Speed of the light is not (and it is at the same time) the same thing with the speed of the photons
The thing that the time dilation causes is that the speed of the photon is not stable but the speed of the light is always stable at the same time. The thing is that gravity would slow the photons but it always slows the time, and that means that the speed of the light is always 299 792 458 m/s. That speed is the fastest possible speed to reach in the straight universe.
So the photon would travel slower than we are walking if the gravity field behind it is strong enough. The time dilation would cause that if we would try to make the race with those photons we would not reach them, and we would meter their speed to the 299 792 458 m/s if we would be in that gravity field.
So what would be first, what drops in the black hole, photon, piece of iron, or the brick? The answer is that gravity would affect all particles in the same way. But there is one rule the escaping velocity must be higher than the speed of light that the photon could drop in the black hole.
And the point where the photon drops in the black hole is called "event horizon". That means that the particle drops through this point speed that is higher than the speed of the light, but does it ever come back? Does the black hole grow until it would form the wormhole with another black hole? Or would every black hole grow until they are eating the entire galaxy?
The speed of light is stable, but the speed of photons is chancing and the time dilation causes that the speed of the light is stable. We know that there are differences in the speeds of photons, but we cannot observe them. The speed of the light is always stable because the gravity would dilate time in the space near the photons.
But before we would see the difference between the speed of photons requires we would step away from our dimension. The reason why I just wrote that the speed of the light is not stable is that it depends on gravity, what effects to photons, what is traveling outside the center of gravity.
But why the speed of the light is still stable if we are looking at the thing in the same dimension is that the gravity dilates the time, and the time would go slower in the strong gravity field. So if the supermassive object would be close enough, that thing would slow the photons, but it also slows the time. And that means that we always would see that the speed of the light is stable.
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