Brane Gravitational Extension of Dirac's "Extensible Model of the Electron"

TL;DR

This paper extends Dirac's model of the electron by incorporating gravity, resulting in a stable, finite-sized charged brane that avoids the classical electron radius problem without fine-tuning.

Contribution

It introduces a gravitational extension of Dirac's brane model, leading to a stable, finite-sized electron-like structure within a 4D bulk.

Findings

The effective potential has a global minimum ensuring finite bubble size.

The model avoids the classical electron radius problem without fine-tuning.

A novel geometrically originated energy-momentum contribution is derived.

Abstract

A gravitational extension of Dirac's "Extensible model of the electron" is presented. The Dirac bubble, treated as a 3-dim electrically charged brane, is dynamically embedded within a 4-dim $Z_{2}$-symmetric Reissner-Nordstrom bulk. Crucial to our analysis is the gravitational extension of Dirac's brane variation prescription; its major effect is to induce a novel geometrically originated contribution to the energy-momentum tensor on the brane. In turn, the effective potential which governs the evolution of the bubble exhibits a global minimum, such that the size of the bubble stays finite (Planck scale) even at the limit where the mass approaches zero. This way, without fine-tuning, one avoids the problem so-called 'classical radius of the electron'.