Correct me if I’m wrong, but from books I’ve read it is a apparent that black holes are cold. I can understand it being cold from an outsiders perspective since heat would have a hard time escaping, but wouldn’t all that matter, being so compressed, produce tremendous internal heat like the sun but magnitudes larger?
Also internally, wouldn’t fusion reactions be the norm and eventually fuse into a single gigantic nucleus-like atom?
Can a black hole continue to collapse once all the space between particles is taken up, or will multiple particles exist in a single space?
A black hole is already collapsed. All the matter which fell into it is compressed beyond fusion (as in stars), beyond forming a single massive ball of neutrons and protons (as in a neutron star), to the point where it essentially becomes a one-dimensional point.
The mass contained in a black hole doesn’t have a temperature as we usually consider it. But according to Hawking, energy constantly leaks out at a rate determined by the size of the black hole. In a large black hole the Hawking radiation is effectively at a very low temperature. Very small black holes theoretically have a very high temperature of Hawking radiation.
AndrewL is right; but let me say a little more about the “insides” of black holes. The geometry inside the event horizon of a black hole is not how you’re probably imagining it. From the outside, a (nonrotating) black hole looks like a spherical blackbody, radiating at some (usually) very low temperature. But from the inside, a black hole does not look like the inside of a sphere, empty except for some dense concentration of mass at the center. Inside of a black hole, spacetime is warped so much that the direction “toward” the singularity (the “center” of the black hole) becomes timelike. The singularity isn’t “over there,” it’s “tomorrow” (or, more likely, a few microseconds from now). On your brief trip to the singularity, tidal forces will stretch and compact you, which will raise your temperature, but the temperature “at” the singularity is a meaningless concept because it’s a one-way trip.