Abstract: We study the massless Vlasov equation on the exterior of the subextremal and extremal Reissner-Nordström spacetimes. We prove that moments of solutions decay at an exponential rate in the subextremal case and obtain a sharp inverse polynomial decay rate along the event horizon for the extremal case. Furthermore in the extremal case we derive a condition under which transversal derivatives of certain components of the energy--momentum tensor do not decay along the horizon. Our results may be viewed as analogous to the Aretakis instability. Our proof does not rely on the existence of a conservation law.