Electromagnetic helicity wavelets: a model for quasar engines?

TL;DR

This paper introduces electromagnetic wavelets based on complex distance functions, modeling quasar engines with focused beams and jets, providing a new mathematical framework for astrophysical phenomena.

Contribution

It develops a novel electromagnetic wavelet basis using complex spheroidal coordinates, modeling quasars with a simplified flat spacetime analogy.

Findings

Wavelets have integer angular momentum and specific helicity.

Total charge of wavelets is zero, arising from polarization currents.

Model represents quasar features like accretion disks and jets geometrically.

Abstract

The complex distance function $\zeta$, which plays a prominent role in the definition of scalar (acoustic) wavelets, is found to determine a complex extension of the spherical coordinate system that is ideally suited for the construction of highly focused electromagnetic beams with helicities conforming to the oblate spheroidal geometry of $\zeta$. This is used to build a basis of electromagnetic wavelets $F^m$ radiated or absorbed by the branch disk $D$ of $\zeta$. $F^m$ has integer angular momentum $m$ around the z axis and definite spheroidal helicity. We use a regularization method to compute its singular charge-current density and show that the total charge vanishes. Hence $F^m$ is due solely to electric and magnetic polarization currents. $D$ acts as a magnetic dipole antenna, and its axis as a coupled electric dipole antenna. We propose this as an idealized electromagnetic model for quasars (in flat spacetime, without gravity), with $D$ representing the accretion disk and the vortex singularities along its axis representing the jets. In the regularized version, the accretion disk is represented by a solid flat oblate spheroid and the jets by two solid narrow semi-hyperboloids.