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Magnetic frame-dragging correction to the electromagnetic solution of a compact neutron star

Neutron stars are usually modelled as spherical, rotating perfect conductors with a predominant intrinsic dipolar magnetic field anchored to their stellar crust. Due to their compactness, General Relativity corrections must be accounted for in Maxwell's equations, leading to modified interior and exterior electromagnetic solutions. We present analytical solutions for slowly-rotating magnetised neutron stars taking into account the magnetic frame-dragging correction. For typical compactness values, i.e. $R_s \sim 0.5 [R_*]$, we show that the new terms lead to a percent order correction in the magnetic field orientation and strength compared to the case with no magnetic frame-dragging correction. Also, we obtain a self-consistent redistribution of the surface azimuthal current. We verify the validity of the derived solution through two-dimensional particle-in-cell simulations of an isolated neutron star. Defining the azimuthal electric and magnetic field amplitudes during the transient phase as observables, we prove that the magnetic frame-dragging correction reduces the transient wave amplitude, as expected from the analytical solution. We show that simulations are more accurate and stable when we include all first-order terms. The increased accuracy at lower spatiotemporal resolutions translates into a reduction in simulation runtimes.