What effect does a black hole have on matter?
A black hole spaghettifies anything that crosses over it's event horizon, even light.
It does not pull anything in like most people believe, but if anything crosses its event horizon, it cannot ever come out of it. If you were observing something that was going towards a black hole, no matter how fast it may have been going, it will appear to slow and stop just outside of the event horizon. The object itself never stops moving really, and doesn't notice a change in speed, but an observer would see it slowly fade from existence as any light that was bouncing off of an object would not be able to escape the black hole.
A black hole has an extremely powerful gravitational field which affects all matter near to it.
Black holes were first predicted when Karl Schwarzschild found the first exact solution to the field equations of Einstein's theory of General Relativity. The solution has a singularity at the Schwarzschild radius
If all of the mass of the body is contained in a radius less than
Any matter approaching a black hole will be affected by the strong gravitational field. Contrary to popular belief, black holes do not consume everything in its vicinity. Material has to actually have a trajectory which intersects the event horizon to fall into the black hole.
We can't be sure exactly what happens when matter approaches the event horizon. Einstein's field equations are very complex. They consist of 10 second order partial differential equations. The Schwartzschild solution makes a number of assumptions which reduce the field equations to 3 easily solvable differential equations. Near the event horizon the assumptions are no longer valid which makes the solution meaningless.
Also, near the event horizon, quantum effects will be important. As quantum mechanics and general relativity are currently incompatible, we need new physics to describe black holes completely.