Since the 1970s, it has been known that black holes are not completely black. In fact, they emit very low-energy radiation called Hawking radiation. The lower the mass of a black hole, the higher the energy of the emitted Hawking radiation. As a black hole radiates, its mass decreases, and it starts emitting more and more radiation, causing it to evaporate more and more rapidly. Eventually, it shrinks to around the Planck mass, the point at which its DeBroglie wavelength is equal to the Schwarzschild radius. At this point, we no longer know what happens, since to describe physics at the Planck scale requires a theory of quantum gravity.
The apparent paradox here is that the radiation being emitted from a black hole is completely thermal, at least to lowest order (so perhaps black holes are black after all - black bodies, that is). This means that no matter what you make the black hole out of - a star, an encyclopedia, Oreo cookies - the same thing will come out of the evaporation. Looking at this process in reverse, thermal radiation combines to make a white hole, and then anything at all can come out of it. There is no way, even in principle, to predict what it will be.
All the evidence suggests that physics is completely deterministic at some level. We may not be able to actually collect all the data we need to make accurate predictions, but the information is there nonetheless. Therefore, the loss of information in black hole evaporation presents a puzzle - is the information actually being lost? If it is, how can we reconcile this with the deterministic world we observe? If it is not, how does the information escape the black hole?
There are many different proprosals for resolving this puzzle, but all of the suggestions have problems of their own. Some say that information is lost, but for some reason the effects are highly suppressed at scales we can observe. Another proprosal is that black hole evaporation ends with a massive remnant, and that all the information about how the black hole was formed is somehow stuffed into this single Planck scale object. Another suggestion is that when an object crosses the black hole's event horizon, information about it is somehow transferred to the outgoing Hawking radiation. The difficulty here is that to an object falling into the black hole, there is nothing special about the horizon - it looks just like everywhere else, aside from some tidal forces which will be small for a large enough black hole. Once it is inside the event horizon, there is no way that information about it could escape without going faster than light. Ultimately, no one has been able to come up with a completely satisfactory answer.
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October 29, 1997