that it compressed the matter within the core to such a degree that all energy was squeezed out. All atomic and subatomic particle movement was so crushed together that all movement stopped.

That cannot happen. Energy isn't like a liquid you can squeeze out of objects like water from a sponge. It is an intrinsic property of objects, even when they aren't moving. Two electrons held a distance apart from one another will have energy due to their potential energy interactions, even if they are not moving. But that isn't possible either, since particles ALWAYS move, as I'll address now...

With all movement stopped, there was absolutely no heat generated (absolute zero), but because of the extensive mass, an inescapable gravitational field was formed.

An object at 0K will still have moving particles. If they stopped they you'd be able to measure their positions and momenta so precisely you'd violate the uncertainty principle. At absolute zero particles still jitter about, just not as much as at higher temperatures. This is similar to the quantum vacuum not being empty, it always has matter and energy in it even if you remove everything you can, as particles flitter in an out of existence due to the uncertainty principle and the relativity relation $$E^{2} = (mc^{2})^{2} + (pc)^{2}$$.

As this captured mass was drawn into the center of this massive gravitational field at an ever increasing rate of acceleration (at a rate approaching c^2)

The units of acceleration are not equal to the units of $$c^{2}$$, it is physically meaningless to say what you just said.

it gradually begins to transform all its energy into mass [m=(c^2)/E]. The converted energy (into mass) then accumulates on the core at absolute zero.

Something falling into a black hole will indeed increase the black hole's energy and mass yes.

Could such a region of space tie "relativity" and "quantum mechanics" together?

You need to understand what the "Tying them together is hard" means. Quantum mechanics plus

*special* relativity is already combined, it is called quantum field theory, developed from the 1930s onwards. It is the QFT stuff which models how mass and energy of particles relate, allowing them to convert into other particles or to appear and disappear via uncertainty. If you only consider a very small region of space, even near, on or inside an event horizon, then you can model the particles using standard QFT. What presents a problem is considering particles moving over non-tiny distances within a strong gravitational field, this requires tying together quantum mechanics and

**general** relativity, which is the difficulty.

There are various partial solutions, semi-classical field theory for instance, which make some simplifying assumptions about the gravitational field, ignore a number of otherwise complicated processes and lead to things like Hawking radiation and black hole thermodynamics. Provided the gravitational field isn't too strong and the particles aren't too massive then semi-classical field theory is viable. It's when you get particles close to the Planck mass and/or particles within a few Planck lengths of the black hole singularity that it all goes to hell in a hand basket. It might sound counter intuitive but the event horizon itself isn't much of a problem, provided you're careful and you've formalised everything properly. Unless you have a micro-black hole of only a few Planck masses the event horizon is far enough away from the singularity that you can do semi-classical calculations and use current field theory models to describe particle dynamics. Once you're within a few Planck lengths of the singularity you can no longer ignore all of the quantum gravity corrections which semi-classical field theory throws away. Then you either need quantum gravity or you need to go home.

The Planck scale is, in a qualitative way, the distance at which gravity stops looking like Einstein's gravity and starts looking like quantum mechanics but in a way we currently do not understand. Provided you aren't considering Planck scale physics there isn't too much of an issue between quantum mechanics and relativity. Unfortunately Planck scale physics is where a lot of interesting cosmology and 'theory of everything' questions lie, since at some time in the past ALL of the universe was contained with the Planck scale.