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A black hole doesn't have an edge. It is a point mass but it appears to have an edge. This edge is in fact the Schwarzschild radius, or, the "point of no-return!" Ha, this is the distance from the black hole (which is a point) that the escape velocity is greater than the speed of light. Thus, nothing can escape because nothing can travel faster than light. This makes it look like there is a "black hole" in space but really there is only a super-dense point.

the positron, with its negative gravity

Doesn't Hawkins say something about an Electron and a Positron forming near the event horizon of a black hole. The electon escapes and the positron, with its negative gravity, is drawn into the black hole.On another tack, what is at the middle of a black hole?