Is there a singularity at the center of a black hole? Or, are there undiscovered repulsive fundamental forces preventing complete collapse whose effects manifest only at extremely high densities found inside black hole event horizons?
On one hand, because it takes place inside the event horizon, we may never know. On the other hand, particle accelerator experiments, cosmic ray observations, astronomical observations of the aftermath of the Big Bang, and possibly observations of a naked singularity (perhaps artificially constructed) may provide information about additional fundamental forces.
Assuming there is another force, what might the inside of a black hole's event horizon look like / be like? The accretion disc probably continues inward, though radiation from it does not escape. A central sphere of condensed matter. General relativity will make space and time very weird inside.