# The force-free dipole magnetosphere in non-linear electrodynamics

## TL;DR

This paper investigates how quantum electrodynamics-induced non-linear electrodynamics modifies the force-free magnetosphere structure of pulsars, deriving corrected solutions that show stronger polar magnetic fields.

## Contribution

It derives the first-order non-linear corrections to the pulsar magnetosphere in a general framework, extending classical models to include quantum effects.

## Key findings

- Corrected dipole fields converge towards the rotational axis.
- Polar magnetic fields are stronger in the non-linear models.
- Solutions provide a more accurate description of magnetar and pulsar magnetospheres.

## Abstract

Quantum electrodynamics (QED) effects may be included in physical processes of magnetar and pulsar magnetospheres with strong magnetic fields. Involving the quantum corrections, the Maxwell electrodynamics is modified to non-linear electrodynamics. In this work, we study the force-free magnetosphere in non-linear electrodynamics in a general framework. The pulsar equation describing a steady and axisymmetric magnetosphere is derived, which now admits solutions with corrections. We derive the first-order non-linear corrections to the near-zone dipole magnetosphere in some popular non-linear effective theories. The field lines of the corrected dipole tend to converge on the rotational axis so that the fields in the polar region are stronger compared to the pure dipole case.