Here is a spacetime diagram, where time points up out of the screen and the z-direction is omitted, showing the region near a black hole and the light cones for three identical spaceships at different positions relative to the hole. The future light cones poke up out of the screen and the past light cones lie on the other side of the screen.

The boundary around a black hole where the escape velocity is c is called the "horizon". The entire causal future of anything inside the horizon remains inside the horizon and is drawn toward the black hole. No information reaches the rest of the universe from inside or on the horizon.

A region that an observer cannot receive any information from is called a "hidden region" for that observer. An observer may have other hidden regions besides the horizons of black holes that they lie outside of. For example, as I mentioned before, the portion of an expanding universe that lies far enough away from an observer is a hidden region for that observer. As this example shows, hidden regions may differ for different observers. All observers outside of a black hole will agree on the existence and location of the black hole's horizon and the region that the horizon encloses is a hidden region for.these observers But the region inside of the horizon is not a hidden region for any observers inside the horizon.

Black holes act as gargantuan microscopes that stretch space and slow time enough so that we might be able to see the quantum structure of spacetime if we look at light traveling very close to the horizon of a black hole. To understand what we might expect to see, it is useful to imagine what it would be like to hover near the horizon of a black hole. In this situation, it would be necessary to continuously accelerate to avoid falling through the horizon. Accelerating in empty space is similar to this situation in many ways and it is useful to consider what happens under those conditions before continuing our discussion of black holes.