Conformal symmetry in force-free electrodynamics

TL;DR

This paper demonstrates that conformal symmetry, specifically M"obius transformations, can be present in force-free electrodynamics, revealing structural links between solutions and mapping regions inside and outside magnetospheric horizons.

Contribution

It shows that the force-free electrodynamics equations are invariant under M"obius transformations for certain free functions, uncovering new symmetries and solution mappings.

Findings

The stream equation in FFE is invariant under M"obius transformations.

Conformal symmetry links solutions inside and outside magnetospheric horizons.

Certain free functions in FFE admit conformal invariance.

Abstract

It is shown that conformal symmetry exists in force-free electrodynamics (FFE) in Minkowski spacetime, a foundational framework for describing magnetospheres around astronomical objects. In force-free magnetospheres, charges are constrained to move along magnetic field lines and experience zero Lorentz force, due to the everywhere perpendicular orientation of electric and magnetic fields. However, a general angle-preserving conformal mapping of force-free fields does not necessarily produce another physically admissible force-free configuration when sources are present. In this work, we demonstrate that such invariance can nevertheless arise for certain choices of the free functions. Specifically, the governing stream equation is shown to be invariant under M\"obius transformations. This symmetry reveals a structural linkage between known solutions and, notably, maps the region inside a magnetospheric horizon (the lightsurface) of one solution to the exterior of its dual counterpart, and vice versa.