Some remarks on the "needle radiation"

TL;DR

This paper demonstrates that the classical wave equation cannot describe needle-radiation phenomena, but a modified Klein-Gordon type equation can, highlighting a potential new approach to modeling such radiation.

Contribution

It introduces a simple modification to the wave equation that admits solutions representing needle-radiation, addressing a gap in classical wave theory.

Findings

Classical wave equation lacks needle-radiation solutions

Augmented wave equation (Klein-Gordon type) admits needle-radiation solutions

Proposes a new mathematical framework for needle-radiation modeling

Abstract

It is shown that the classical wave equation is lacking solutions corresponding to the concept of "needle-radiation", while the simplest augmented version of the wave equation -- essentially the Klein-Gordon equation -- obtained by adding a linear term, does have such a solution.