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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.

The Theory Of Everything

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    $\begingroup$ In whose coordinate system? $\endgroup$ – user12029 May 10 '16 at 21:30
  • $\begingroup$ ??! What. In spacetime..... GR $\endgroup$ – RaSullivan May 10 '16 at 21:39
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    $\begingroup$ The sense in which "a ray of light hovers on the edge of a black hole" is that the world-line of a particle $(ct,R,0,0)$ (as the coordinate $t$ advances and $R$ is constant right on the edge of the black hole, the Schwarzschild radius) covers zero proper time with the Schwarzschild metric. This is a very precise statement and it's very easily misunderstood by an audience looking for popular science! $\endgroup$ – user12029 May 10 '16 at 22:03
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    $\begingroup$ (My point being: your question has, built into it, the assumption of a coordinate system, and the notion of a coordinate suggestively labeled $t$.) $\endgroup$ – user12029 May 10 '16 at 22:10
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    $\begingroup$ Additionally. I am making a serious inquiry and you should not preassume my intellectual status in your comments, ThankYou! $\endgroup$ – RaSullivan May 11 '16 at 0:18
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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.

There are lots of questions and material about this and related subjects on physics.stackexchange which might be helpful.

Aside: Apologies for the extremely pedantic and unhelpful comments you received on your question.

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  • $\begingroup$ Extremely helpful. $\endgroup$ – RaSullivan May 11 '16 at 17:47
  • $\begingroup$ What about the outgoing light, same thing? Outside observers couldn't tell in infalling or outgoing? $\endgroup$ – RaSullivan May 11 '16 at 17:49
  • $\begingroup$ For outgoing light-rays, it would be the reverse idea. If they start very near the event horizon, they seem to be going incredibly slowly (though still moving away somewhat) and as the distance from the BH grows, they seem to be moving faster and faster. Most light we see comes from distances of a few times the event-horizon radius, instead of right up next to it though. $\endgroup$ – DilithiumMatrix May 11 '16 at 18:04
  • $\begingroup$ Very helpful. I appreciate the knowledge, and I get it! $\endgroup$ – RaSullivan May 11 '16 at 23:41
  • $\begingroup$ Awesome, glad I could help! $\endgroup$ – DilithiumMatrix May 11 '16 at 23:45

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