Can Black Holes Actually Die Out?

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Given why black holes are what they are, it is difficult to fathom that the constant influx of matter and energy into its core would somehow eventually cause it to dissipate and disappear. Would not the addition of matter and energy simply contribute more and more to the gravity? It would seem that the only way a black hole can fade is if it is never fed.
 
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Quite right, infalling matter and radiation does indeed contribute to the BH's mass. The only time the black hole shrinks is when the hawking radiation is greater than the matter and radiation the BH is absorbing. Note that this condition isn't even attainable in the present universe, as the cosmic microwave background completely swamps the hawking radiation from a stellar mass black hole.
 

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