# Temp inside a Black Hole?

Would I be correct to think that the lowest temperatures possible in the universe would be in a black hole, and if so, how cold would that be?

Why would you expect it to be cold? You still have photons and matter streaming in from outside the event horizon.

I think the lowest temperatures occur in laboratory experiments designed to create negative temperature.

The temperature in a black hole is (AFAIK) theoretical only, but it is apparently quite cold. Google for “temperature of a black hole” - sample link looks like this. Hope that helps.

Or as Spike Milligan might have said;

‘Don’t touch it, then!’

That’s the surface temp. of a black hole and it’s a function of the mass of a black hole.

It’s quite a subjective question, but everything inside the event horizon no matter what it’s temp. will radiate any heat towards the singularity, but it’s going out on a limb to say that this means that the singularity is at absolute zero.

Sorry my partial answer was ambiguous.

Normally temperature is a measure of molecular motion, but that doesn’t apply to a black hole. Another way to define temperature is to define how much radiation it emits, as in Nanoda’s link.By that definition, black holes are very, very cold. The only radiation emitted by a black hole is Hawking radiation.

By the question was “temperature inside a black hole”, which I took to mean the temperature of the space inside the event horizon. You can’t use either of the above definitions to measure temperature of empty space, but you can use yet another definition: the energy density of the radiation passing through the space. In another words, the equilibrium temperature of an object placed in that location. By that definition, the temperature of earth orbit in full sunlight is around 300K. The temperature of the space inside a black hole can be anything, but it’d be copmparable to the temperature outside the black hole.

But, since there is no volume or space inside the Black Hole, isnt the answer “no temperature at all”?

‘Inside a black hole’ is usually taken to mean inside of the event horizon which is a space with volume.

Shouldn’t the singularity be blazingly hot? I realize that nothing can emanate from the singularity so just one micron away from it you would measure no heat (or anything else) coming from the singularity. Further, there is no way to measure the temperature of the singularity and tell anyone about it since no information can leave. Nevertheless, as a thought experiment, couldn’t one reasonably assume that an object as dense as a singularity would be staggeringly hot? Everything else in the universe heats up when compressed…why not a singularity? I want to suggest that the temperature is infinite but I’m afraid that would imply infinite energy which I don’t think can be the case so I’ll stick with stupendously hot till I learn better.

Mu.

To elaborate: We can’t really scientifically answer any question about anything inside the event horizon of a black hole, since nothing inside can ever communicate with anything outside. What we can do is make some simple assumptions that things stay “smooth” as you cross the event horizon, and analytically extend what we know about the space outside to the space inside, and thus sort of mathematically answer questions about the inside. So the question “What is the temperature inside a black hole?” can be answered, at least at a reasonable guess. But for the singularity itself, not only can we never (even in principle) make measurements of it, but we also can’t analytically extend anything to it. So there’s no sensible way to answer questions about a singularity. Yes, everything else heats up when you compress it to anything other than a singularity, but this tells us nothing about what happens when you compress things to a singularity, because all the rules change there.

Now, as for that reasonable guess I mentioned, analytical extentions of the black hole solutions suggest that, to an observer falling straight in to a black hole, the event horizon isn’t locally noticeable. While you may be shredded by tidal forces, exactly where the shredding occurs doesn’t have any particular relation to where the event horizon is. So I’d agree that, if you measured the temperature of the cosmic background radiation (which seems the most relevant definition of temperature, here), that you’d see the same 2.7 Kelvins inside the hole as you saw outside.

Note that if you’re hovering just above the event horizon, then the temperature you measure will be higher (potentially much higher), because all of the photons falling in to you will be greatly blueshifted. But if you’re falling in freely, then there will also be a Doppler redshift from your motion, and unless I’m mistaken, the two effects must exactly cancel out. If you keep your rocket’s engines going after you cross the horizon (a bad idea, incidentally, but never mind that), that’ll surely change the temperature(s) you see around you, but I’m not quite certain in what manner.

According to Steven Hawking and Werner Israel’s article in my Encyclopedia of Physics the temperature of a black hole is given by:

T = K(h/4pi[sup]2[/sup]kc)

K = surface gravity at black hole horizon = GM[sup]2[/sup]/c. M is mass of black hole

h = Planck’s constant
k = Boltzman constant

Brilliant.

How about Neutron Stars? Are the neutrons rubbing against each other and if so would such motion generate energy?

Yes that’s the surface temperature, which is a function of the amount of Hawking radiation emitted.

Yes that’s the surface temperature. But isn’t the surface the only thing we can get at? Does the “internal temperature” of a black hole have any physical meaning?

Well, you can go inside the event horizon and start measuring tempertaures, but that would be the last anyone ever heard of you, though we can model the interior of the event horizon.

My point is, can’t you postulate anything you want to about the “interior” of a black hole and draw from the postulates conclusions which will have absolutely no effect on the universe outside the hole in which everything that is of consequence to us takes place?

You can postualte about the interior of a black hole as it can be described in the equations which govern the behaviour of space-time in the vicinty of a balck hole. Still point taken these quantities, while you can perform experiments to measure them, cannot be communicated outside.

The coldest temperatures in the known universe occur only in special laboratory experiments in which small regions are actually made colder than the background radiation of the universe. Unless some aliens are performing the same sorts of experiments out there, those are the coldest spots in the universe.

Well the surface temp. of a black hole can also be alot lower than the CMBR temp.