Questions regarding Hawking radiation

  • I
  • Thread starter Buzz Bloom
  • Start date
  • #26
2,791
591
Feel free to think so, I have doubt that this is a valid result. I would say that there exist some regularizations which will show Hawking radiation. This is what has to be expected if the regularized picture is non-static. Instead, regularizations where the regularized black hole is static do not show Hawking radiation.
What regularization are you talking about?
The point being? Once we talk about Hawking radiation, we talk about radiation observable to a far away observer. So, why would the nearby infalling observer matter at all?
The point being that the surface of the star actually falls behind the horizon, its just that the observer at infinity can't observe this because of his peculiar time.
A nice argument that there cannot be any Hawking radiation for a longer period of time.
Hawking radiation doesn't originate at the horizon!
And that it uses quite nonsensical assumptions about the validity of the calculation in horribly trans-Planckian regions is completely clear too.
Outside the horizon of a black hole is not a trans-Planckian region. Its not even a high curvature region if the black hole is massive enough.
 
  • #27
2,791
591
Don't cry.
I let this inappropriate behavior slide this time!
It originates in a region arbitrary close to the horizon. This can be proven, my modifying the classical background, replacing it with a collapse which stops at the radius rS+εr_S + \varepsilon with arbitrary small ε\varepsilon. In this case, the Hawking radiation stops once the stable state is reached. See https://arxiv.org/abs/0906.1768v2 for details. If we have Hawking radiation in one case and no Hawking radiation in the other case, the origin is the region where they differ. The two solutions differ only below rS+εr_S + \varepsilon, so, the origin is this region.
The paper is pretty clear on what its talking about and it doesn't at all support what you claim. Its about the thermal radiation from quantum fields while the star is still collapsing. If the collapse doesn't result in a horizon, the radiation will stop. But if it does result in a horizon, the radiation will continue and that's the famous Hawking radiation. Just read the conclusion part of the paper.
 
  • #28
2,791
591
My point is that this difference is sufficient to identify the origin of Hawking radiation. The origin cannot be in a region where above solutions do not differ, because in this case the radiation would be the same. It has to be originated in a region where they differ. And the region where they differ, and which can causally influence the observer at infinity (which is done by having Hawking radiation or not), is the exponentially thin region between rSr_S and rS+e−105lPlr_S + e^{-10^5} l_{Pl} one second after the collapse of a solar-sized BH.
The presence of the horizon matters. Its not like we need a special place for Hawking radiation, we need the horizon itself.
In fact it has been proven that the Hawking radiation originates from a region around the horizon whose size is comparable to the size of the horizon itself. Also, the wavelength of this radiation is larger than the radius of the horizon so you can't pinpoint an infinitesimal region where the radiation originates.
 
  • #30
674
83
The presence of the horizon matters. Its not like we need a special place for Hawking radiation, we need the horizon itself.
Not good for Hawking radiation being a reliable thing if it depends on this. This would mean that we have to know the future to find out if there is Hawking radiation or not. Because you can easily define a time-like coordinate so that the horizon is formed only in the future. Schwarzschild time would do it.
In fact it has been proven that the Hawking radiation originates from a region around the horizon whose size is comparable to the size of the horizon itself.
Thank you for the link. A Physics Letters paper which can easily shown to be wrong is good news for getting a Physics Letters paper refuting it.
Also, the wavelength of this radiation is larger than the radius of the horizon so you can't pinpoint an infinitesimal region where the radiation originates.
As if this would prove anything.

Hm, let's try. Take a charge and move it, up and down, at home once in a second. What will be the wavelength of the EM wave created by this moving charge? What does this tell us about the size of the origin of this wave?
 
  • #31
2,791
591
Not good for Hawking radiation being a reliable thing if it depends on this. This would mean that we have to know the future to find out if there is Hawking radiation or not. Because you can easily define a time-like coordinate so that the horizon is formed only in the future. Schwarzschild time would do it.
I don't quite understand what you're trying to say.

As if this would prove anything.

Hm, let's try. Take a charge and move it, up and down, at home once in a second. What will be the wavelength of the EM wave created by this moving charge? What does this tell us about the size of the origin of this wave?
Here we're talking about particles. If there is an electron with de Broglie wavelength of the order of a stadium, it doesn't make sense to say where in the stadium that electron is.
 
  • #32
674
83
I don't quite understand what you're trying to say.
Hm, let's try again. I think a theory which predicts that I observe / do not observe radiation in dependence of some fact which happens only in the future, with everything which has already happened in the past, and up to now, being equal, would have a big problem with causality.

This holds for every time-like coordinate. If I have a time-like coordinate, and the fact if I observe Hawking radiation or not depends on something which is, according to this time coordinate, in the future, this sounds like a problem for Einstein causality, not?

For every event for an observer at infinity, who observes Hawking radiation, one can easily find a time-like coordinate where the horizon is not yet formed. Outside the collapsing body, standard Schwarzschild time will define one such coordinate. So, your claim
"The presence of the horizon matters. Its not like we need a special place for Hawking radiation, we need the horizon itself."
suggests me that such a position has a serious problem with Einstein causality.

In my opinion, all what can matter for the prediction of Hawking radiation at some far away event is what is part of the past light cone of this event. And this part does not contain any horizon, for all those events horizon formation is yet only future, so that it may be not even certain if a horizon will form or not.
Here we're talking about particles. If there is an electron with de Broglie wavelength of the order of a stadium, it doesn't make sense to say where in the stadium that electron is.
Sorry, no, I'm not talking about particles. I'm talking about radiation. And I know that to attribute a position to a photon is not unproblematic, so I do not talk about such positions. I was talking about the region which has caused the radiation. My example suggest that such a region may be much smaller than what the wavelength suggests.
 

Related Threads on Questions regarding Hawking radiation

  • Last Post
Replies
7
Views
878
  • Last Post
Replies
7
Views
3K
Replies
30
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
15
Views
3K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
5K
  • Last Post
2
Replies
46
Views
7K
Top