Intuitively - why aren't black holes hot?

[Tim13]

from a layperson's perspective - if a supermassive black hole is more massive than a million suns then why is it cold? An answer in plain english is truly appreciated for the layperson like me.

 

[Chronos]

Electromagnetic radiation cannot escape the event horizon of a black hole.

 

[Tim13]

Electromagnetic radiation cannot escape the event horizon of a black hole.

Nt sure tht is an answr. If yu re syng that the tmperatre of a blck hole is not measurable because electromagnetic radiation can't escape the event horizon - then how does that mean that a supr masive blck hle is cld? If it is nt measurable, homework is it ether cld or ht??

 

[twofish-quant]

from a layperson's perspective - if a supermassive black hole is more massive than a million suns then why is it cold?

You have to distinguish between the black hole itself and the stuff around the black hole.

But you can see why the black hole is cold by thinking about what "cold" is. If I have a glass of ice water, what does it mean to say that it's cold? Well, it means that if I put something next to it, the ice water will absorb energy from something next to it.

Now if I have something sitting right outside the black hole, the energy will flow from that thing to the black hole, but almost nothing will come back. I.e. the black hole is cold.

 

[Tim13]

You have to distinguish between the black hole itself and the stuff around the black hole.

But you can see why the black hole is cold by thinking about what "cold" is. If I have a glass of ice water, what does it mean to say that it's cold? Well, it means that if I put something next to it, the ice water will absorb energy from something next to it.

Now if I have something sitting right outside the black hole, the energy will flow from that thing to the black hole, but almost nothing will come back. I.e. the black hole is cold.

I get the analogy of a glass of ice water but it is a non-sequitor. The BH absorbs energy due to gravity not temp or is that wrong?

 

[twofish-quant]

I get the analogy of a glass of ice water but it is a non-sequitor. The BH absorbs energy due to gravity not temp or is that wrong?

This is the topic that made Stephen Hawking famous, since he was one of the first people to point out that temperature and gravity are related.

It turns out that it doesn't matter *why* the BH sucks up energy. As long as it sucks up energy, you can associate a temperature with it.

Hawking also pointed out that one consequence of this is that black holes must have some radiation. If black holes sucked up all radiation and energy then they would have a temperature of absolute zero and you could create a perpetual motion machine. Since this would be impossible, black holes must emit a tiny amount of radiation and Hawking showed how to calculate that amount of radiation.

 

[Tim13]

This is the topic that made Stephen Hawking famous, since he was one of the first people to point out that temperature and gravity are related.

It turns out that it doesn't matter *why* the BH sucks up energy. As long as it sucks up energy, you can associate a temperature with it.

Hawking also pointed out that one consequence of this is that black holes must have some radiation. If black holes sucked up all radiation and energy then they would have a temperature of absolute zero and you could create a perpetual motion machine. Since this would be impossible, black holes must emit a tiny amount of radiation and Hawking showed how to calculate that amount of radiation.

I don't accept this explanation by Hawkins. Any household appliance sucks up energy. All household appliances radiate energy. Temperature of a BH shouldn't be "associated" or "assumed" to be based on energy absorbed without any reference to energy radiated. Am I missing something??

Moreover there is fundamentally something different about measuring the temperature of a BH which bend space time. If I ask you to measure the temp of an object in a closed system while knowing you can't - what's the point? Would you really try to give me an answer? And what if the BH creates its own universe separate from ours - how do you measure its temp??

I apologize for this speculative response.

 

[clamtrox]

I don't accept this explanation by Hawkins. Any household appliance sucks up energy. All household appliances radiate energy.

and how many household appliances have temperature zero?

See, if you have something that can absorb energy while still maintaining zero temperature, then the laws of physics (and thermodynamics in particular) don't really work anymore. That would correspond with the black hole having infinite degrees of freedom (or entropy, if you prefer)

 

[twofish-quant]

I don't accept this explanation by Hawkins. Any household appliance sucks up energy. All household appliances radiate energy.

And black holes suck up energy but because of gravity they don 't radiate it.

Temperature of a BH shouldn't be "associated" or "assumed" to be based on energy absorbed without any reference to energy radiated. Am I missing something??

Black holes can't generate radiation from the inside.

 

[kbar1]

and how many household appliances have temperature zero?

See, if you have something that can absorb energy while still maintaining zero temperature, then the laws of physics (and thermodynamics in particular) don't really work anymore. That would correspond with the black hole having infinite degrees of freedom (or entropy, if you prefer)

That is what Hawking thought, I think. A black hole (if we assume that it doesn't have a temperature, i.e. doesn't emit energy) violates the second law of thermodynamics, by sucking up everything that falls on it (reducing the entropy of the universe), but doesn't compensate for it (by emitting energy). Therefore, it must emit particles/energy in some way, and have an temperature, which is predicted by the second law.

 

[Tim13]

That is what Hawking thought, I think. A black hole (if we assume that it doesn't have a temperature, i.e. doesn't emit energy) violates the second law of thermodynamics, by sucking up everything that falls on it (reducing the entropy of the universe), but doesn't compensate for it (by emitting energy). Therefore, it must emit particles/energy in some way, and have an temperature, which is predicted by the second law.

If it really emits no energy (in this universe) then isn't it like a one way street to a different universe? I apologize if that is too speculative for this forum. But the problem I have conceptually or intuitively is that we know a black hole exists from the effect of its gravity and yet we can't measure it, only its effects. And if we could measure something that massive why wouldn't it be very hot? Aren't very massive objects (not beyond an event horizon) really very hot?

 

[twofish-quant]

If it really emits no energy (in this universe) then isn't it like a one way street to a different universe?

It has to emit some energy. Hawking figured out how to get black holes to emit something.

And if we could measure something that massive why wouldn't it be very hot? Aren't very massive objects (not beyond an event horizon) really very hot?

No particular reason why massive objects have to be hot.

 

[Tim13]

No particular reason why massive objects have to be hot.

I suppose you are right. There is no particular reason why the mass of millions of suns (equal to a supermassive black hole) when compressed to a tiny volume would get hot. It is probably cold enough to make ice cream.

 

[Antiphon]

I suppose you are right. There is no particular reason why the mass of millions of suns (equal to a supermassive black hole) when compressed to a tiny volume would get hot. It is probably cold enough to make ice cream.

Nobody said that wouldn't be hot. The fact is it would cool off eventually to about 2.8K. Everything does including your biggest black hole.

A black hole can't give off lots of heat unless it's really small. So it's typically colder than the universe's average temperature. It might be burning hot on the inside; but the outside would freeze your eyeballs if you stared too closely into it. Much too cold to make ice cream unless you like to eat solid helium.

 

[twofish-quant]

I suppose you are right. There is no particular reason why the mass of millions of suns (equal to a supermassive black hole) when compressed to a tiny volume would get hot.

There's a difference between the black hole and the region right outside the black hole. The region right outside the black hole gets heated up to hundreds of millions of degrees, and the heat comes because when something collapses, it releases a massive amount of gravitational energy.

So the region right outside the black hole is enormously hot.

Now the black hole itself is very cold for the reasons that have been mentioned.

 

[H2Bro]

Hawking radiation is when virtual particle pairs are asymmetrically captured by the black holes event horizon, releasing one member of the pair into the free space. This is how BHs radiate, correct? Or have I mistaken hawking radiation?

Also, if the temperature just outside the BH is millions of degrees there may still be a net energy loss from a person or spacecraft etc in that area because the energy density is still extremely low, is that correct? I am analogizing to the upper stratosphere where the 'temperature' as measured by average velocity is quite high but one would still radiate heat outwards because there are so few particles about.

thanks in advance,
H2bro

 

[Tim13]

There's a difference between the black hole and the region right outside the black hole. The region right outside the black hole gets heated up to hundreds of millions of degrees, and the heat comes because when something collapses, it releases a massive amount of gravitational energy.

So the region right outside the black hole is enormously hot.

Now the black hole itself is very cold for the reasons that have been mentioned.

I really wasn't referring to the region right outside of the black hole. Perhaps part of the problem is the phrase "black hole" which can mean different things to different people. I understand (perhaps mistakenly) the phrase to mean only the actual supermassive body beyond the event horizon (and also the event horizon it creates). Please correct me if that understanding is wrong.

That body may or may not be radiating heat well above the average temperature of the universe but because space/time is "bent" (for lack of a better description) there is no way that light (much less heat) can escape past the event horizen. Therefore it is not possible to measure the heat of the body called a black hole.

Now here is where I confess I get confused. If you can't measure its temperature how do some postulate that black holes are cold? Maybe they are maybe not. If you assume that a black hole is cold, you might as well assume that it is dark. Yet on the inside of the event horizon, the black hole body might be the brightest object in the universe. How would we know since nothing gets past the event horizon?

Intuitively I would suspect the body is radiating heat well above the average temperature of the universe. But I was careful in choosing the word "intuitively" since I have absolutely no observable data to support that conclusion. My apologies to anyone who feels this post is just too speculative for the forum.

 

[Antiphon]

You can measure the temperature of a black hole with a pyrometer, a standard temperature measurement method.

Unless its the size of a pea, and if there's no matter falling into it and getting hot, the hole will read on the pyrometer as the coldest da*ned thing you've ever measured, colder than the icy cold of deepest space.

 

[twofish-quant]

I understand (perhaps mistakenly) the phrase to mean only the actual supermassive body beyond the event horizon (and also the event horizon it creates). Please correct me if that understanding is wrong.

It's right, but the fact that the stuff around the black hole is very hot is an important gotcha. Also the heat that a black hole does radiate, technically doesn't come from the black hole, but from a tiny surface just above the event horizon.

Therefore it is not possible to measure the heat of the body called a black hole.

Temperature something that you can measure. Temperature involves the interaction of the black hole with it's surroundings.

Think about this. I can't touch the sun, but I know that the sun is hot. How do I know this?

If you can't measure its temperature how do some postulate that black holes are cold?

You can measure the temperature of the black hole. You put different objects near the black hole and see if heat flows to the black hole or away from it. Something that is hotter than the black hole will have heat move toward the black hole. Something that is colder than the black hole will absorb heat from the black hole.

Since the black hole is black, it's going to be very cold.

I know the sun is hot because I can feel the heat of the sun. If I stand in the sun, it transfers heat to me. The point here is that you don't have to physically touch the sun to measure it's temperature. Same for black holes. If you were standing near a black hole, it would start to *feel* cold because the black hole will be sucking up energy from it's surroundings and you would feel the coldness of the black hole in the same way that you feel the heat of the sun.

Intuitively I would suspect the body is radiating heat well above the average temperature of the universe.

That's the point. The black hole is black. It's not radiating. One thing that was a puzzle which Stephen Hawking solved was naively you'd think that the black hole wouldn't be radiating anything at all. If that were true then the black hole would be absolute zero and you could generate a perpetual motion machine from a black hole. Hawking showed that there is a small amount of radiation from the black hole which keeps it from going to absolute zero.

 

[Tim13]

You can measure the temperature of the black hole. You put different objects near the black hole and see if heat flows to the black hole or away from it. Something that is hotter than the black hole will have heat move toward the black hole. Something that is colder than the black hole will absorb heat from the black hole.

Since the black hole is black, it's going to be very cold.

If you were standing near a black hole, it would start to *feel* cold because the black hole will be sucking up energy from it's surroundings and you would feel the coldness of the black hole in the same way that you feel the heat of the sun.

I understand and agree with you at a certain level. I guess it is somewhat irrelevant how the apparent coldness is caused.

But is it possible that the black hole draws something hot towards the black hole not because the black hole is colder but because it warps space/time? And isn't it also possible that something (apparently) colder than the black hole might still be pulled into the black hole because of the warped space/time? If these things are theoretically possible then would you admit that it just isn't possible to measure the temperature of a black hole?

Last question - If a tree falls in a forest and no one is around to hear it, does it make a sound?

 

[clamtrox]

I understand and agree with you at a certain level. I guess it is somewhat irrelevant how the apparent coldness is caused.

No it's not...

But is it possible that the black hole draws something hot towards the black hole not because the black hole is colder but because it warps space/time? And isn't it also possible that something (apparently) colder than the black hole might still be pulled into the black hole because of the warped space/time? If these things are theoretically possible then would you admit that it just isn't possible to measure the temperature of a black hole?

Black holes pull things towards them because of gravity of course. This has nothing to do with temperature: they would do it even if they were really hot (like the sun pulls earth). The reason one says black holes are cold is that they radiate so little. If you have a ~300K astronaut floating near a black hole, the astronaut will radiate with higher surface power than the black hole if the black hole's mass is bigger than something like 10²¹kg. Over time, the astronaut loses more energy through radiation than she gains, and therefore her temperature drops.

Last question - If a tree falls in a forest and no one is around to hear it, does it make a sound?

Of course, sound is just vibrations of air molecules and anyone who thinks otherwise is a mischievous hippie.


As a side note, since supermassive black holes have huge mass, they also are very very cold indeed. For a black hole with mass of 1 million solar masses, the temperature is ~10^-13 K. Therefore they remain colder than the cosmic microwave background for a long time. Assuming that dark energy does not dilute and neglecting everything else, it should take about 30 times the current age of the universe for the black hole to have same temperature as CMB. Only after that they start to lose energy through radiation.

 

[kbar1]

What's the current hypothesis as to what happens when the black holes become too small to exist?

 

[twofish-quant]

But is it possible that the black hole draws something hot towards the black hole not because the black hole is colder but because it warps space/time?

Doesn't matter. Temperature is temperature. The black holes gravity sucks up heat and the event horizon keeps it from reradiating. That makes it cold.

And isn't it also possible that something (apparently) colder than the black hole might still be pulled into the black hole because of the warped space/time?

Doesn't matter.

If these things are theoretically possible then would you admit that it just isn't possible to measure the temperature of a black hole?

There is a precise definition of temperature in the zeroth law of thermodynamics. You can take the definition of temperature and they show that black holes have a temperature that can be measured.

 

[clamtrox]

What's the current hypothesis as to what happens when the black holes become too small to exist?

So the temperature of Hawking radiation is proportional to 1/M where M is the mass of the black hole. The power thermal objects radiate is P ~ AT⁴ where A is the surface area. For a black hole, A~M² so all in all you have P~M² M^-4 ~ M^-2. If you also remember that mass is energy, we can write the power as P ~ dM/dt ~ M^-2 and integrating this expression, you will find that it will take a finite time to radiate all the energy away for a black hole of any size. You can also see that when M is very small, the radiation energy increases sharply. Basically when the black hole gets small enough, it explodes releasing the rest of its energy in a very short time period.

As for what happens with the singularities and all that, no one knows.

 

[Tim13]

Doesn't matter. Temperature is temperature. The black holes gravity sucks up heat and the event horizon keeps it from reradiating. That makes it cold.



Doesn't matter.



There is a precise definition of temperature in the zeroth law of thermodynamics. You can take the definition of temperature and they show that black holes have a temperature that can be measured.

Your help is much appreciated. Thanks.

 

[lazypast]

So the temperature of Hawking radiation is proportional to 1/M where M is the mass of the black hole. The power thermal objects radiate is P ~ AT⁴ where A is the surface area. For a black hole, A~M² so all in all you have P~M² M^-4 ~ M^-2. If you also remember that mass is energy, we can write the power as P ~ dM/dt ~ M^-2 and integrating this expression, you will find that it will take a finite time to radiate all the energy away for a black hole of any size. You can also see that when M is very small, the radiation energy increases sharply. Basically when the black hole gets small enough, it explodes releasing the rest of its energy in a very short time period.

As for what happens with the singularities and all that, no one knows.

I find that very interesting and understandable. How long would it take for a black hole to come to the end of its life? I can only assume it's longer than the age of the universe.

Im wondering about what goes on inside black holes. How do we know our laws of physics don't break down? Is it an assumption or is there theoretical or practical evidence showing the laws don't change. (My next question leads to the 1x10^-43 seconds after the big bang, however this may be too offtopic)!

 

[clamtrox]

I find that very interesting and understandable. How long would it take for a black hole to come to the end of its life? I can only assume it's longer than the age of the universe.

It gets more complicated if you actually want numbers, but let's try anyway. We have A = 16\pi M^2, P = \frac{\pi^2}{60} A T^4 and T = \frac{1}{8 \pi M} so for the differential equation you get
dM/dt = \frac{\pi^2}{60} 16 \pi M^2 \frac{1}{(8\pi M)^4} = \frac{1}{15360\pi M^2}
and so you get
t = 5120\pi M^3
where mass and time are given in Planck units.

The age of the universe is about 10⁶⁰ Planck times, so a black hole with mass of 10¹⁹ Planck masses decays in the age of the universe. In standard units, that's about the amount of trash the United States produces every year (http://www.wolframalpha.com/input/?i=10^19+planck+mass).

Anything lighter decays faster, and heavier things decay slower. The mass of the Sun is about 10³⁸ Planck masses, so a black hole with similar mass would decay in 10^{38*3 + 4} = 10¹¹⁸ Planck times = 10⁵⁸ ages of the universe, so quite slowly.

 

[enosis_]

I'm not sure why the area outside of the BH is important to this discussion?

 

[Chronos]

Radiation cannot escape a black hole unless emitted outside its event horizon.

 

[enosis_]

Radiation cannot escape a black hole unless emitted outside its event horizon.

Yes, as your first post clarified. Unless I misunderstood the OP - we are concerned with the internal temperature of the black hole - rather than the area surrounding it?