I am well aware of what the conventional model states, such as, I am well aware we have been led to believe that the speed of light cannot change. Yet I give you an example in which the extreme current model of gravitational physics predicts light can completely slow down around a black hole. Is it now moving at the speed of light?
Also, light does not possess a frame of reference, which means, to which observer is the photon moving at the speed of light constantly? To an observer sitting outside a gravitational system, we can feel quite comfortable to say that the speed of light technically varies in a [general sense] while the speed of light is constant in absence of gravitational field (which is by no other name), [special relativity]. We don't destroy anything fundamental within relativity by stating these things, in fact, the notion of a gravitational aether (and later models that predicted that light can escape black holes) solves many problems. For instance, light does not come to a standstill around a black hole, you will eventually see a test pilot pass the event horizon. Information additionally is allowed to escape, which is an on-going mystery.
As I said, nothing in relativity breaks down, but under gravitational aether theory, we not only understand why curvature should exist, but we come to understand solutions to other very important questions that surround the theoretical black hole and other various gravitational studies. I have plenty references, for instance, supporting the gravitational aether. Perhaps tomorrow I will go to my blog and chase a few up for you.
My last words for now would be, be careful just accepting that the speed of light cannot vary, when experimentally speaking, we know light slows down in gravitational fields. If light could not slow down, we wouldn't have ridiculous notions of observers sitting outside an event horizon in which they never see their test pilot pass the boundary because the light never reaches them. But if light can only approach zero, then we avoid these kinds of paradoxes. Variable Newton's constant, also required in this theory, is [at least] backed with some hard evidence and anomalies suggested it is not a constant.