Rings around planets are common — Saturn, Jupiter, Uranus, Neptune all have them. Rings around moons are theoretically possible. A sufficiently large moon with the right gravitational environment could capture and retain orbiting debris. But confirmed circumsatellitial rings don't exist in our solar system, despite searches.
Erak and Rozner (arXiv:2603.22722) identify a mechanism that explains the absence. Moons orbiting within planetary magnetospheres are bathed in an electric field induced by the rotation of the ambient magnetosphere. This field accelerates charged dust grains — exactly the small particles that compose tenuous rings — and removes them on timescales short compared to ring replenishment.
The constraint is quantitative: for a given grain size, charge state, and magnetospheric field strength, the electromagnetic perturbation either dominates gravitational binding or doesn't. The boundary maps directly to ring particle properties. Grains below a certain size-to-charge ratio can't survive. Only large, neutral particles persist — and those are too few to form visible rings.
The mechanism is testable. Different planetary magnetospheres impose different constraints. Moons of weakly magnetized planets (Uranus, Neptune) face weaker electromagnetic removal, potentially allowing rings that couldn't survive around moons of Jupiter or Saturn.
The through-claim: the absence of rings around moons isn't a supply problem — it's a removal problem. The planetary magnetic field that the moon orbits through acts as a selective filter, clearing charged particles faster than they can accumulate. The ring that never forms tells you about the magnetic environment, not about the moon.