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Gavin Polhemus
science forum beginner
Joined: 11 Jun 2005
Posts: 1
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 Posted: Sat Jun 11, 2005 7:46 am Post subject:
Hawking radiation and black hole formation
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I'm reading Birell and Daveies' "Quantum Fields in Curved Space". On
pp. 272-3, in a discussion of end point of black hole evaporation, they
note, "Gerlach (1976) claims that the horizon will not form at all."
The reference is to
THE MECHANISM OF BLACK BODY RADIATION FROM AN INCIPIENT BLACK HOLE.
By U.H. Gerlach (Ohio State U.),. 1976.
Published in Phys.Rev.D14:1479-1508,1976
The argument seems to be that Hawking radiation removes energy from the
black hole so that the horizon (and presumably the singularity) cannot
form. This process will be hugely red shifted, so you won't be able to
tell that there isn't a horizon through casual observation.
I would expect that that in the nearly thirty years since Gerlach's
paper this issue has been put to rest. However, in the 2001 paper
"Essential and inessential features of Hawking radiation," by Matt
Visser (hep-th/0106111) he says, "There is an unpopular minority opinion
that takes the view that because of Hawking evaporation a black hole
will never form a true event horizon." I'll ignore the question of
wether it is the opinion of and unpopular minority or just a minority
opinion that is unpopular (somewhat redundant)
Is there a calculation to back up either side in this debate? I haven't
found anything. The calculation doesn't appear to be terribly
difficult, but I don't want to invest a lot of time in it if it's been
done.
Thanks,
Gavin |
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Hontas F. Farmer III
science forum beginner
Joined: 05 May 2005
Posts: 38
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| Posted: Mon Jun 13, 2005 6:15 am Post subject:
Re: Hawking radiation and black hole formation
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Gavin Polhemus wrote:
| Quote: | I'm reading Birell and Daveies' "Quantum Fields in Curved Space". On
pp. 272-3, in a discussion of end point of black hole evaporation, they
note, "Gerlach (1976) claims that the horizon will not form at all."
The reference is to
THE MECHANISM OF BLACK BODY RADIATION FROM AN INCIPIENT BLACK HOLE.
By U.H. Gerlach (Ohio State U.),. 1976.
Published in Phys.Rev.D14:1479-1508,1976
The argument seems to be that Hawking radiation removes energy from the
black hole so that the horizon (and presumably the singularity) cannot
form. This process will be hugely red shifted, so you won't be able to
tell that there isn't a horizon through casual observation.
I would expect that that in the nearly thirty years since Gerlach's
paper this issue has been put to rest. However, in the 2001 paper
"Essential and inessential features of Hawking radiation," by Matt
Visser (hep-th/0106111) he says, "There is an unpopular minority opinion
that takes the view that because of Hawking evaporation a black hole
will never form a true event horizon." I'll ignore the question of
wether it is the opinion of and unpopular minority or just a minority
opinion that is unpopular (somewhat redundant)
Is there a calculation to back up either side in this debate? I haven't
found anything. The calculation doesn't appear to be terribly
difficult, but I don't want to invest a lot of time in it if it's been
done.
|
"...a true event horizon." Classically this would be an absolute and
deterministic boundary between the interior and exterior of a black hole a
sharply defined hyperspheroid. The horizon being an absolute boundary
beyond which there is no hope of return.
The problem with this interpretation, with Hawking radiation thrown into the
mix, is the problem contains nontrivial quantum mechanics. In quantum
mechanics everything is about probabilities and uncertainty (Heisenberg
Uncertainty). So instead of a sharply defined horizon what you have is a
blurry, fuzzy, roughly hyperspheroid boundary. Particles near the boundary
have a finite probability of passing to either side of the boundary.
The concept one has to accept is that a black hole is nothing more than a
deep finite gravitational potential well. Then because the potential well
is finite there is a nonzero probability that a particle will be tunnel out
of the black hole. The equations needed are a Schrodinger type equation
with the potential of gravity and appropriate boundary conditions. Exactly
what equations one needs to solve depends on which theory of quantum
gravity they prefere.
--
Let me get this straight we "advanced" from telgraphs to email?-GeorgeCarlin
http://www.geocities.com/hontasfx |
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Ilja Schmelzer
science forum Guru
Joined: 11 May 2005
Posts: 377
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| Posted: Tue Jun 14, 2005 5:22 am Post subject:
Re: Hawking radiation and black hole formation
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"Gavin Polhemus" <gavinpublic@comcast.net> schrieb
| Quote: | The reference is to
THE MECHANISM OF BLACK BODY RADIATION FROM AN INCIPIENT BLACK HOLE.
By U.H. Gerlach (Ohio State U.),. 1976.
Published in Phys.Rev.D14:1479-1508,1976
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Nice. I would also like to hear comments about this.
| Quote: | I would expect that that in the nearly thirty years since Gerlach's
paper this issue has been put to rest. However, in the 2001 paper
"Essential and inessential features of Hawking radiation," by Matt
Visser (hep-th/0106111) he says, "There is an unpopular minority opinion
that takes the view that because of Hawking evaporation a black hole
will never form a true event horizon."
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I'm part of this minority.
On the other hand, I think that the issue cannot be uniquely solved,
until we have a theory beyond semiclassical gravity.
The point is that the evaporation needs a renormalization of the
energy-momentum tensor. This seems to be, IMHO,
equivalent to fixing a preferred vacuum state (~ the state
where the renormalized energy-momentum tensor has
minimal energy). And fixing a preferred vacuum state is
similar to fixing a preferred system of coordinates.
If we follow Gerlach's scenario we, essentially, prefer
the Schwarzschild time coordinate.
That's why, I think, people who hope for a coordinate-
independent approach to quantum gravity reject it and
hope for something better. In the "better" scenario,
the infalling observer has equal rights until he hits the
singularity, therefore there should be a horizon. But,
essentially, this is only a hope.
Ilja |
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Baugh
science forum addict
Joined: 06 May 2005
Posts: 79
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| Posted: Sat Jun 18, 2005 5:38 am Post subject:
Re: Hawking radiation and black hole formation
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Gavin Polhemus wrote:
| Quote: | I'm reading Birell and Daveies' "Quantum Fields in Curved Space". On
pp. 272-3, in a discussion of end point of black hole evaporation, they
note, "Gerlach (1976) claims that the horizon will not form at all."
The reference is to
THE MECHANISM OF BLACK BODY RADIATION FROM AN INCIPIENT BLACK HOLE.
By U.H. Gerlach (Ohio State U.),. 1976.
Published in Phys.Rev.D14:1479-1508,1976
The argument seems to be that Hawking radiation removes energy from the
black hole so that the horizon (and presumably the singularity) cannot
form. This process will be hugely red shifted, so you won't be able to
tell that there isn't a horizon through casual observation.
I would expect that that in the nearly thirty years since Gerlach's
paper this issue has been put to rest. However, in the 2001 paper
"Essential and inessential features of Hawking radiation," by Matt
Visser (hep-th/0106111) he says, "There is an unpopular minority opinion
that takes the view that because of Hawking evaporation a black hole
will never form a true event horizon." I'll ignore the question of
wether it is the opinion of and unpopular minority or just a minority
opinion that is unpopular (somewhat redundant)
Is there a calculation to back up either side in this debate? I haven't
found anything. The calculation doesn't appear to be terribly
difficult, but I don't want to invest a lot of time in it if it's been
done.
Thanks,
Gavin
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I haven't read the reference so am expressing an uninformed opinion but...
Given a black-hole can classically form with arbitrary original size
and given the Hawking radiation is reduced by size I would assume that
in general the Hawking radiation couldn't prevent general large event
horizon "formation".
Technically the event horizon(s) is(are) there before the mass
forms a black hole in the form of an expanding light-cone.
Think of a light cone as an event horizon expanding at the speed of
light. (Note that these are coordinate surfaces with physical
significance but not physically existant objects).
As the mass goes up the future light-cone for a centered event will
eventually be bent into a cylinder (2-sphere x time line). This "moving
event horizon" becomes stationary. If the inclusion of Hawking's
radiation makes it "almost stationary" then its still effectively there.
I don't see what can be ment by the event horizion failing to exist.
Given a large enough stellar collapse the in-falling mass must
exceed outflux of Hawking radiation and so eventually there will
be a boundary between "collapsing event horizons" and "expanding event
horizons" an the stationary one usually refered to.
Inclusion of the quantum effects shouldn't change this except that
the interpretations may become statistical instead of exact. Keep
in mind things do not get small at the event horizon but rather
near the singularity so that the distinction between classical
and quantum predictions should converge to nil at the event horizon
as the considered mass grows.
Unless one is talking primordial black holes I don't see how
the assertion can be justified.
--
Regards,
James Baugh |
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