# Are black holes hot?

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?

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.

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!!!