A thought I always had is a singularity is the point where mass as we know it breaks down. Like an atom. He has a nuclei and electrons on very specific orbits depending on the type of atom. We know that even electrons have a very small amount of mass, but it does have mass.
At some point, a gravitational field theoretically could become so strong that even that electron cannot maintain its orbit around whatever nuclei it's orbiting. At that point, mass (the atom) is no longer an atom as we know it. It's crushed down into what we call a singularity.
So lets ask the question. What is a singularity? Well, in science a gravitational singularity is a point in space where literally space (coordinates) and time (literal time) cease to exist / function as we know it in normal space-time. We (humans) can perceive space in three dimensions, but we also know that gravity is fully capable of manipulating space which was predicted by Einstein and an experiment dreamed up by Sir Frank Watson Dyson later confirmed.
We also know that gravity can affect time through the effects of time dilation. This tells us that time moves more slowly the closer to a massive object you are. (even though we do not perceive the difference in real time) Well, the closer to a black hole you get, the more time slows down. (though as noted above, we would experience it like any other rate of time)
From from the previously two paragraphs, we know space gets squished down where miles of space become a point and time slows down where to someone from the outside, years would equate to minutes or maybe even seconds inside the black hole's Schwarzschild radius. (aka event horizon)
Just a quick note, just because time gets squished down like space, time never becomes infinite as some have said. Time is finite and as noted. We would experience events inside of Schwarzschild radius at speeds we expect events to occur outside of it. People outside looking in would see it happen much more slowly. Also to note, some people have said you would never see the image of someone falling in ever go away because the photons are stuck between exiting black hole and the pull of gravity and it would be like a photo never changing. That too isn't true either. Redshift would cause the image (colors of light) to fade to black over time as the light waves frequency get stretched out. It would be more like the Schwarzschild radius overcomes the image of those falling in.
Anyway, back to my original though. (very easy to go off on a tangent with these awesome topics) Once an atom is no longer an atom due to it being crushed. What is it? Not only that, at what point does many objects become one object if there is no "space" between the mass they are made up of? The singularity.
There is also the note that black holes create rips in space-time. While I don't have a great grasp on this, I want to point out that it's not quite as clear as it seems. You see examples of E=MC squared as a stretchy rubber mat, but that is not what space is. It's more of a
manifold. I would also like to point out that if there was a rip that you could go through. Wouldn't the mass of the black hole go through it thereby lowering the mass within the point in space-time that the black hole existed in the first place? Black holes are only thought to lose mass via Hawking Radiation.
When you see (bare with me here) a black hole. That black hole is exactly where you see it. There is no deep hole that you fall "down" into. Though in the strictest sense, you are falling into it. As you move towards it your moving through space even if that space is stretched or compressed. That space that you traveled as you fall is much longer distance than it appears from the outside. (though like falling in normal space, the longer you fall. The more speed you pick up. Especially if there isn't anything like air to create friction to slow you down)
