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A lightyear is a system of measurement based off of how much distance light will travel in a year. But if light is heading away from a black hole that is close enough to be pulling it closer, isn't a lightyear in the negatives? Isn't the light travel speed slower in some places than others?

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Einstein's special theory of relativity is based on two simple postulates:

1) The laws of physics are invariant in all inertial systems.

2) The speed of light in a vacuum is the same for all observers.

The special theory has proven to be an accurate description of physics and thus these postulates are generally accepted as fundamental truths of the universe. Until an experiment is performed that violates any of the predictions of special relativity, we will continue to accept it as truth. Thus, according to postulate 2, the speed of light is the same no matter where you are in the universe, even close to the vicinity of black hole.

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    $\begingroup$ I think the OP is referring to co-ordinate speed, in particular the apparent light speed near the Schwarzschild horizon from the standpoint of an observer infinitely far away from the hole (which is what the co-ordinate $t$ in the Schwarzschild metric refers to). This apparent light speed indeed is slower near the hole. You need to stress that your point 2 is the local freespace light speed, i.e. that measured by an observer in a local laboratory confined to their momentarily comoving inertial frame. I think the OP needs a clarification of the difference between local and co-ordinate $c$. $\endgroup$ – WetSavannaAnimal Dec 7 '16 at 4:09

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