General Relativity tells us that we live in a four-dimensional spacetime 'fabric', with three dimensions of space and one dimension of time. Imagine this fabric as a rubber sheet. Any massive spherical object in this fabric, such as blackholes and stars, will bend and shape it. Then much like a marble rolling down a rubber sheet, the other objects living in the spacetime fabric will move along paths that are dictated by this curved spacetime fabric. That's why the Earth orbits the Sun, and the Moon orbits the Earth - they are all following paths in spacetime!
This simulation shows what happens when objects such as light or massive particles approach a black hole. Specifically, we look at a Schwarzschild black hole: a spherical, stationary black hole that doesn't spin. This black hole is immersed in a vacuum spacetime - this just means that its the only object that is shaping the fabric around it, and hence it is what dictates the interesting trajectories taken by light and massive particles near it.
There are some fascinating properties of the paths light and massive objects take around a black hole that depend on the mass of the black hole M, the radial distance from the black hole, and the angular momentum L. The angular momentum essentially tells us how much an object is 'swirling' as it moves around something.
The Schwarzschild black hole is surrounded by a spherical boundary at a radial distance of 2M - the 'event horizon' or point of no return: any ray of light or massive object that crosses the event horizon is unable to exit; its fate lies inside the black hole.
The more angular momentum an object has, the more 'stubborn' it is about changing its path. This means that an object with a large angular momentum will be incredibly stubborn, and hence might be able to escape the pull of the black hole. On the other hand, a small angular momentum might result in an object completely giving in to the black hole's pull, and falling inside it. The right balance would give us a stable orbit of an object around a black hole; much like the Earth orbiting the Sun.
Play around with the values of L and r in the simulation and see what paths for light and matter you are able to get. See if you are able to answer these questions:
Can light escape to infinity?
Can light move in a circular orbit around the black hole?
What's the smallest radius for which an object orbits the black hole?
Does increasing the angular momentum or decreasing it help an object escape to infinity?
Are you ever able to escape to infinity when the radial distance is less than 2M?
Search for answers to these questions using the simulation, and see if you can make up, and then answer, your own questions!
A massive object needs a certain minimum angular momentum L to be able to escape the pull of the black hole.
If L < 3.4641M, the particle will eventually fall into the black hole!
If L > 3.4641M, we get elliptical patterns in the orbits of massive objects
If L = 3.4641M, a massive object obtains a stable circular orbit for r=6M
Light orbits the black hole most stably at a radius of r=3M for all values of L
Can you verify these facts using the simulation? Note that M = 1.