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The reason why it is often stressed that Hawking radiation is in a pure state, is that this is in apparent contradiction to the fact that Hawking radiation is also said to be thermal. The apparent contradiction is solved when one realizes that in a general curved spacetime there is no unique definition of the vacuum state and therefore the whole Hilbert ...

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If one assumes no other matter is supplied to the black hole (which is difficult to describe in a general manner as it depends on the details of the environment), the question if black holes evaporate depends on the difference between the emitted Hawking radiation and the absorbed cosmic microwave background radiation. According to the Stefan-Boltzmann law ...

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... is this what is responsible for Radioactive Decay? Sort of ... radioactive decay occurs when the final state (result of the decay) has lower energy than the initial nucleus and the barrier is occasionally surmounted. This barrier penetration and the virtual pair at the black hole horizon are both quantum processes, so they have a little physics in ...

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I'm going to give this a shot, cause I think it's a fun question, but you probobly should work it out a bit more. Virtual particles, or particle/anti-particle creation looks like 1 electron and 1 anti electron (for example) existing briefly then cancelling each other out. If it happens in the void of space, they interact with each other and - poof, gone. ...

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At least for the radioactive decay that most people are familiar with, and that you're probably talking about, electroweak force is the cause.

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The light due to Hawking radiation will only ever be detected from very tiny black holes. The Hawking radiation scales as the inverse square of the black hole mass, but the radiation causes the black hole mass to decrease. This causes accelerated emission, such that all tiny black holes will go through a phase of emitting all their rest mass as $10^{22}$ J ...

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Hawking radiation is such a miniscule effect we can be sure we'll never detect it for a real astrophysical black hole. The Wikipedia article gives some numbers: For a black hole of the mass of the Sun, the power emitted in Hawking radiation amounts to $9\times10^{-29}\ \mathrm{W}$. Even if all this energy were converted to visible-light photons ...

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Yes and no. Electrons - and all other elementary particles - may be viewed as microstates of very tiny black holes. As one considers increasingly heavy elementary particles (e.g. those in the Hagedorn spectrum of string theory), they increasingly morph into black hole microstates. When the elementary particle masses sufficiently surpass the Planck scale, ...

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