Redshift and time dilatation of Hawking radiation

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Discussion Overview

The discussion centers on the relationship between redshift, time dilation, and Hawking radiation emitted by micro black holes. Participants explore the implications of these phenomena for observers at varying distances from the black hole, particularly in the context of quantum processes and the nature of emitted radiation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests that extreme redshifting and time dilation should occur for Hawking radiation emitted close to the event horizon, questioning how this affects observations from a distance.
  • Another participant emphasizes the quantum nature of Hawking radiation, arguing that it should not be viewed purely mechanistically and that the radiation is a global effect rather than localized at the event horizon.
  • A participant acknowledges that if the wavelength of emitted particles is comparable to the size of the black hole, the anticipated redshift may be less significant than initially thought, but still questions whether some redshift occurs as photons escape the gravitational influence of the black hole.
  • There is a request for calculations regarding the redshift of Hawking radiation as photons climb out of the gravity well.
  • One participant states that Hawking radiation is already expressed for an asymptotic observer, implying that no additional redshift should be considered.

Areas of Agreement / Disagreement

Participants express differing views on the significance of redshift in the context of Hawking radiation and whether it should be considered for distant observers. The discussion remains unresolved regarding the extent and implications of redshift and time dilation in this context.

Contextual Notes

Participants note the complexity of the phenomena involved, including the dependence on quantum mechanics and the definitions of terms like "thermal bath" and "global effect." There are unresolved questions about the calculations related to redshift and the comparison between Unruh radiation and Hawking radiation.

timmdeeg
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Micro black holes should in principle be observable by emitting Hawking radiation. However, as this takes place extremely close to the event horizon, shouldn't one expect then extreme redshifting (z = 1/(1-Rs/R)^-1/2 -1, Rs = Schwarzschildradius, R = Radius of Emission) and time dilatation?
In other words, shouldn't see the far away observer the Hawking radiation almost 'frozen'? How long does it take to reach him in far away coordinates?
 
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timmdeeg, It's important to remember that Hawking radiation is fundamentally a quantum process, and therefore one shouldn't try to take a view of it which is purely mechanistic. All one can say is that the vacuum "in" state contains near future null infinity a thermal bath of outward-going particles. For example where are the particles created? In the vicinity of the hole. You can't say whether it occurs on the surface or near the surface - it is a global effect. And in fact the predominant wavelength of the created particles is about as large as the hole itself.
 
Bill_K said:
All one can say is that the vacuum "in" state contains near future null infinity a thermal bath of outward-going particles. For example where are the particles created? In the vicinity of the hole. You can't say whether it occurs on the surface or near the surface - it is a global effect. And in fact the predominant wavelength of the created particles is about as large as the hole itself.
Thank you, Bill, your answer is very helpful. So, if the wavelength is in the order of the black hole, the redshift is much less significant than I was anticipating it. But there should still be some redshift, as the photon climbs out of the gravity well of the hole, right? Are there any calculations?

You mentioned the thermal bath. Could you kindly explain, whether there is any physical difference between Unruh radiation and Hawking radiation near the horizon?
 
the Hawking radiation is already expressed for an asymptotic observer, so there's no additional redshift
 
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Ok, thanks for clarifying.
 

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