# 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. – Chappo May 29 '18 at 2:03
• Closely related to What is the temperature inside a Black Hole? (asked Jan 5 '16). – Rob May 29 '18 at 3:47

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!

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

Because of the infinite gravitational time dilation. The thing to understand is that temperature is a measure of motion. A hot gas is one where the molecules are, on average, moving faster than in a cold gas. See the Wikipedia temperature article and note this: "The coldest theoretical temperature is absolute zero, at which the thermal motion of all fundamental particles in matter reaches a minimum". Gravitational time dilation means things are moving slower. When the gravitational time dilation is infinite, things aren't moving at all. This is why the black hole was originally known as the frozen star.

Stephen Hawking wrote a paper in 1972 with Brandon Carter and Jim Bardeen where they said "It should however be emphasized that κ/8π and A are distinct from the temperature and entropy of the black hole. In fact the effective temperature of a black hole is absolute zero”.

Robert Wald said much the same in black hole physics. On page 69 he said in classical black hole physics “κ has nothing whatever to do with the physical temperature of a black hole, which is absolute zero by any reasonable criteria”.

The black hole is said to have an effective temperature by virtue of Hawking radiation, but as Fraser Cain said, it's very low. And as Mark said, "under GR alone, BHs are utterly black and don't have a temperature at all". More importantly, Hawking radiation is said to be emitted from outside the event horizon. So it isn't actually the temperature of the black hole. Just as "the accretion disk that surrounds a BH can be very hot indeed" but it isn't actually the temperature of the black hole.

You got some very good answers already. I just want to point out this:

The "temperature" of a black hole is more like just "a way of speaking". It's not temperature as normally understood.

There is this process called the Hawking radiation where vacuum near a black hole produces a stream of particles, borrowing energy from the black hole's gravity to create those particles - and so it appears like the black hole "emits" radiation. Since this is radiation, you could in theory measure its temperature. But that's just the temperature of the Hawking radiation.

Obviously you couldn't stick a thermometer into a black hole.