What is Black Hole Complementarity?
I think I can tell you what it is, but I cannot tell you what the consequences are. The principle is based on the fact that Hawking radiation arises from the different definitions of particles and vacuum for a freely falling observer and for a locally accelerated observer located at a constant radius from the black hole. The observer at a constant radius perceives the black hole exerting a thermal radiation (Hawking radiation) and he can consider the black hole to be at a specific temperature. He also observers matter falling into the black hole. The freely falling observer just crosses the horizon towards the singularity without measuring anything of that. Black hole complementarity means an equivalence of both descriptions. Now, regarding consequences, note that this is not just like two different descriptions from two different coordinate systems, because a horizon exists which breaks any possible correlation between events inside and outside the black hole. May be someone can tell us more about this.
I thought that an accelerated observer would perceive Unruh radiation not Hawking, no?
If an accelerated observer as you say perceives Hawking radiation, then we on Earth would not see this Hawking radiation since we are not that observer?
Unruh radiation is not a gravitational effect. An observer at a fixed position in Schwarzschild spacetime would detect Hawking radiation.
Um, aren't they really the same thing when you come right down to it? Accelerated observer in a relativistic quantum vacuum?
Yes. Because of the principle of equivalence.
You are right, it is only an issue about terminology for two different scenarios, as both are physically the same due to the equivalence principle.
Separate names with a comma.