According to Prof. Hawking, light rays will 'hover' on the edge of a black hole. If this is true, and the light 'stops' on the edge, how can the electric/magnetic fields which, constitute the light, continue their self-perpetuating state?
What does Hawking mean? His quote is,
the boundary of the black hole, the event horizon, is formed by rays of light that just fail to getaway from the black hole. Instead, they stay forever, hovering on the edge of the black hole.
Hawking, I believe, is referring to a more metaphorical 'hovering'. As light, or anything, approaches the event horizon, it becomes more and more redshifted---it's motion appearing to go slower and slower and slower, approaching zero apparent velocity to an outside observer (approximately) infinitely far away. Anything falling into a BH, thus appears to end up 'hovering' just outside of it.
From the perspective of the object falling into the BH, or an observer traveling nearby/similarly to it, nothing special happens. To the infalling observer, time still seems to pass normally... everything is the same. So there is no problem with the electromagnetic wave itself behaving (basically) normally as it approaches the blackhole.
Aside: Apologies for the extremely pedantic and unhelpful comments you received on your question.
