Correct.The Speed of Light as Measured by Non-Inertial Observers

That the speed of light depends on position when measured by a non-inertial observer is a fact routinely used by laser gyroscopes that form the core of some inertial navigation systems. These gyroscopes send light around a closed loop, and if the loop rotates, an observer riding on the loop will measure light to travel more slowly when it traverses the loop in one direction than when it traverses the loop in the opposite direction. This is known as the Sagnac Effect. The gyroscope does employ such an observer: it is the electronics that sits within the gyro. This electronic observer detects the difference in those light speeds, and attributes that difference to the gyro's not being inertial: it is accelerating within some inertial frame. That measurement of an acceleration allows the body's orientation to be calculated, which keeps it on track and in the right position as it flies.

You will sometimes find discussions that insist the only correct way to describe the Sagnac Effect is by reference to an inertial frame: they will say that the only concept with meaning is the locally measured speed of light, which is c, and that what the non-inertial observer sitting on the loop says about the motions of two light rays has no physical meaning. Whilst the Sagnac effect is easy to calculate using an inertial frame—because then we can use the simple equations of adding velocities in special relativity—it doesn't follow that any non-inertial description of it is invalid. Those who insist that non-inertial descriptions are invalid are like the man whose house is about to be picked up by a cyclone: they will shout "Don't worry folks! The wind isn't really circulating at 300 km/h. It's really Earth that's rotating in an inertial frame, and the resulting differential motions give rise to the illusion that the wind is about to shred this house." Yes, it's certainly valid to analyse the situation using Newton's laws in an inertial frame. But you might want to hang on to your house while doing so.

You might also find it said that the Sagnac Effect is somehow not measuring the speed of the two light beams sent around the loop, but "merely" their times of flight, as if that's somehow different to measuring their (average) speed. But the simple fact is that if you send two horses in opposite directions around the same race track, then the horse that crosses the finish line first must have run faster. The different arrival times of the two light beams have nothing to do with anything strange going on with "the geometry of spacetime": this discussion holds in the absence of any gravity, in which case spacetime can be flat, and if it's flat for one observer, it's flat for all, including those sitting on rotating loops. The observer sitting on the rotating loop concludes that the beams simply move at different speeds. And that's all right, because it's only either an inertial observer who must measure their speeds to be both c, or an observer sitting right next to the light beams. But the observer on the loop is neither inertial nor sitting right next to each beam at all times of its flight.

Discussing non-inertial observers can be simpler if we consider not the rotating frame of a laser gyroscope, but the "uniformly accelerated" frame of someone who sits inside a rocket, far from any gravity source, accelerating at a rate that makes them measure their weight as constant. ...

Is The Speed of Light Everywhere the Same?

But the sagnac effect probably isn't the most direct example of varying c as observed from two different, non-inertial reference frames.

One can simply take a black hole, whose radiation will never reach earth (implying c=0) from the point of view of an observer on earth. However, for an observer within the event horizon of a black hole, radiation is still travelling at the speed of light.