit specific symmetries and generalized peeling properties.