Accelerating electromagnetic magic field from the C-metric

TL;DR

This paper explores the properties of the electromagnetic field generated by accelerated charged black holes and discs, connecting classical solutions with the potential field of an accelerated spinning electron.

Contribution

It introduces the concept of an accelerating magic field derived from the C-metric, linking black hole solutions with electromagnetic fields of accelerated charged objects.

Findings

The accelerated discs' charges move along spiral paths at light speed.

The field reduces to the Kerr-Newman magic field when acceleration is zero.

The accelerating magic field may relate to the field of an accelerated electron.

Abstract

Various aspects of the C-metric representing two rotating charged black holes accelerated in opposite directions are summarized and its limits are considered. A particular attention is paid to the special-relativistic limit in which the electromagnetic field becomes the "magic field" of two oppositely accelerated rotating charged relativistic discs. When the acceleration vanishes the usual electromagnetic magic field of the Kerr-Newman black hole with gravitational constant set to zero arises. Properties of the accelerated discs and the fields produced are studied and illustrated graphically. The charges at the rim of the accelerated discs move along spiral trajectories with the speed of light. If the magic field has some deeper connection with the field of the Dirac electron, as is sometimes conjectured because of the same gyromagnetic ratio, the "accelerating magic field" represents the electromagnetic field of a uniformly accelerated spinning electron. It generalizes the classical Born's solution for two uniformly accelerated monopole charges.