Photons orbiting a Black Hole

In article <ECJ6d.4419$nj.1925@newssvr13.news.prodigy.com>, T wrote:
 > So, if photons have mass, and velocity, then in the case when they are
 > captured by a 'black hole' is there a place where they orbit but are not
 > impacted into the body itself?
 >
For black holes above a certain size (complex calculation), I
believe so.
About a decade ago, Scientific American (IIRC) did an article about
this.

 > And if the mass and velocity are constant (based on my as yet
 > unresearched assumptions)
 >
Research them by applying a hammer to a nail. Mass and velocity are
not, and have never (seriously) been proposed to be constant. That's like
saying that cheese is constant (when we all know that cheese decays by the
irregular emission of cheesons).

--
Aidan Karley,
Aberdeen, Scotland,
Location: 57°10'11" N, 02°08'43" W (sub-tropical Aberdeen), 0.021233<!-- ~MESSAGE_AFTER~ -->
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Aidan Karley wrote:

 > For black holes above a certain size (complex calculation), I
 > believe so.
 > About a decade ago, Scientific American (IIRC) did an article
 > about
 > this.

It's true for all black holes, and the calculation is not exactly
complex.

--
__ Erik Max Francis && max RemoveThis @alcyone.com && <a style='text-decoration: underline;' href="http://www.alcyone.com/max/" target="_blank">http://www.alcyone.com/max/</a>
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So, I now have enough of a clarification (about both photons/black holes
AND cheese) to go "Hmmmm" and ponder my initial question further.

I'll be back....


Thx,
TBerk
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T <tberk DeleteThis @sbcglobal.net> wrote in message news:<ECJ6d.4419$nj.1925@newssvr13.news.prodigy.com>...
 > [No, it's not directly from a Niven story, but it's in the same vein so to
 > speak.]
 >
 > So, if photons have mass, and velocity, then in the case when they are

Photons don't have a mass. However, they do have momentum, equal to
E/c, where E is the energy of the photon. That means that they respond
to gravitational fields, and that they can generate them as well. They
have the same amount of gravitational pull as the amount of mass that
would have to be annihilated to create those photone: E/c2.

 > captured by a 'black hole' is there a place where they orbit but are not
 > impacted into the body itself?

Yes. If I remember correctly, that occurs for an orbit with a
circumference equal to 3/2 the circumference of the event horizon (I
talk about circumference, rather than radius, because the only
meaningful radius you can calculate for the event horizon is
infinite).

 > And if the mass and velocity are constant (based on my as yet unresearched
 > assumptions) does this mean the orbit is also a constant and therefore
 > chock full of orbiting photons?
 >
 > What might be the result of a 'solid' (applied loosely to mean 'packed full
 > of') orbit of photons be like? What happens when more crowd in but there
 > isn't any 'room' left?

Erik has already addressed the conceptual errors behind that question.
I'll talk about an interesting, related concept.

One of the more interesting theoretical objects ever concieved is
called a KugelBlitz (Ball of Light). It's made up entirely of photons
circling the center of the KugelBlitz. Why are they circling? Because
of the graviational field of the KugelBlitz. Why does it have a
gravitational field? Because of the energy content of those photons.

Neat! Unfortunately, because of quantum effects, it's unstable.
Photons that were originally in the correct orbit have a finite chance
of transitioning into an orbit that allows them to escape. However,
for a sufficiently large KugelBlitz, the decay rate is so low that a
KugleBlitz as old as the Universe could still retain enough photons to
hold them in a circular orbit.<!-- ~MESSAGE_AFTER~ -->
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Erik Max Francis <max.TakeThisOut@alcyone.com> wrote in message news:<415B725B.A3305532.TakeThisOut@alcyone.com>...
 > T wrote:
....
 > Photons are bosons, so they don't obey the Pauli exclusion principle. Even
 > if there were a stable photon orbit, you could have as many photons
 > as you wanted there; photons don't interact with each other, and any


They do interact, but only very weakly. Primarily they interact by the
formation of a particle and it's anti-particle, which then collide
with each other to create a new pair of photons. In general, the new
photons will be traveling in a different direction from the originals,
so the net effect is as if the photons had collided and bounced off
each other.

For photons with less energy than the ones created by
electron-positron annihilation, this process is very weak, because
creation of the intermediate particle-antiparticle pair is
energetically forbidden. That doesn't mean it doesn't happen. Quantum
mechanics allows violations of conservation of Energy by delta_E, so
long as the violation lasts for a period of time delta_T not much
longer than h_bar/delta_E, where h_bar is an extremely tiny number. As
a result, the cross section for such collision is extremely low, but
not zero.<!-- ~MESSAGE_AFTER~ -->
 >> Stay informed about: Photons orbiting a Black Hole 

In article <8b42afac.0410021930.41205909 DeleteThis @posting.google.com>, James
Kuyper wrote:
 > One of the more interesting theoretical objects ever concieved is
 > called a KugelBlitz (Ball of Light). It's made up entirely of photons
 > circling the center of the KugelBlitz. Why are they circling? Because
 > of the graviational field of the KugelBlitz. Why does it have a
 > gravitational field? Because of the energy content of those photons.
 >
 > Neat! Unfortunately, because of quantum effects, it's unstable.
 > Photons that were originally in the correct orbit have a finite chance
 > of transitioning into an orbit that allows them to escape. However,
 > for a sufficiently large KugelBlitz, the decay rate is so low that a
 > KugleBlitz as old as the Universe could still retain enough photons to
 > hold them in a circular orbit.
 >
Errr, wouldn't that imply an energy density at the centre of the
KlugelBlitz that was so high that massive particles/ antiparticles would
be created, whose mass would then trigger gravitational collapse into a
black hole?

I wondered once about what happens in an evaporating (Hawking
radiation) black hole, as it went through it's catastrophic decay phase.
[Small black hole size leads to highly curved space near the event
horizon, leads to rapid increase in mass loss through Hawking radiation,
leads to smaller black hole leads to positive feedback loop.] At some
point the intensity of the radiation is going to increase to the state
that the average Hawking radiation particle pair that would be produced
would have an "E=m.c²" rest mass over half the rest mass of the black
hole. So that particle pair would be emitted, and one would escape.
Which would leave the black hole needing to emit another particle of
greater (average) mass, but without the mass/energy to produce such a
particle.
Would the black hole then have become stable against decay by
Hawking radiation?

--
Aidan Karley,
Aberdeen, Scotland,
Location: 57°10'11" N, 02°08'43" W (sub-tropical Aberdeen), 0.021233<!-- ~MESSAGE_AFTER~ -->
 >> Stay informed about: Photons orbiting a Black Hole 

Aidan Karley <aidan.RemoveThis@abuse.demon.co.uk.invalidated> wrote in message news:<VA.0000021a.04792b2f.RemoveThis@abuse.demon.co.uk.invalidated>...
 > In article <8b42afac.0410021930.41205909.RemoveThis@posting.google.com>, James Kuyper wrote:
 >
  >> One of the more interesting theoretical objects ever concieved is
  >> called a KugelBlitz (Ball of Light). It's made up entirely of
photons
  >> circling the center of the KugelBlitz. Why are they circling?
Because
  >> of the graviational field of the KugelBlitz. Why does it have a
  >> gravitational field? Because of the energy content of those
photons.
  >>
  >> Neat! Unfortunately, because of quantum effects, it's unstable.
  >> Photons that were originally in the correct orbit have a finite
chance
  >> of transitioning into an orbit that allows them to escape. However,
  >> for a sufficiently large KugelBlitz, the decay rate is so low that
a
  >> KugleBlitz as old as the Universe could still retain enough photons
to
  >> hold them in a circular orbit.
  >>
 >
 > Errr, wouldn't that imply an energy density at the centre of the
 > KlugelBlitz that was so high that massive particles/ antiparticles would
 > be created, whose mass would then trigger gravitational collapse into a
 > black hole?


Actually, no. A KugelBlitz is necessarily a thin shell, empty inside.

With Newtonian gravity, it's easy to prove that in a spherically
symmetric distribution of mass, the gravitational pull at any
particular field point depends only upon the total amount of mass that
is closer to the center than the field point. General Relativity gets
a little more complicated, but says essentially the same thing.
Therefore, since there's no mass or energy inside a KugelBlitz,
there's no net gravitational field there. Objects move in a straight
line at constant velocity, until they reach the inner edge of the thin
shell. As a test particle moves through the shell of light going
outward, the total energy that is closer to the center than the test
particle rises extremely rapidly, and therefore so does the
corresponding gravitational field. As you approach the outer edge of
the thin shell, the gravitational field becomes just strong enough to
keep light moving in a closed orbit. If it were any stronger, the
light would start moving inward, and the thing would rapidly collapse.
If it were any weaker, some of the light would escape and the thing
would rapidly evaporate.

Now, pair production could occur in the shell, rather than the center.
However, a sufficiently large KugelBlitz has a very low energy
density, even in the shell, and the pair production is proportional to
the square of the density. However, if two photons collide to produce
a particle /antiparticle pair, then each particle will necessarily
have less than the orbital velocity for their current location. As a
result, they will both end up moving in toward the center. Once
they've reached the interior of the thin shell, they'll feel no net
gravitational pull, and will therefore travel in a straight line until
they escape from the center. Since the two particles will have exactly
the same total four momentum as the photons that they replaced,
there's no reason that I'm aware of why this process should trigger
gravitational collapse.

 > I wondered once about what happens in an evaporating (Hawking
 > radiation) black hole, as it went through it's catastrophic decay phase.

Everyone who understands the concept well enough to understand that
question has wondered about that.

 > Would the black hole then have become stable against decay by Hawking
 > radiation?

Good question. I haven't been keeping up with current events in that
field the way I used to; the last I'd heard is that this was still an
open question.<!-- ~MESSAGE_AFTER~ -->
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In article <8b42afac.0411030400.7b6db7f7 RemoveThis @posting.google.com>, James Kuyper
wrote:
 > With Newtonian gravity, it's easy to prove that in a spherically
 > symmetric distribution of mass, the gravitational pull at any
 > particular field point depends only upon the total amount of mass that
 > is closer to the center than the field point.
 >
Yeah. I remember having to do the proof when I was at school.

  > > I wondered once about what happens in an evaporating (Hawking
  > > radiation) black hole, as it went through it's catastrophic decay phase.
 >
 > Everyone who understands the concept well enough to understand that
 > question has wondered about that.
 >
Good. I like giving people headaches <G>.

--
Aidan Karley,
Aberdeen, Scotland,
Location: 57°10'11" N, 02°08'43" W (sub-tropical Aberdeen), 0.021233<!-- ~MESSAGE_AFTER~ -->
 >> Stay informed about: Photons orbiting a Black Hole 

Aidan Karley wrote:
 > In article <8b42afac.0411030400.7b6db7f7.DeleteThis@posting.google.com>, James Kuyper
 > wrote:
<snip>
   >>> I wondered once about what happens in an evaporating (Hawking
   >>>radiation) black hole, as it went through it's catastrophic decay phase.
  >>
  >>Everyone who understands the concept well enough to understand that
  >>question has wondered about that.
  >>
 >
 > Good. I like giving people headaches <G>.
 >

Hah. :])

As is the case with many people, I have invented and discover 'for the
1st time' many things over the years.

In the case of this thread I don't consider it a can of worms that was
opened but am learning from what spilled out on the table.


TBerk<!-- ~MESSAGE_AFTER~ -->
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