A note on the electrostatic Born-Infeld equation with radial charge density

TL;DR

This paper offers a new proof for solving the electrostatic Born-Infeld equation with radial charge, utilizing conformal methods and the Spacetime Positive Energy Theorem to ensure classical, spacelike solutions.

Contribution

It introduces a novel proof approach for the electrostatic Born-Infeld equation with radial charge, emphasizing classical and spacelike solutions.

Findings

Proof of solvability using conformal method

Solutions are automatically classical and spacelike

Method leverages the Spacetime Positive Energy Theorem

Abstract

In this note, we present a new proof of the solvability of the electrostatic Born-Infeld equation with radial charge, based on the conformal method and the Spacetime Positive Energy Theorem. An advantage of this approach is that the resulting solutions are automatically classical and spacelike.