When I first heard about the black hole information paradox, I thought it had no content. At the time, papers about it had been written for numerous years and they keep on coming. Now that the press got wind of Hawking's latest one, I thought I should ask about it:
The information paradox relies on the no-hair conjecture. However, all its proofs I'm aware of rely on the fact that we end up with a stationary black hole. So once we introduce Hawking radiation, the theorem evaporates right besides its subject.
Basically, we're wondering why a theorem we have proven for the stationary case does not hold for the non-stationary case. That seems hardly surprising to me, but I may have missed something obvious.
On a related note, I always found the no-hair theorem somewhat suspicious because it means after formation of the black hole, we end up with a result stronger than Gauss's law, whereas before formation of the black hole, the generalizations of Gauss's law to relativistic gravity are (again, as far as I know) generally weaker.
To illustrate the argument from a different point of view, let me describe the thermodynamic information paradox:
First, lets start with the no-hair theorem, which states that isolated systems will tend towards a stationary equilibrium state, uniquely described by just a few parameters.
While going forward, instead of looking at completely isolated systems, we now allow interaction via absoption and emission of radiation.
The asumption is that because the system has no hairs, no matter the incoming radiation, the outgoing radiation will obey the totally probabilistic thermal laws.
Let's also assume that we're going to reach $T=0$ after all energy has been radiated.
This is, as far as I can tell, a pretty close analogy to the black hole paradox, and has a simple resolution: Physical equilibrium states fluctuate and thus have hairs. In fact, thermal radiation alone will disrupt equilibrium, and just assuming that it doesn't leads to nonsense.
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