Coherent electromagnetic wavelets and their twisting null congruences

TL;DR

This paper constructs special electromagnetic wavelets that are null, coherent, and twist around a null congruence, linking them to the Kerr-Newman black hole geometry and providing insights into electromagnetic radiation and inertia.

Contribution

It introduces a method to generate null, coherent electromagnetic wavelets with twisting null congruences, connecting them to Kerr-Newman black hole structures.

Findings

Electromagnetic wavelets are null and propagate immediately without loitering.

The wavelets define a twisting null congruence identical to the Kerr congruence.

The construction links pulsed electromagnetic beams to black hole geometries.

Abstract

We construct an electromagnetic field whose scalar potential is a pulsed-beam wavelet Psi (an analytic continuation of a classical Huygens wavelet). The vector potential A is determined up to three complex parameters by requiring that (a) it satisfies the Lorenz gauge condition with Psi, (b) its current density is supported on the same disk D as the charge density of Psi, (c) it is axisymmetric, and (d) it has the same retarded time dependence as Psi. By choosing one of the parameters in A appropriately, the electromagnetic field generated by the four-potential (A, Psi) can be made null, meaning that E^2=B^2 and E dot B=0. We call such fields coherent because upon being radiated, they do not loiter around the source, generating electromagnetic inertia (a new concept related to reactive energy) but immediately propagate out at the speed of light. The coherent EM wavelets define a twisting null congruence of light rays in Minkowski space, which we show to be identical to the Kerr congruence associated with the Kerr-Newman metric. The latter represents a black hole due to a time-independent charge-current density on a massive disk D spinning at the angular velocity c/a, where a is the radius of D. By contrast, our coherent wavelets are electromagnetic pulsed beams radiated by pulsed charge-current distributions on D, still spinning at the uniform rate c/a.