How do black holes evaporate?
This is a tough one. Back in the 1970’s, Stephen Hawking came up with theoretical arguments showing that black holes are not really entirely black: due to quantum-mechanical effects, they emit radiation. The energy that produces the radiation comes from the mass of the black hole. Consequently, the black hole gradually shrinks. It turns out that the rate of radiation increases as the mass decreases, so the black hole continues to radiate more and more intensely and to shrink more and more rapidly until it presumably vanishes entirely. Actually, nobody is really sure what happens at the last stages of black hole evaporation: some researchers think that a tiny, stable remnant is left behind. Our current theories simply aren’t good enough to let us tell for sure one way or the other. As long as I’m disclaiming, let me add that the entire subject of black hole evaporation is extremely speculative. It involves figuring out how to perform quantum-mechanical (or rather quantum-field-theoretic