Charged black points in General Relativity coupled to the logarithmic $U(1)$ gauge theory

TL;DR

This paper derives an exact solution for a charged black point in a non-linear logarithmic U(1) gauge theory, revealing finite electromagnetic mass and conditions for horizon formation, leading to a new type of black object.

Contribution

It provides the first exact spherically symmetric solution for a charged point in a logarithmic U(1) gauge theory, introducing the concept of a black point with finite electromagnetic mass.

Findings

Electromagnetic self-mass is finite in the solution.

A specific relation between mass, charge, and coupling constant yields a black point.

Horizon conditions fix the mass to be slightly less than the charge.

Abstract

The exact solution for a static spherically symmetric field outside a charged point particle is found in a non-linear $U(1)$ gauge theory with a logarithmic Lagrangian. The electromagnetic self-mass is finite, and for a particular relation between mass, charge, and the value of the non-linearity coupling constant, $\lambda$, the electromagnetic contribution to the Schwarzschild mass is equal to the total mass. If we also require that the singularity at the origin be hidden behind a horizon, the mass is fixed to be slightly less than the charge. This object is a {\em black point.}