Q: Will black holes ever release their energy and will we be able to tell what had gone into them?

Physicist: In any reasonable sense the answer to both of these questions is a dull “nope”.  In theory however, the answer is an excitable “yup”!

Blackholes lose energy through “Hawking Radiation”, which is a surprising convergence of general relativity, quantum mechanics, and thermodynamics.  Hawking (and later others) predicted that a blackhole will have a blackbody spectrum.  That is, it will radiate like people, the sun, or anything that radiates by virtue of having heat.  Hawking also calculated what temperature a blackhole will appear to be radiating at.  He found that for a blackhole of mass M: $T = \frac{\hbar c^3}{8 \pi G k M}$, where everything other than M is a physical constant (even the 8, depending on who you talk to).  A more useful way to write this is to plug in all the constants to get:

$T = \frac{1.21 \times 10^{23}}{M}$, where M is in kilograms and T is in degrees Kelvin.  That “$10^{23}$” makes it seem like blackholes should be really hot, and in fact small ones (like those we hope to see at CERN) are crazy hot.  However, if the Sun ($M = 2 \times 10^{30}$ kg) were a blackhole its temperature would be about 60 nK (nano Kelvin).  …!  You wouldn’t want to lick it, or your tongue would stick.

Here’s the point.  Deep space glows.  It has a temperature of about 2.7K, which means that any blackhole that could reasonably form ($M > 10^{31}$ kg, or several Suns) is going to be way colder than that.  Since the blackhole is colder it will actually absorb more energy than it emits.  In order for a blackhole in the universe today to actually shrink it must have a temperature above 2.7K, and so it must have a mass less than $4.5 \times 10^{22}$, or around half the mass of the Moon.  Alternatively, you could wait several trillion years for the universe to cool down, and then the blackholes would start to evaporate.

As for the second half of the question: General relativity would suggest that when things fall into a blackhole they are erased.  Once they fall in, there’s no way to tell the difference between a ton of Soylent Green and a ton of Pogs (metric tonnes of course).  This makes quantum physicists really uncomfortable, because in addition to all the usual conservative laws (energy, momentum, drug policy) quantum physicists have “conservation of information”.  Lucky for them they also get to play with entanglement.  So if you chuck in a copy of War and Peace the blackhole will radiate thermally (which is the most randomized way to radiate) and will seem to scramble everything about Tolstoy’s pivotal work.  If you look at one outgoing photon at a time you’ll gain almost zero information.  If however, you can gather every outgoing photon, interfere them with each other and analyze how they are entangled you could (in theory) reconstruct what fell in.  However, you’d need to catch at least half of the photons before you could demonstrate that they hold any information at all.

This view of blackholes, that they hide information in the “quantum entanglement” between all of their radiated photons, makes them suddenly far more interesting.  Without going into to much detail, if you have N non-entangled 2-state particles you can have N bits of information, but if you have N entangled 2-state particles you can have 2N bits of information.  Allowing for entanglement frees up a lot of “extra room” to put information.

Suddenly, you’ll find that most (as in “almost all”) of the entropy in the universe is tied up in blackholes.  Also (again in theory), a carefully constructed blackhole can be the fastest and most powerful computer that it will ever be possible to create.

So, yes, blackholes will release all their energy, but you have to wait for the universe to cool down almost completely.  And, yes, we can tell what went into them, but we’ll have to wait for them to evaporate completely (after the universe has cooled down) and catch, without disturbing, almost every single particle that comes out of them.

This entry was posted in -- By the Physicist, Astronomy, Entropy/Information, Physics, Quantum Theory. Bookmark the permalink.

3 Responses to Q: Will black holes ever release their energy and will we be able to tell what had gone into them?

1. Andrew says:

Stephen Hawking stated that the information inside a black hole is lost forever as the black hole evaporates. Leonard Susskind argued that that violates the conservation of information and too much of the established world of physics. Since Leonard was so troubled by Hawking’s assertion, Hawking said that Susskind was the only one in the room who really grasped what he was implying. It took 28 years for Susskind to formulate his theory that would prove Hawking wrong. (And Hawking conceded.) But boy-oh-boy, the results are that there is a thoroughly weird complementarity between what is observed from outside a black hole and what is “observed” by anything entering the black hole. From the outside, all info gets violently shredded apart and is indeed lost forever. The stuff going into the black hole “observes” no big deal and it’s info is conserved.
Don’t blame me; it’s not my theory. I’m don’t pretend to fully understand it either. But Hawking eventually conceded Susskind’s point, which also led Susskind and Gerard t’Hooft to develop a holographic model of the universe. It’s all in Susskind’s The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics.
Any thoughts on this stuff???

2. The Physicist says:

Unfortunately not. Beyond what you’ve just written, I don’t have any useful details to add.

3. Xerenarcy says:

something doesn’t quite make sense to me about black holes and their thermodynamic properties.

at absolute zero, a gas (if it can still be in that state) would have low entropy; the states the particles can take on are limited and therefore through boltzmann’s relation, the entropy and temperature are low.

when entropy hits a maximum, the particles have the most degrees of freedom and the temperature is supposed to be rather high, plank-scale or up there. but entropy is not a linear function when the number of states has to do with the possible configurations. in other words, just like the binomial distribution has a maximum smack in the middle, so does entropy. therefore there can be such a thing as negative absolute temperature, which is still proportional to entropy but simultaneously hotter than hot and colder than cold. this happens when the particles are so saturated with energy that the only place they can go is into higher energy states, not lower.

the particle velocity distribution for a regular hot gas would show that most particles are found towards the colder temperature / lower speeds and a smaller and smaller set populate the higher energy states / faster speeds. in negative absolute temperature the reverse happens, particles are found closer to maximal energy states with fewer and fewer occurring at lower energy states. both scenarios have low entropy at the extreme ends and high entropy at the really hot +- inf range.

what bothers me with black holes, given the above is two things:

first, why is a black hole considered a maximal-entropy object if it is so cold? could it be experiencing negative absolute temperature behavior?

second, if time slows down in a stronger gravitational field, wouldn’t temperature be lowered as well relative to an outside observer? as in, to a black hole, a blackbody would appear to spontaneously cool as it approached? therefore wouldn’t space itself appear colder in the near vicinity of a black hole (relative to it) and incoming radiation would appear more energetic the more distant the source (assuming the same temperature black body from near and far)?