Main Question or Discussion Point
A black hole evaporates through hawking radiation, what I don't get is the requirement for an energy-negative energy pair production. Since it's the black hole's gravitational energy that's responsible for the pair production, even if one of them escapes, the black hole would lose energy anyway. Also, if it's gravitational energy is not responsible for pair production, it's still responsible for "boosting" the virtual pair into real particles, and then too if one escapes, the black hole would lose energy. So what's the requirement of a negative energy particle entering the black hole?