Coulomb field of an accelerated charge: physical and mathematical aspects

TL;DR

This paper explores the electromagnetic properties of an accelerated charge's Coulomb field using gauge invariant potentials, revealing unique features and radiation effects in accelerated frames compared to inertial frames.

Contribution

It introduces a gauge invariant formulation of Maxwell's equations in accelerated frames and analyzes the Coulomb field's properties and radiation reaction in this context.

Findings

Larmor radiation reaction equals electrostatic attraction in accelerated frames

Spectral decomposition suggests charge effects resemble lattice distortions

Coulomb field exhibits unique properties in accelerated frames

Abstract

The Maxwell field equations relative to a uniformly accelerated frame, and the variational principle from which they are obtained, are formulated in terms of the technique of geometrical gauge invariant potentials. They refer to the transverse magnetic (TM) and the transeverse electric (TE) modes. This gauge invariant "2+2" decomposition is used to see how the Coulomb field of a charge, static in an accelerated frame, has properties that suggest features of electromagnetism which are different from those in an inertial frame. In particular, (1) an illustrative calculation shows that the Larmor radiation reaction equals the electrostatic attraction between the accelerated charge and the charge induced on the surface whose history is the event horizon, and (2) a spectral decomposition of the Coulomb potential in the accelerated frame suggests the possibility that the distortive effects of this charge on the Rindler vacuum are akin to those of a charge on a crystal lattice.