# Remarks on Heisenberg-Euler-type electrodynamics

## TL;DR

This paper explores a generalized nonlinear electrodynamics model extending Heisenberg-Euler theory, analyzing corrections to Coulomb's law, black hole solutions, and energy conditions, with implications for charged black hole metrics.

## Contribution

It introduces a two-parameter nonlinear electrodynamics model encompassing Heisenberg-Euler theory and derives new corrections to classical solutions.

## Key findings

- Finite total electrostatic energy for charged particles
- Corrections to Coulomb's law at large distances
- Modified black hole solutions with asymptotic behaviors

## Abstract

We consider Heisenberg-Euler-type model of nonlinear electrodynamics with two parameters. Heisenberg-Euler electrodynamics is a particular case of this model. Corrections to Coulomb's law at $r\rightarrow\infty$ are obtained and energy conditions are studied. The total electrostatic energy of charged particles is finite. The charged black hole solution in the framework of nonlinear electrodynamics is investigated. We find the asymptotic of the metric and mass functions at $r\rightarrow\infty$. Corrections to the Reissner-Nordstr\"{o}m solution are obtained.