The question I'm asking is the following: at which state is the matter inside a black hole? I know that supermassive black holes have a density very low, while stellar black holes have a very high density. However, the concept of density cannot be defined within a black hole because the metric tensor diverges, and therefore the concept of distance cannot be defined. But I think it is not even a question of density, but of defining whether matter is composed, for example, of atoms or elementary particles.
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I know that supermassive black holes have a density very low, while stellar black holes have a very high density.
This is not true. The interior of a black hole can have matter with any density you like, including zero. The standard black hole models that people normally study are vacuum solutions, so the density is zero everywhere.
However, the concept of density cannot be defined within a black hole because the metric tensor diverges,
I would put this in a different way. Everything misbehaves at the singularity, but we can still define the notion of a singularity that is or is not a strong curvature singularity (SCS). As matter approaches an SCS, its density goes to infinity. As matter approaches a non-SCS singularity, it can be subjected to infinite tidal forces (spaghettification), but its density stays finite. Astrophysical black holes probably have non-SCS singularities, as do all the simple mathematical models of black holes that we normally study. Therefore the density remains finite at all times -- in fact, it stays constant as the matter infalls. The matter that reaches the singularity simply doesn't exist in our spacetime manifold anymore.
But I think it is not even a question of density, but of defining whether matter is composed, for example, of atoms or elementary particles.
The infinite tidal forces would certainly destroy atoms and nuclei. We don't know what happens at the Planck scale.