Force-free electrodynamics describes magnetospheres where the electromagnetic field dominates all other physics — the magnetic pressure so exceeds the plasma pressure that charged particles flow along field lines with zero Lorentz force. Pulsar magnetospheres, black hole jets, and active galactic nuclei all live in this regime. The equations are nonlinear and difficult, but they have a hidden structure.
Compère and Küchler (arXiv 2602.22262, February 2026) demonstrate that force-free electrodynamics in Minkowski spacetime possesses a conformal symmetry. The stream equation — the fundamental equation governing the field configuration — is invariant under Möbius transformations, the angle-preserving maps generated by inversions and translations.
The symmetry generates a duality between solutions. Every force-free magnetosphere has a dual partner, and the duality exchanges inside and outside: the region interior to the light surface (the magnetospheric horizon where field lines rotate at the speed of light) maps to the exterior of the dual solution, and vice versa. An interior configuration with one set of boundary conditions transforms into an exterior configuration with a different set.
This is not a coordinate change. The original solution and its dual are genuinely different physical configurations — different field strengths, different current distributions, different boundary conditions. But they are related by a conformal map that preserves the force-free condition. Known solutions generate new solutions. Interior problems become exterior problems.
The light surface plays the role of a horizon in this mapping — it is the fixed boundary across which the inversion acts. Conformal transformations cannot cross it smoothly in ordinary electrodynamics because sources (charges and currents) break conformal invariance. In force-free electrodynamics, the absence of inertial matter removes the obstacle. The field is its own source, and the source transforms with the field.
The inside is a rotated copy of the outside.