What happens when a black hole evaporates?

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I seriously never understood this. What does it mean for a black hole to evaporate?
 
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Exactly that - it loses rest-mass until it is gone.
http://casa.colorado.edu/~ajsh/hawk.html
 

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So I know that electrons are fundamental, there's no 'material' that makes them up, it's like talking about a colour itself rather than a car or a flower. Now protons and neutrons and quarks and whatever other stuff is there fundamentally, I want someone to kind of teach me these, I have a lot of questions that books might not give the answer in the way I understand. Thanks
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