Black holes and the classical model of a particle in Einstein non-linear electrodynamics theory

TL;DR

This paper explores a modified non-linear electrodynamics model with a logarithmic term, leading to regular black hole solutions and a classical particle model with properties linked to the Born-Infeld parameter.

Contribution

It introduces a new NED model with a logarithmic modification, revealing unique integrals and conditions for regular black hole solutions and classical particle representations.

Findings

Surface stresses vanish at a specific BI parameter value.

The model describes a classical particle with radius equal to the horizon.

Charged particles behave as conducting shells with radius proportional to BI parameter.

Abstract

Modified by a logarithmic term, the non-linear electrodynamics (NED) model of the Born-Infeld (BI) action is reconsidered. Unlike the standard BI action, this choice provides interesting integrals of the Einstein-NED equations. It is found that the spherical matching process for a regular black hole entails indispensable surface stresses that vanish only for a specific value of the BI parameter. This solution represents a classical model of an elementary particle whose radius coincides with the horizon. In flat space time, a charged particle becomes a conducting shell with a radius proportional to the BI parameter.