Inside a black hole? Consider a neutron star with mass 1 gram less than needed for it to become a black hole. Since the neutron star is not (yet) a black hole, we can 'see' it. Send in the 1 gram and watch while the neutron star converts to a black hole
where, as usually proposed, the mass that was the neutron star suddenly shrinks to the "singularity" at the center of the black hole.
Now, it appears that there is a huge change -- neutron star to a black hole -- from a small input, the 1 gram, that is, in math terms, there is a jump discontinuity.
There was something about the physics of the neutrons that kept the neutron star from shrinking to a singularity. Well, maybe that something also keeps that mass plus the 1 gram from shrinking to a singularity. That is, if there is no jump discontinuity, the inside of that black hole is essentially just like that neutron star.