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Thread: Hawking radiation and graviational redshift ... ?

  1. #1 Hawking radiation and graviational redshift ... ? 
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    If Hawking radiation emanates from infinitesimally outside the event horizon, how could it ever be observed, even in principle, since it is coming from infinitesimally close to a 'surface of infinite redshift'? Given its starting point, a particle arising from an event 'at' or 'very close to' the event horizon would surely never have time to reach a distant observer, or if a photon, would be so red-shifted as to be undetectable?

    If it turns out that it cannot be observed, what evidence might we seek to establish whether it exists or not?
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    Quote Originally Posted by lesaid View Post

    If it turns out that it cannot be observed, what evidence might we seek to establish whether it exists or not?
    What do you think? How can you "seek to establish" if you cannot observe?
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    That is part of my point! From what I have read, there seems to be an assumption that in principle, Hawking radiation, if it exists, would be detectable, though we'll have a problem detecting it because we don't have any tiny black holes in the lab to experiment with. The Hawking radiation from large astronomical objects would be faint and swamped by other radiation, from accreting material or whatever else is going on in the region.

    But, I don't understand how that radiation would be detectable at all by a distant observer because of gravitational redshift/time dilation. If it truly is undetectable and has no other indirectly detectable consequences, then what difference does it make to any useful theory, since whether it exists or not would seem irrelevant to everything. That cannot be right. Hence my confusion!

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    Quote Originally Posted by lesaid View Post
    That is part of my point! From what I have read, there seems to be an assumption that in principle, Hawking radiation, if it exists, would be detectable, though we'll have a problem detecting it because we don't have any tiny black holes in the lab to experiment with. The Hawking radiation from large astronomical objects would be faint and swamped by other radiation, from accreting material or whatever else is going on in the region.

    But, I don't understand how that radiation would be detectable at all by a distant observer because of gravitational redshift/time dilation. If it truly is undetectable and has no other indirectly detectable consequences, then what difference does it make to any useful theory, since whether it exists or not would seem irrelevant to everything. That cannot be right. Hence my confusion!

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    The redshift is not infinite. This is your mistake.
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    Thank you for the swift replies

    I think I have a problem in principle (highly likely - I am a rookie at this!). I notice that the wiki link you posted quotes an unfamiliar (to me) metric while I had been considering equations derived using SW coordinates. I am aware of the 'coordinate' nature of the singularity at the event horizon using the SW coordinates. However, I also understand that (in this coordinate system) at a large distance, coordinate times and observed 'proper' times converge. This seems to predict an observed (distant) redshift that tends to infinity as the radius of the emission event tends towards that of the event horizon.

    If the above is true, then I have a problem getting my head around the notion that a different metric describing the same SW solution will make a different prediction of what would actually be observed by such a distant observer? If different metrics result in different 'proper' predictions for the same observer, how do we reconcile the differences?


    Or was your comment referring to the observation of the redshift being from a finite (if very large) rather than infinite distance, and that (using the SW coordinates) the emission event must be at some tiny distance outside the EH - so in principle, the redshift would actually be finite, if huge?

    Could you elaborate please?
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    Quote Originally Posted by lesaid View Post
    Thank you for the swift replies

    I think I have a problem in principle (highly likely - I am a rookie at this!). I notice that the wiki link you posted quotes an unfamiliar (to me) metric while I had been considering equations derived using SW coordinates. I am aware of the 'coordinate' nature of the singularity at the event horizon using the SW coordinates. However, I also understand that (in this coordinate system) at a large distance, coordinate times and observed 'proper' times converge. This seems to predict an observed (distant) redshift that tends to infinity as the radius of the emission event tends towards that of the event horizon.
    But the "emission" does NOT happen from the EH. It is from ABOVE the EH. Hence, the redshift is not infinite.

    If the above is true, then I have a problem getting my head around the notion that a different metric describing the same SW solution will make a different prediction of what would actually be observed by such a distant observer?
    It doesn't make a "different" prediction.


    If different metrics result in different 'proper' predictions for the same observer,
    They don't.


    Or was your comment referring to the observation of the redshift being from a finite (if very large) rather than infinite distance, and that (using the SW coordinates) the emission event must be at some tiny distance outside the EH - so in principle, the redshift would actually be finite, if huge?
    Yep.
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    Thanks!

    That brings a further question to mind - how far above the EH might we be talking about? As I understand one of the interpretations, this would depend on the likelihood that tidal forces would separate a pair of newly created virtual particles. This would seem to depend on the gravitational gradient at that point and would be independent of where the EH actually was. So for a small enough black hole, the point of radiation could be considerably above the EH, and involving not just a finite redshift but a relatively small redshift. Have I the right idea?
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    Quote Originally Posted by lesaid View Post
    Thanks!

    That brings a further question to mind - how far above the EH might we be talking about? As I understand one of the interpretations, this would depend on the likelihood that tidal forces would separate a pair of newly created virtual particles. This would seem to depend on the gravitational gradient at that point and would be independent of where the EH actually was. So for a small enough black hole, the point of radiation could be considerably above the EH, and involving not just a finite redshift but a relatively small redshift. Have I the right idea?
    For a very good treatment, see here.
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  9. #9  
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    thank you
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