Merging black holes makes them less dense, so

Question

According to What is exactly the density of a black hole and how can it be calculated? (more specifically, John's answer here made me think: if you merge a whole load of chunks of an element heavier than iron (to prevent them from fusing), the resulting object would either be more dense than a black hole of the same mass, or would become less dense by becoming a black hole.

So which one of these would happen, in this hypothetical situation? Or would neither happen, but some completely different situation? Both seem impossible to me, since such heavy objects would have no way to prevent gravity from crushing them down (which implies it must become a black hole), but if a black hole would form, it would require gravitational energy input in order to become less dense. So that would exclude both possibilities, right?

Of course this situation would never occur in real life, but this hypothetical situation would have no angular momentum in the system, so no mass would be ejected.

Answer 1

If I understand you correctly you are concerned that a black hole somehow manages to become less dense than the matter that made it, as if it somehow expands against its own gravity to increase its volume.

However a black hole event horizon is not an object - it is just a place in spacetime. Although we can calculate a density by calculating the volume inside the event horizon this density is of no physical significance. The matter inside the event horizon is not uniformly distributed, as it is in a ball of iron, so all we are calculating is an average density.

Anything falling into a black hole rapidly reaches the singularity at the centre where the density is infinite (actually it's undefined, but let's save that complication for another day). So inside the event horizon you have empty space with a singularity at the centre. While there's nothing to stop you calculating an average density for this object your result doesn't have any special meaning.

Answer 2

There is nothing wrong in having something more dense than a black hole, large black holes can have densities less than water. If you put a lot of iron together it might or not become a black hole. An object of any density can be large enough to fall within its own Schwarzschild radius. The larger the black hole the lower the density, so you iron ball will become a black hole when it reaches the Schwarzschild radius: $r_s=\frac{2MG}{c^2}$, or $M=\sqrt{\frac{3c^6}{32 \pi \rho_{iron}G^3}}$

At that specific mass, the black hole has the same density as the iron, for larger masses the black hole will be less dense, and for less masses there will be no black hole. Thus, there is no way to create a black hole more dense than the mass used to make it. The created black hole, of any mass, will be less dense (or equal, if the mass satisfy the above equation) than the original material.