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Little thought experiment. An observer places a mirror and a clock 1 lightyear away from a black hole. He then goes in the black hole's gravitational field at a point where he sees the clock tick at 2 seconds per second. When he blinks a laser towards the mirror, he should see the light return to him in about 1 year from his reference frame, although the light traveled 2 lightyears total.

Is it more accurate to describe that the light really only traveled 1 lightyear, or that it traveled at 2c? Are they both equally good ways to describe the situation?

Just to push this a little bit, approaching the event horizon, the light signal would return almost instantly (The observer always stays at a constant distance from the black hole when waiting for the signal to return). Does space farther from the black hole contract to 0 from the observers frame or is it better to describe it as light moving at nearly infinite speed?

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    $\begingroup$ I think you may be looking for proper length and proper time in general relativity? $\endgroup$
    – g s
    Commented Oct 14, 2023 at 21:55

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It really doesn’t matter. Neither way is more or less accurate than the other.

Remember, the requirement that the speed of light is $c$ is only for inertial frames. In curved spacetime inertial frames are only local. So there is no requirement or constraint on the time or the distance in your scenario. You can literally choose the time to be whatever you like and the distance to be whatever you like and there will be some coordinates where that is correct.

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