The question that ponders upon the thought if the speed of light really is constant is a fairly common question. However, I was wondering about something and MAYBE this can provide some backup to the theory that the speed of light isn't constant, please point out any mistakes I make in stating theories wrongly, using the wrong theories in the wrong context of use, etc as I am just learning about physics. If Einstein's General Relativity states (just as an example that uses General Relativity) that light bends when it gets close to the Sun because of the Sun's huge gravitational pull, then wouldn't the speed of light (when close to the Sun and is bent) increase because the gravity is pulling it down faster as it gets closer? Is it the path of the light or is it light itself that is "bending"? Is light simply following the contour of space-time which doesn't change it's speed? It's like when you put the bowling ball on a trampoline, then you put a billiards ball on there, then the billiards ball falls towards the bowling ball cause it has more mass and so if we let the trampoline symbolize the fabric of space-time, the bowling ball as perhaps the Sun or any star for that matter, and the billiards ball as light (photons), the billiards ball increases momentum and speed as it reaches the bowling ball, same thing with light, it increases momentum and speed as it reaches the Sun (any star), and for it to have momentum, it must have mass, if it has mass, then it's affected by gravity, therefore, gravity affects light changing its speed at certain times, am I correct?