Where does Hawking radiation come from?

Assuming Hawking radiation is detected some day, it is still unclear where it came from.

Let’s first recall what happens to a signal emitted by something falling into a black hole. The closer the source of emission gets to the event horizon, the weaker, slower and “redder” the signal detected by an outside observer becomes. Theoretically, it takes forever for an outside observer to see the infalling object reach the event horizon. More practically, the detected signal gets weakened and redshifted to undetectability exponentially quickly, so that after only a short time after the redshift becomes significant the signal all but disappears, its wavelength exceeding the size of the universe.

Now, the Hawking radiation would be seen coming straight out of a black hole, but, if you trace it back to its source, where would it be? Clearly it cannot have come from the black hole horizon itself, since nothing can leave the horizon. If the black hole in question is paired with a white hole, then Hawking radiation can conceivably come from the white hole. It would have to originate somewhere near the white hole singularity and then be hurled out through the white hole event horizon. But there is no clear reason why thermal radiation would be the only thing emitted. After all, the known laws of physics are likely to break down near the singularity and we have no idea what is going on there. Besides, the original calculation by Hawking and others assumes only that the black hole event horizon exists, and nothing more exotic, like white holes or singularities.

Let us come back to how Hawking originally popularly explained the origin of the black hole radiation. He interpreted his calculations as follows. A wave packet (a short “ray of light”)  going outward near the black hole horizon “splits into two”, one with “positive frequency” (and positive energy) going outward and one with “negative frequency” (and negative energy) going inward and getting trapped inside the black hole. Thus the black hole “sucks in” negative energy and loses mass. But where does the original wave packet come from? According to Hawking, the vacuum fluctuations are the source. A fluctuation with total zero energy gets split as described and the part with positive energy goes outward and becomes part of the thermal radiation. In essence, he treated black hole as an atom in a highly excited state, only with gravitational field instead of electromagnetic one.

So, according to this logic, Hawking radiation originates somewhere close to the black hole horizon, since the vacuum field fluctuations have to live long enough for the negative-energy part to be consumed by the black hole. But remember that the signal emitted from near the horizon gets extremely weakened when escaping the black hole. Which means that if it is still measurable, it must have been really really strong near the horizon. How strong? A typical thermal photon detected far away from a stellar black hole has been weakened over billion billion billion billion times. It must have been fantastically strong near its birthplace. It would have to be more energetic than anything we ever observed in the Universe. More energetic than anything LHC can ever hope to produce. Stronger than gamma-ray bursts coming out of supernova explosions or colliding neutron stars. One would be hard-pressed to attribute the birth of such energetic photons to mere vacuum fluctuations near horizon.

So, what on Earth (well, in space) is going on? There is no clear answer, as far as I know. The hints from the so called AdS/CFT Correspondence suggest that “black holes are time-reverse dual to themselves, and thus black hole and white hole are the same object”. How is this statement to be understood in a more macroscopic context? I hope to return to this question when I figure it out 🙂

Slightly more calculational details and mildly illuminating pictures are at http://www.scholarpedia.org/article/Hawking_radiation and http://physics.stackexchange.com/questions/22498/from-where-in-space-time-does-hawking-radiation-originate.

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