Extended solution of the dipolar neutron star vacuum fields

Neutron stars are usually assumed to be perfect spherical conductors with a predominant intrinsic dipolar magnetic field anchored to their stellar surface. When including General relativity in the vicinity of compact objects, Maxwell's equations are modified, leading to changes in the exterior vacuum solution of compact neutron stars. In this regime, approximate solutions were obtained up to first order in the frame-dragging frequency parameter [e.g. L.Rezzolla et al, MNRAS 322 (2001)]. These corrections are usually considered for the electric field but are neglected for the magnetic field. Our extended solution includes the full first-order correction on both electromagnetic fields. We tested the validity of the derived solution by prescribing it as an initial value problem to two-dimensional particle-in-cell simulations. We discuss the relevance of this solution to particle-in-cell simulations, highlighting the differences to previously proposed solutions. Finally, we address future possible extensions of this work.