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Electromagnetic waves travel mostly in vacuum medium, in outer space, but sometimes in gaseous media, such as in gaseous atmospheres involved in nebulae. If electromagnetic-waves come anywhere in the vicinity of a black-hole, the whole of it enters the black-hole. Can we suppose, that the event-horizon of the black-hole acts in a way like an interface, separating two optical media with different refractive indices : vacuum (the medium from which EM waves are "incident"), and the unknown medium beyond. If, this supposition holds true, then, we would know one thing at least regarding this unknown medium, that, EM waves travel in this medium with a velocity > c, as this medium is rarer, than vacuum itself.

(Question of an amateur)

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  • $\begingroup$ Refraction occurs due to a sudden phase velocity change in a physical medium. Crossing the event horizon is not the same and there is no refraction. $\endgroup$ – user6972 May 14 '14 at 16:43
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I'm afraid the behaviour of light near an event horizon is altogether more complicated than you suggest. You work out the path a light follows by calculating the null geodesic, which is not that hard as problems in GR go but it's still formidable for non-nerds.

To give some idea of the complexity, the answer you get depends on who you ask. If you sit outside the event horizon watching the light fall in then you'll never see the light cross the horizon. That's because from your perspective the light slows as it approaches the even horizon and actually comes to a halt at the horizon itself. You would have to wait an infinite time for the light to even reach the horizon let along cross it. However if you're falling into the black hole then after you've crossed the horizon you can see light cross the horiozn after you and catch you up.

You can model the effect of a black hole on light as a change in refractive index near the black hole. However in this model the refractive index rises the closer the light gets to the event horizon and it goes to infinity at the horizon.

It is possible to get refractive indices of less than one, and it can even go negative. This happens in anomalous dispersion. However it's only the phase velocity of the light that is $> c$ so this doesn't violate relativity.

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