What Happens at the Center of a Black Hole?

[morequestions]

i was bored and my mind wandered. a question popped up and it got me interested in what others thought who are more informed than me:

since black hole is a theoretical construct (and hence can be geometrically perfect), what happens at the exact center of it. with uniform (assumed) density the geometric center of the black hole should have centripetally directed equal force of gravity perfectly in all directions, hence net zero force. so what happens there within this "singularity"? theoretically, there should be an equilibrium point of all forces near the center, even in a non-uniform black hole. as one radiates out from that equilibrium point there should be a graduation in variation of the force. as a consequence would there be a event horizon near the center of the black hole?

 

[mathman]

Current physics breaks down inside a black hole - quantum theory and general relativity are incompatable. Anything you suggest is purely speculative.

 

[PeterDonis]

since black hole is a theoretical construct (and hence can be geometrically perfect), what happens at the exact center of it.

There is no "exact center" in a theoretically "perfect" black hole; that is, there is no point at which the radial coordinate $r$ is zero. The singularity is often spoken of as $r = 0$, but the singularity is not part of spacetime.

What happens as you approach the singularity is that tidal gravity gets stronger and stronger. See below.

with uniform (assumed) density

Technically, I guess this is true since a "perfect" black hole is a vacuum solution, with density zero everywhere. But I don't think that's what you meant to say here.

the geometric center of the black hole should have centripetally directed equal force of gravity perfectly in all directions, hence net zero force.

The concept of "force of gravity" is not really a good one to use in GR in general, and it is certainly not a good one to use inside the event horizon of a black hole. Objects falling freely into a black hole feel no force just from falling. The only force they will feel is the force of the internal bonds between their constituent particles resisting tidal gravity.

theoretically, there should be an equilibrium point of all forces near the center

No, as you approach the singularity, as I noted above, tidal gravity gets stronger and stronger, increasing without limit as you get closer and closer to the singularity. Eventually it gets strong enough to overcome the internal forces of any object. There is no equilibrium anywhere.