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If no light can escape black holes, in my mind they would act as a greenhouse, collecting radiation from the stars or CMB or anything. Or is all this energy just absorbed by the black hole?

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The energy of any infalling mass is absorbed by the black hole. Classically, the temperature of a black hole is absolute zero, since it is a perfect absorber.

If you include quantum mechanical effects, as Stephen Hawking did, you can show that black hole horizons will emit radiation in such a way that is consistent with the horizon being a hot body with a given temperature which is proportional to $\frac{1}{M}$. So, small black holes are hotter than large ones.

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Simply because the Second Law of Thermodynamics states:

Entropy > 0  (always)

(think of taking a basketball and squeezing it into a golf ball)

so that the density gets larger as the mass gets smaller.

therefore, Entropy will always increase in a black hole, gaining Entropy [heat] as it gets smaller.The stars reaching critical mass(limiting mass) ~ 1.4 solar suns and the star either becomes:

A Black Hole = [ M > 1.4 Solar suns] (very active)

Dead Neutron Star = [ M < 1.4 Solar suns] (not active)

There can be no loss in bits of information (Entropy) based on a congruent partition function as beta gets bigger with more "time" so-to-speak. also see Law of Conservation. So if you treat Entropy as Heat then yes it is very very HOTTTT!!!

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