I was about to post just what Drakkith posted...
As a general comment, the 'singularity' at the center of a black hole is likely not anything 'infinite'...it's far more likely that such a result means our math doesn't work at those incredibly high gravities. Odd things seem to happen at such tiny,tiny Planck scales.
If you are referring to Heisenberg uncertainty then the answer as far as is known is definitely not...nothing 'faster than light'. It seems that at Planck scale, smaller than anything we can experimentally probe so far, instead of anything 'accelerating' without bound, what happens is that we are no longer able to distinguish between space, mass, time, and so forth...See 'quantum foam'
descriptions... It's a little like trying to distinguish water waves from sky when the waves get frothy...
Also, just so you know, 'acceleration beyond c' has no meaning...'c' is a velocity, acceleration is, well, acceleration...the rate of change of velocity. When you get a ticket for driving too fast, that's 'velocity' related no 'acceleration'.
In addition there is no 'exponential' mass associated with black holes. When a black hole
absorbs some energy or mass those are directly reflected, one to one, as a change in the mass and size of the horizon of the black hole.
If you search 'black holes' in these forums [via SEARCH, top of this page] you'll find lots of discussions on black holes...