Bill Unru thought about the spacetime around a black hole, and he realized that it was actually very similar to a subset of the spacetime in flat space. In good old ordinary Minkowski space with no black holes, no gravity at all, if you cut out a wedge and look at just that wedge, it has many of the properties that a black hole spacetime does. And then he realized that if you were an accelerating observer, an observer that accelerated at a constant acceleration forever, you could stay inside that wedge forever. It would be like that was the whole spacetime in which you lived.