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This question already has an answer here:

Prior to a black hole reaching sufficient (size ) to stop radiating light (due to excessive gravity ) would the speed of radiation of light slow smoothly down to zero (as the hole draws closer to the critical size)

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marked as duplicate by Qmechanic May 16 '18 at 20:02

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    $\begingroup$ have a lool at the answer here physics.stackexchange.com/q/145110 to get a feel of what is happening with the speed of light in general relativity $\endgroup$ – anna v May 16 '18 at 17:48
  • $\begingroup$ I'm interested in the smoothness of the velocity change in the question.... $\endgroup$ – RaSullivan May 17 '18 at 19:40
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The local speed of light, as measured in the coordinates of any inertial observer, is always the same. There is no change during the formation of a black hole.

The coordinate velocity of the speed of light could change during formation of a black hole, depending on what coordinates you're using. This is of little interest, because you can always make a coordinate velocity be whatever you like, by choosing the necessary coordinates. This is true regardless of whether there is a black hole or a gravitational field.

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