Would particles still obey laws of quantum mechanics once it enters a black hole?

Many people seem not to understand that the solutions to the General Relativity field equations - which we use to describe black holes - are continuous across the event horizon. This means that space-time changes smoothly across the event horizon. There is no discontinuous change in space-time so there should be no discontinuous change in the laws of physics.

The Scharzschild solution for a black hole unfortunately uses coordinates that are singular at the event horizon. This has led to confusion that something dramatic happens at the event horizon. A proper choice of a coordinate system is perfectly well behaved across the event horizon - no drama at all.

There is an active area of research concerning disagreements between General relativity and quantum mechanics at the event horizon (firewall problem). Not sure whether anyone can definitively say whether one, or the other, or both need to change.

Since spacetime and mass are not inherently quantum, we can expect quantum mechanics to hold everywhere there are particles. So across the event horizon for sure, quantum mechanics will hold.

Since we now believe it is possible that this Universe is "a" black hole in a container Universe, then we can easily say that quantum mechanics is expected to hold for the entire fall to the "central singularity", and is responsible for Hawking radiation (which is quantum tunneling back out of the black hole).

This is something that I have been pondering for some time. A static singularity would hold any particle in stasis, unable to move, we are led to believe - this would seem to foil so much of what we understand about particle physics. There could be no superposition, and no uncertainty. It would also mean we would know exactly the position of a particle - i.e. no speed, and one fixed location, which defies our understanding of the fabric of the universe. I'm sure someone cleverer than I can explain this somehow, but it defeats me.

It's an excellent question. One physicist regards the area within the Event Horizon as a 'different universe' - one with it's own set of rules and properties that *must* differ from our own. There have been attempts to model the inside of a black hole - one I read about conjectures that beyond the Event Horizon in our universe, there's a second, "inner" event horizon that must be encountered as well, that must regulate the amount of speed matter must have before hitting the singularity at the center.

For my money, I would bet there are different rules for matter *inside* the event horizon, than for what we have in "our" universe.

If the singularity exists, which is unproven and unknown then the particle which enters the black hole would no longer exist, but its gravity would still exist.

I have doubts about the existence of the singularity, even if it is mathematically "provable"