### Why black holes are extremely cold?

• "The most massive black holes in the Universe, the supermassive black
holes with millions of times the math [sic] of the Sun will have a
temperature of 1.4 x $$10^{-14}$$ Kelvin. That's low. Almost absolute zero,
but not quite. A solar mass black hole might have a temperature of
only 0.00000006 Kelvin."

September 5, 2016 by Fraser Cain, Universe Today

Black holes absorb every form of energy, even light. Absorption of energy should raise its temperature but still it is extremely cold, why?

I've found the source of the quote. Interestingly, the typos ("math" instead of "mass", and an errant decimal point) are in the linked doc on phys.org, and are repeated in many other places. The article itself is not very accurate, and fails to mention Hawking's fundamental proposition that a BH's temperature is inversely proportional to its mass. Supermassive = super-cold. Absorb more mass/energy, get even colder.

Closely related to What is the temperature inside a Black Hole? (asked Jan 5 '16).

• Mark Olson Correct answer

4 years ago

Under General Relativity (GR) alone, a Black Hole's (BH's) event horizon is a point of no return -- anything that passes through the event horizon is lost and gone forever, and nothing comes out. Hence, under GR alone, BHs are utterly black and don't have a temperature at all.

This is why the absorption of radiation (or anything else) by a BH doesn't raise its temperature -- it just gets swallowed up and lost. (It's mass, angular momentum and charge do remain, but that's all -- see the No Hair Theorem.)

(Note: The accretion disk that surrounds a BH can be very hot indeed, but that's another thing entirely.)

Stephen Hawking discovered that applying quantum mechanics to BHs showed that BHs would emit a random spray of radiation, and that that radiation was precisely what a black body would emit -- black body radiation. This is called Hawking radiation.

Black body radiation is simply the thermal emission of a perfect absorber of radiation, and leads to the inescapable conclusion that a BH does have a non-zero temperature. Interestingly, Hawking's analysis showed that the effective temperature of the BH is inversely proportional to its mass and that solar-mass BHs (which are the smallest for which we have actual evidence) would have a temperature of about 0.00000006 K. Kinda cold, but still not zero.

Note that, unintuitively, a solar mass BH get colder as it absorbs radiation. Because any radiation (or anything else) it absorbs increases its mass, and since higher mass BHs are colder, the more energy you dump into one, the colder it gets!

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