# Multipolar electromagnetic fields around neutron stars: general-relativistic vacuum solutions

## TL;DR

This paper derives approximate analytical solutions for multipolar electromagnetic fields around neutron stars in a general-relativistic framework, accounting for strong gravity and rotation effects, and assesses their impact on neutron star spindown and radiation.

## Contribution

It extends Newtonian multipole solutions to include general relativity and frame dragging effects around neutron stars, providing new formulas for electromagnetic fields and luminosity estimates.

## Key findings

- Frame dragging has negligible effect on spindown luminosity.
- Higher multipoles can radiate more efficiently via electric fields.
- Corrections due to strong gravity and spin are quantified.

## Abstract

Magnetic fields inside and around neutron stars are at the heart of pulsar magnetospheric activity. Strong magnetic fields are responsible for quantum effects, an essential ingredient to produce leptonic pairs and the subsequent broadband radiation. The variety of electromagnetic field topologies could lead to the observed diversity of neutron star classes. Thus it is important to include multipolar components to a presumably dominant dipolar magnetic field. Exact analytical solutions for these multipoles in Newtonian gravity have been computed in recent literature. However, flat spacetime is not adequate to describe physics in the immediate surrounding of neutron stars. We generalize the multipole expressions to the strong gravity regime by using a slowly rotating metric approximation such as the one expected around neutron stars. Approximate formulas for the electromagnetic field including frame dragging are computed from which we estimate the Poynting flux and the braking index. Corrections to leading order in compactness and spin parameter are presented. As far as spindown luminosity is concerned, it is shown that frame dragging remains irrelevant. For high order multipoles starting from the quadrupole, the electric part can radiate more efficiently than the magnetic part. Both analytical and numerical tools are employed.