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How does negative energy from Hawking Radiation cause a Black Hole to shrink? [duplicate]

Hello this is expanding upon a question that was previously asked on stack exchange that I linked below. From what I understand of Black Holes is that overtime Hawking Radiation results in the Black ...
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Black holes and positive/negative-energy particles

I was reading Brian Greene's "Hidden Reality" and came to the part about Hawking Radiation. Quantum jitters that occur near the event horizon of a black hole, which create both positive-energy ...