In The Universe in a Nutshell chapter 4, Hawking explains the warping of spacetime according to general relativity.
Near a massive but ordinary star, spacetime is warped such that the light emitted from the star appears to move slower when near the star, and appears to "speed up" to the constant speed of light c when away from the star, from the viewpoint of an outside observer. Of course, we can't directly measure this experimentally because there is no way to measure the speed of light near a star from the reference point far away from a star. (Do I have this right?)
Hawking writes that this "slower" light is due to the warping of spacetime near the star, and this leads into the discussion of how spacetime and light behaves near a black hole.
I've always heard that light cannot escape a black hole due to the extreme gravity from the super-dense black hole (star). And so it make sense that near an ordinary massive star, light can escape but "struggle" to do so, going "slower" near the star before "breaking free" and "speeding up" to what we see as the speed of light farther away from it. (I use scare quotes as I realize these idioms are shortcuts for understanding relativity and not literally true. Feel free to correct me if I am using them incorrectly.)
So which is it? Is the light escaping from a massive star held back a bit by the pull of gravity, or by the warping of spacetime near it? Or is it both, additively? Or are both concepts two sides of the same coin in a way I am missing?