The understanding I have is that the speed of light is considered to be the highest attainable speed in physics. Of course there are theories of tachyons but since those haven't been proven we'll dismiss them for this statement. So, thinking mathematically, the speed of everything else is relative to the maximum value (using this logic I've always had an issue with believing there IS a max value instead of just infinity).
Using this line of thinking, how is it possible for some force to be able to overcome this universal constant? For example, the gravity of a black hole. Shouldn't that at most be able to equal the amount of force carrying a photon (or other body traveling at the speed of light) in the opposite direction? By this logic the only place that gravity could possibly even match the speed of light is at the center of the singularity, so it wouldn't trap any photons at all that weren't generated at that exact point.
I guess my point is that mathematically speaking, the largest "number" is infinity, and you can't have "infinity minus one" so why should the absolute largest possible speed be able to be influenced at all, let alone in a way that it can be completely negated and then some? Doesn't that completely invalidate $c$ as being the fastest possible speed? Perhaps it's just the fastest speed we've observed?
People far smarter than me have developed these theories and built whole areas of physics off of them, so I don't expect to be right. But can someone please explain to me why that's wrong?