Hawking radiation and the Cancellation problem
| HAWKING RADIATION |
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Hawking radiation and the Cancellation problem |
In the popular description of Hawking radiation, a particle-pair is created outside a black hole, with one member of the pair escaping and its antiparticle being swallowed. The creation of the particle pair is described as being associated with the creation of a two-particle energy-deficit in the black hole's field, one particlesworth of which is then repaid when the infalling member is absorbed. The end result is that one particle escapes, and the black hole mass and radius shrinks accordingly.
A more difficult problem concerns the black hole's information content. For the black hole to shrink, its information-density must reduce when it emits the particle. The information encoded in the emitted particle must be a mirror-image copy of the information in its antiparticle. For the black hole's content to reduce rather than increase when it swallows the antiparticle, suggests that the antiparticle is then cancelling with another positive image of the same information when it enters the hole.
This would mean that when the antiparticle is absorbed, an equivalent particle of information must disappear form inside the horizon, which means that the particle that disappears inside r=2M must be identical to the particle that appears outside the horizon. To all intents and purposes, the particle that is emitted IS the particle that disappears from inside r=2M.
if the physical description, separated from coordinate-system language and projective extrapolations, is that a particle disappears from inside r=2M and is then seen outside the horizon heading outwards, the simplest "unsophisticated" description is that the hole is somehow leaking particles, in violation of GR1960's physics.
How it could be leaking particles is more involved, but that's what we must appear to see happening. Hawking radiation is not random – the emitted particles or groups of particles must carry information that previously fell into the hole, and must appear to correspond to part of the hole's contents.}}
Notes
Since this apparent emission of contained particles appears to wreck with GR1960's insistence that nothing can leave a black hole an early suggestion was that the emitted particles HAD to be random, and could not possibly correspond to the hole's contained information. This left us with the problem of explaining where the contained information went to when the hole finally completely evaporated, which led to the suggestion that perhaps a residual Planck-scale feature was left behind that contained all the information of the original hole (with the remnant dubbed a "cornucopion"). With the gaining acceptance of the idea that the horizon area corresponded to the information-content of the hole this idea had to be dropped., and we had to accept that the information encoded in Hawking radiation really did originate with the hole's contents.
