For big galaxies with bulges, the mass (not density) of the black hole is about 1/700 of the mass of the bulge. No one knows why but some kind of joint evolution is the most popular theory.
No firm correlation between galaxy and central black hole mass has been established to date. The central black hole masses of Andromeda and our galaxy are quite modest compared to the monster black holes in some similarly massive galaxies. Black hole density, however, is an easier question. All black holes are equally dense.
"All black holes are equally dense."
This is not true unless you are thinking of the infinitely dense singularity.
The radius of a black hole is proportional to its mass.
The volume is proportional to its radius cubed.
Therefore its density is inversely proportional to the mass squared.
It is very high for stellar mass black holes, but comparable to ordinary densities for supermassive black holes.
Yes, I was thinking about that thing at the center. I do not believe it is infinitely dense, but, so close as not to matter. Infinities suggest the model has broken. When we have a working theory of quantum gravity, the infinite density thing should go away.
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