Black Hole Lab is an open source physics simulation of a rotating black hole and two observers, Alice and Bob. You can launch Alice and Bob on paths around or into the black hole and watch events play out. The simulation lets you see a slice of the physics with one or two dimensions of space plus one of time.
As a fun extra, Alice and Bob each have a beacon that can transmit a radio wave in all directions. The simulation calculates and shows the wavefront of these signals, accounting for the warping of space and time by the black hole. The simulation also records whenever Alice and Bob receive each other's transmission.
The simulation takes pains to respect Einstein's equations of general relativity. To the precision of the numerical integration, the effects shown in Black Hole Lab are really what the math of general relativity says will happen. Black Hole Lab specifically uses the Kerr metric, which is an exact solution to Einstein's equations of general relativity for a rotating mass. That said, physicists agree that general relativity cannot be the final word on black hole physics. Nobody can say what would really happen to Alice and Bob.
My original goal for black hole lab was to try to understand the strange time compression effects at the inner horizon, which physicists call infinite blueshift. IMHO, Black Hole Lab succeeds in showing this effect in an understandable way. I added a specific discussion of infinite blueshift in the readme.