2025MNRAS.543..273S

Magnetar phenomena are likely intertwined with the location and structure of magnetospheric currents. General-relativistic effects are important in shaping the force-free equilibria describing static configurations, though most studies have quantified their impact only in cases of axial symmetry. Using a novel methodology based on physics-informed neural networks, fully three-dimensional configurations of varying stellar compactness are constructed. Realistic profiles for surface currents, qualitatively capturing the geometry of observed hotspots, are applied as boundary conditions to deduce the amount of free energy available to fuel outburst activity. It is found that the lowest energy solution branches permit only a ${\approx} 30~{{\ \rm per\ cent}}$ excess relative to current-starved solutions in axisymmetric cases with global twists, regardless of compactness, reducing to ${\approx} 5~{{\ \rm per\ cent}}$ in 3D models with localized spots. Accounting for redshift reductions to their inferred dipole moments from timing data, explaining magnetar burst energetics therefore becomes more difficult unless the field hosts non-negligible multipoles. Discussions on other aspects of magnetar phenomena are also provided.