Black Holes are regions of space where things get weird [Citation Needed]. Past the event horizon of a black hole, any moving particle instantaneously experiences a gravitational acceleration towards the black hole that will cancel out it's current velocity, even light. That means that the gravity well of the black hole must be able to accelerate from -C¹ to 0 instantly². Given that fact, we can assume the gravitational acceleration of black holes is C/instant³. Given this, it stands to reason that in successive instants, the particle will be moving at speeds greater than C, because it is experiencing greater gravitational forces and continuous gravitational acceleration.

Does this actually make sense? Is there something I'm missing here? By this logic, it seems like anything inside of the event horizon of a black hole could and should move faster than C due to gravitational acceleration. 

**Edit:** I showed this question to a friend and he questioned if the hypothetical particles that were radiating from the singularity (The photon traveling exactly away from the black hole) might be hawking radiation; that is, the gravitation acceleration of a black hole is only strong enough to curve the path of light around a non-zero radius (thus not actually stopping it, but altering it's course), and not powerful enough to decelerate light. Is this actually what hawking radiation is, or is he as confused as I am?

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¹ Where movement towards the singularity would be considered a positive value, movement away from the singularity is a negative value, that is, anything moving at the speed of light away from the singularity would be moving with a velocity of -C relative to the singularity.

² If it couldn't accelerate from -C to 0 instantly, any photon traveling exactly away from the black hole would be able to escape the event horizon.

³ An instant is an arbitrary amount of time, it could be a fraction of a second, a second, a minute....