Gravity Role in Classical Electrodynamics of Charged Point Source

TL;DR

This paper investigates the stability of a charged point source in general relativity, revealing an instability in linear perturbation theory and estimating conditions where stability, related to electron spin, might be achieved.

Contribution

It introduces a perturbation analysis of charged point sources in GR, highlighting an instability absent in classical electrodynamics and estimating the stability conditions linked to electron spin.

Findings

GR predicts unlimited dipole perturbation growth unlike classical electrodynamics.

Unstable rotational perturbation mode identified as cause of instability.

Estimated momentum value corresponds to electron spin magnitude.

Abstract

This paper deals with the problem of a point-like charged source under the influence of the external electromagnetic field in terms of perturbation theory for GR equations. It is obtained that GR, in contrast with the classical electrodynamics, in linear perturbation theory predicts an unlimited growth of the dipole perturbation. It is shown that the reason for this unlimited perturbation growth might be related to the presence of the unstable rotational perturbation mode. The analysis of the conditions under which this instability may disappear is performed. The momentum value at which the stability is reached is estimated. These estimations give the electron spin by the order of magnitude (when charge value is equal to elementary one).