>>12000808The key word is "average". It is easy to obtain the estimate , where is the BH's mass. However, the problem here is about the physical meaning of this parameter. We are using the definition of density, of course, but one is using an estimate based on the Schwarzschild radius, so that's only an average, which moreover is assuming that the BH's mass is distributed all over the spherical region enclosed by it. We cannot know that, as far as I am concerned. We do not have information about the "real" volume where all the mass is actually compressed. So, IMO, the density calculated in such way is just a lower bound to the real density, as we cannot know any further. (For the sake of absurdity, all the mass could be squeezed into a point and then you would have , considering that point in the origin of our coord. frame. That would produce a infinite density for any non-zero mass)
So, a more honest response, but quite disappointing, is that the density of a black hole is not well-defined, because several definitions have problems with the physical interpretation.
