Quantum electrodynamical corrections to a magnetic dipole in general relativity

TL;DR

This paper calculates quantum electrodynamical and general relativistic corrections to the magnetic dipole field of neutron stars, revealing small multipolar components induced by these effects.

Contribution

It introduces a new 3+1 formalism to compute QED and GR perturbations to magnetic dipoles in neutron stars, including higher-order multipolar corrections.

Findings

Identification of small dipolar and hexapolar components due to QED and GR effects.

Development of a formalism applicable to strong-field astrophysical objects.

Quantitative estimates of non-linear electromagnetic corrections in neutron star environments.

Abstract

Magnetized neutron stars are privileged places where strong electromagnetic fields as high as $\BQ=4.4\times10^9$~T exist, giving rise to non-linear corrections to Maxwell equations described by quantum electrodynamics (QED). These corrections need to be included to the general relativistic (GR) description of a magnetic dipole supposed to be anchored in the neutron star. In this paper, these QED and GR perturbations to the standard flat space-time dipole are calculated to the lowest order in the fine structure constant~$\alpha_{\rm sf}$ and to any order in the ratio $\Rs/R$ where $R$ is the neutron star radius and $\Rs$ its Schwarzschild radius. Following our new 3+1~formalism developed in a previous work, we compute the multipolar non-linear corrections to this dipole and demonstrate the presence of a small dipolar~$\ell=1$ and hexapolar~$\ell=3$ component.