Consider a pair of identical extremal black holes at rest. It is a fact that they exert no net force on each other and remain in static equilibrium. Now, clearly, each of the black holes is in equilibrium under the combined action of the gravitational and electromagnetic forces. Thus, none of the black holes is in a free fall. This implies that each of them should be emitting electromagnetic radiation in accordance with the equivalence principle--because they are accelerated with respect to the local inertial frames. But this would mean that they are losing mass without losing charge. And clearly, this means that they get spontaneously converted into naked singularities. Is there a flaw in this line of reasoning?