This reminds me of a question I’ve had for a while, and have not been able to formulate it well enough to do any searching for an answer on my own (total layman here).

Do we have any hypotheses of what the matter inside a black hole might be like? I mean “hypotheses” in a strict sense; I do not mean “a good/definitive answer”

To oversimplify a bit: white dwarves are supported by electron degeneracy pressure, and if such pressure is exceeded by gravity then e.g. a neutron star can form. Neutron stars are supported by neutron degeneracy pressure, and if such pressure is exceeded by gravity then a black hole can form.

For each of those “steps” we have an idea of what the matter within must be like to support/exceed such pressures. Are there any hypotheses for what the matter might be like after such known pressures are exceeded and a black hole is formed?