Strongly magnetized rotating dipole in general relativity

TL;DR

This paper develops a numerical method to solve Maxwell's equations in spherical coordinates, incorporating general relativity and quantum electrodynamics, to study the electromagnetic emission of rotating magnetized stars.

Contribution

It introduces a spectral method-based algorithm for time-dependent Maxwell equations in curved spacetime with QED corrections, applied to astrophysical rotating neutron stars.

Findings

Quantum electrodynamics has negligible effect on spindown luminosity.

Relativistic corrections do not significantly alter the braking index.

The classical dipole model remains valid even with strong magnetic fields.

Abstract

Electromagnetic waves arise in many area of physics. Solutions are difficult to find in the general case. In this paper, we numerically integrate Maxwell equations in a 3D spherical polar coordinate system. Straightforward finite difference methods would lead to a coordinate singularity along the polar axis. Spectral methods are better suited to deal with such artificial singularities related to the choice of a coordinate system. When the radiating object is rotating like for instance a star, special classes of solutions to Maxwell equations are worthwhile to study such as quasi-stationary regimes. Moreover, in high-energy astrophysics, strong gravitational and magnetic fields are present especially around rotating neutron stars. In order to study such systems, we designed an algorithm to solve the time-dependent Maxwell equations in spherical polar coordinates including general relativity as well as quantum electrodynamical corrections to leading order. As a diagnostic, we compute the spindown luminosity expected from these stars and compare it to the classical i.e. non relativistic and non quantum mechanical results. It is shown that quantum electrodynamics leads to an irrelevant change in the spindown luminosity even for magnetic field around the critical value of $\numprint{4.4e9}$~\si{\tesla}. Therefore the braking index remains close to its value for a point dipole in vacuum namely $n=3$. The same conclusion holds for a general-relativistic quantum electrodynamically corrected force-free magnetosphere.