Albert Einstein‘s general relativity theory of gravity includes black holes. Black holes are basically where this theory of gravity breaks down, also known as a singularity.

The mathematical model describes gravity extremely well and has been proven to be correctly describe and predict our observations of the cosmos.

You can look into the models behind it. To really understand physics beyond vague descriptions, you need to understand the math that describes it.

This MIT class on General Relativity includes 23 video lectures. The first 9 lectures explain the mathematics, black holes are described in the last two.

(Not a professional physicist.)

My understanding is that we have a very good model for how gravity should work, and we've used that model to predict a lot of things we can observe. A few I can think of offhand:

1. Light bending. We've taken many telescope readings through their general neighborhoods. In each case, we see the distortion and optical effects we would expect from our model. (A similar experiment is what really cemented relativity as accurate iirc.)
2. We do have a photo of a black hole, and it looks as we would expect (accretion disk included!). It would be difficult to explain the torn apart hyper-accelerated cloud of atoms around the black hole if the black hole didn't tear things apart.
3. There are computational models for galaxy formation and trajectory. My understanding is that (modulo dark energy/matter), these models match what we see reasonably well. I think the galaxies we see would be quite different if black holes never fed on matter (they would be much smaller, for example).

Math and observation.

Before we finally found one in reality, we just had math telling us what to look for.

Math also suggests the possible existende of the opposite of a blackhole; a white hole. Where matter is constantly being ejected instead of vaccuumed up. We have yet to find one of these, tho.

Black holes aren't the only objects capable of tearing things apart with their mass. Neutron stars, for example, are more than capable of tearing apart objects that pass nearby. Even planets. We've seen Jupiter tear apart passing asteroids.

You can find videos of an active black hole:

https://youtu.be/TF8THY5spmo

You cannot “see” the black hole directly, but you can see the stars orbiting the black hole and the effect of gravitational lensing.

In a similar way when you see your own hands, are aren’t really seeing your hands, but the photons bouncing off your hands into your retina.

Math.

Well for one Einsteins general relativity equations predicted the possibility of black holes before we ever found any!