With the density function of a black hole defined by the arguments given earlier, it begins to makes sense to ask "just what is it that black holes are made of?". We already know what they are made from - from neutrons from a neutron star - either by slow accretion or as an intermediate stage in the direct creation of a black hole from collapsing stellar matter. When a white dwarf becomes too large, we know it cannot sustain itself anymore and collapses to form a neutron star. All of the protons and electrons in it combine to form neutrons which will pack at a greater density. There is a sudden change of state. We could expect a similar change of state when a neutron star exceeds its size limit. We would expect that each neutron then becomes something else; something that can be compacted even more.
Neutrons are fermions. If they could, in any way, be converted into bosons, then there would be no immediate limit to the amount of compression they could sustain as bosons are not restricted from occupying the same point in spacetime, in the way fermions are.We could consider the possibility of Cooper pairs or a Bose-Einstein condensate (BEC). Others1,2 have already postulated the creation of such exotic species at the centre of a neutron star. Clearly, if either of these was created at the centre of a neutron star, the effect would be an immediate collapse as the star would start to shrink, creating better conditions for further creation. The neutron star would end up as a black hole. It would then seem natural to consider that the black hole itself would be composed of a Bose-Einstein condensate.