Could subatomic particles exist in a black hole singularity?

Question

Hypotheses of black hole singularities imply infinite density because a singularity is a dimensionless point with mass. However, subatomic particles constantly move. In this case, I see no possible way for a moving particle to exist in a singularity.

Alternately, hypotheses of quantum gravity imply that the center of a black hole is not a singularity but a 3D shape with a minimum radius of 1 Planck length.

Is there any convincing defense for fermions existing in a singularity? Or are all singularity models doomed for failure?

Answer 1

We don’t know.

We have two very successful theories which are relevant to this situation: general relativity, which describes gravity, and quantum field theory, which describes what we colloquially call “subatomic particles.” Each of these theories basically assumes the other doesn’t exist. People have been trying to come up with a way to use quantum field theory in the strong-gravity limit, or to describe gravity in a quantum-mechanical way, for nearly a century. All of the efforts have major problems.

Note that the Planck length is an estimate for quantum gravity’s length scale based purely on unit analysis, but in pop-science accounts it acquires an inappropriate sense of precision. If I told you that some predicted object was the size of a person, you would expect it to be more than a meter tall, but less than three meters. You wouldn’t say “well I’m a person, and I’m 157 cm tall, so this prediction is that the object is 157 cm tall.”

Answer 2

No, nothing can exist in a black hole singularity. The singularity predicted by General Relativity is an artifact of the theory which breaks down at r = 0. Note that the singularity being not a part of the manifold is a point in time. As long as we haven't a theory of quantum gravity we can't say anything about a possible state of matter in the center of a black hole.