Are Unruh radiation and Hawkins radiation manifestations of the same basic phenomenon?
They're similar, for sure. But not completely identical.
The phenomenon of Unruh radiation shows that the number of photons is an observer-dependent feature of the universe: accelerated observers see more radiation. The additional photons can be viewed as stemming from the apparent event horizon that arises in the space-time of an accelerated observer, which makes them very similar to Hawking Radiation.
The difference is that Hawking radiation is visible to all observers, not just accelerated ones.
They are related by the equivalence principle, but an acceleration does not equal a gravitational field; they only imply the same physical effects locally in spacetime.
Actually we don't know whether that is true. In Hawking's original model, it wasn't; an observer free-falling into a black hole would see no Hawking radiation. There are other more recent models in which the free-falling observer does see something, but it still isn't always the same as what the accelerated observer sees. This question probably won't be resolved until the black hole information paradox is resolved.
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