>> edit: Ah, I see the snag. There isn't a second event horizon inside the black hole. Just because opposing gravitational forces cancel each other out in the c

>> edit: Ah, I see the snag. There isn't a second event horizon inside the black hole. Just because opposing gravitational forces cancel each other out in the center (and space is flat there) does not mean time is any less distorted by all the surrounding mass. Exactly. The relationship between mass, space, and time is complicated but there is a causal link going (roughly) in the direction of mass -> space -> time. The presence of mass warps space which dilates time (ignoring special relativity and quantum gravity which makes it weirder). The combined effects of the gravitational force (pressure) necessitates an increase in density, which further warps space, which further dilates time around the singularity. Time dilation isn't "fighting" the force of gravity and the warping of space, it is an observational effect that is only meaningful outside of the reference frame of the singularity. All other forces and phenomenon are already dependent on time so if the laws of nature do exist inside of a singularity, the existence of other effects like brownian motion will be entirely dependent on the mass/gravitational forces (aka they likely wouldn't be relevant due to the overwhelming effect of compressing matter and energy to such a small volume).