Charged shells and elementary particles

TL;DR

This paper reviews a General Relativistic model of charged shells representing elementary particles, analyzing how a minimum length scale affects the ADM mass and its relation to the shell's charge and bare mass.

Contribution

It explicitly derives the ADM mass for charged shells using junction equations and studies the impact of a minimum length scale on the mass-charge relationship.

Findings

ADM mass equals the charge magnitude |Q| in the small-volume limit without minimum length scale.

Introduction of a minimum length scale lambda modifies the ADM mass to match the shell's bare mass m_0.

For lambda around the Planck length, the ADM mass aligns with the bare mass, similar to the neutral case.

Abstract

We review the General Relativistic model of a (quasi) point-like particle represented by a massive shell of electrically charged matter, which displays an ADM mass M equal to the electric charge |Q| in the small-volume limit. We employ the Israel-Darboux's junction equations to explicitly derive this result, and then study the modifications introduced by the existence of a minimum length scale lambda. For lambda of the order of the Planck length (or larger), we find that the ADM mass becomes equal to the bare mass m_0 of the shell, like it occurs for the neutral case.