“Based on a statistical analysis of 740 of the brightest supernovas discovered as of 2014, and the fact that none of them appear to be magnified or brightened by hidden black hole "gravitational lenses," the researchers concluded that primordial black holes can make up no more than about 40 percent of the dark matter in the universe. Primordial black holes could only have been created within the first milliseconds of the Big Bang as regions of the universe with a concentrated mass tens or hundreds of times that of the sun collapsed into objects a hundred kilometers across.”
“An as-yet unpublished reanalysis by the same team using an updated list of 1,048 supernovas cuts the limit in half, to a maximum of about 23 percent, further slamming the door on the dark matter-black hole proposal.”
If you really meant dense then you have to rememberer that the average density of a black hole enjoys an inverse proportionality to its volume. In other words a supermassive black hole is far less dense on average than a much smaller hole. However it is still far far denser than a whole galaxy, which is mostly empty space and diffuse dust.
I don’t think you meant dense though, I think you meant mass, because that’s sort of how your post seems to be phrased. The answer then is that it is a minute fraction of the mass of the galaxy. Sag A* is about 4 million solar masses, and the Milky Way has 250 billion stars, many of which are far more massive than Sol. Even ignoring other objects like stellar remnants and nebulae, the mass of the central black hole is negligable on the scale of the whole galaxy.
Similar hypotheses have been considered. The most popular (edit: AFAICT, but I'm not any kind of scientist), gravastars, would appear to have been ruled out by LIGO, as described here https://astronomy.stackexchange.com/questions/25449/gravasta... in the article linked therein. And as my current sibling comment mentions, they're not much good for dark matter either. They would be exactly as good as black holes for dark matter and, since they are still compact enough to do gravitational lensing, are ruled out by the same test
We know that the rotational velocity of a stellar object is proportional to the mass inside its orbit and inversely proportional to its distance from the center.
From measuring the velocities of stars in other galaxies, we find that the stars distant from the core are orbiting much faster than we'd expect them to. The velocity as you go out from the center should drop off quickly; it doesn't.
Therefore we hypothesize that there is a lot more matter at the outer reaches of a galaxy than what we're seeing.
So... you need not just more mass, but mass that isn't clumpy; mass that is mostly at the outer reaches of a galaxy and not the center.
A massive black hole at the center just doesn't cut it.
We measure black hole mass by their gravitational effect on stars or light (through gravitational lensing). Their density doesn't matter in these calculations since their mass is pretty much the first thing we know about them.
The whole point of a black hole is that nothing can support its own mass past a certain point. A black hole is a region more than it is an object, with a singularity beyond an event horizon. If there really is a singularity, it is a point or ring, not a sphere. There are other conjectures which replace the singularity with something else, like masses of strings, but it doesn’t really matter to the universe outside of the event horizon.
As to it being a source of dark matter, the idea that black holes and other compact objects are dark matter is encapsulated in the MACHO (MAssive Compact Halo Object) theory. It is extremely unlikely to be correct, because observations largely rule this out. Black holes warp spacetime around them and result in detectable phenomena as a result of gravitational lensing. It would appear that such lensing is not common enough to allow for black holes in sufficient quantity to explain dark matter.
“Based on a statistical analysis of 740 of the brightest supernovas discovered as of 2014, and the fact that none of them appear to be magnified or brightened by hidden black hole "gravitational lenses," the researchers concluded that primordial black holes can make up no more than about 40 percent of the dark matter in the universe. Primordial black holes could only have been created within the first milliseconds of the Big Bang as regions of the universe with a concentrated mass tens or hundreds of times that of the sun collapsed into objects a hundred kilometers across.”
“An as-yet unpublished reanalysis by the same team using an updated list of 1,048 supernovas cuts the limit in half, to a maximum of about 23 percent, further slamming the door on the dark matter-black hole proposal.”