Schwarzchild & Plank units

[Mr Skeptic]

Suppose that you had a photon with a wavelength equivalent to the Schwarzchild radius of a mass of equivalent energy. Then

[math]\lambda = \frac{2Gm}{c^2} = \frac{2GE}{c^4} = \frac{2Gfh}{c^4} = \frac{1}{\lambda}\frac{2Gh}{c^3} = \sqrt{\frac{2Gh}{c^3}} = 5.72891594 X 10^{-35} meters[/math]

[math]f = \frac{c}{\lambda} = \sqrt{\frac{c^5}{2Gh}} = 5.23297009 X 10^{42} Hertz[/math]

[math]E = fh = \sqrt{\frac{hc^5}{2G}} = 3.46740157 X 10^9 Joules[/math]

 

Damn! But for the [math]\sqrt{2}[/math], those are Plank units!

 

That can't be a coincidence!

 

This originally from the Schwarzchild radius thread, but I decided to move it to a new thread because it seems important. Coincidences in physics should be thoroughly investigated. I'm way over my head here, though.

 

Anyone have an idea of what is going on here?

 

I'm so excited!

 

Actually, the relevant Plank units are

[math]L_P = \sqrt{\frac{Gh}{2 \pi c^3}}[/math]

[math]\omega_P = \sqrt{\frac{2 \pi c^5}{Gh}}[/math]

[math]E_P = \sqrt{\frac{hc^5}{2 \pi G}}[/math]

 

I got confused by the reduced Plank's constant.

[Martin]

 

That can't be a coincidence!

 

...

 

I got confused by the reduced Plank's constant.

 

It isn't a coincidence. You have discovered by yourself or come across somehow one of several rationales for introducing the Planck units.

There are various stories to tell that lead up to them and it is somewhat a matter of taste. Planck came to them by a different mental pathway.

 

Planck first published them in 1899 and they were the values for the units that you get using the hbar (reduced planck constant)

 

it is still generally customary to define them using hbar

 

although one sometimes sees them defined with h (but this is not so normal)

===================

 

the important thing is to be consistent. there is no god-given right way with units.

 

nowadays QG people (quantum gravitists) often use c, hbar, and 8 pi G

 

(instead of the more common c, hbar, G)

Don't worry about this! You will only see it if you are reading specialized technical papers. Just be alert to the fact that different research lines belong to different "linguistic groups" as far as notation, so that one has to be ready to be bilingual sometimes.

 

for now let's try to stick consistently to c hbar G and the units which they define because it is by far the more common

 

you are right to be using omega for ANGULAR frequency (radians of phase per unit time, or radians of rotation per unit time) since that is the frequency format which is compatible with using hbar.

 

E = hbar omega

 

there will always be advantages and disadvantages with whatever notation system

 

BTW the Schwarzschild radius is only one distance associated with a standard BH. there is also the photosphere---photon orbit radius.

 

I believe that the basic length one should have in mind is

GM/c^2 (even though this length is ordinarily not given a special name)

 

the event horizon radius is TWO times this basic length: 2GM/c^2

and the photon orbit radius is THREE times this basic length 3GM/c^2

 

the photon orbit radius is very beautiful. at that distance from center a photon can circle the black hole at the speed of light in a circular orbit

like a little satellite

 

==========

please Mr Skeptic remember that in German the word SCHILD means "shield" or "sign" like a shieldshaped sign that is hung outside an inn or workshop, for business. Black shield is SCHWARZ SCHILD

 

there is no "child" in the word.

[Mr Skeptic]

It isn't a coincidence. You have discovered by yourself or come across somehow one of several rationales for introducing the Planck units.

There are various stories to tell that lead up to them and it is somewhat a matter of taste. Planck came to them by a different mental pathway.

 

Planck first published them in 1899 and they were the values for the units that you get using the hbar (reduced planck constant)

 

it is still generally customary to define them using hbar

 

although one sometimes sees them defined with h (but this is not so normal)

 

Ah, so more or less in asking physically significant question I ended up with Planck units. And because it does not involve other non-dimensional constants like the mass ratios or the fine-structure constant, it is easily recognizable as Planck units. Or something like that.

 

I used h instead of hbar because I had already used h, and wasn't sure how to put hbar in LaTeX.

 

the important thing is to be consistent. there is no god-given right way with units.

 

nowadays QG people (quantum gravitists) often use c, hbar, and 8 pi G

 

(instead of the more common c, hbar, G)

Don't worry about this! You will only see it if you are reading specialized technical papers. Just be alert to the fact that different research lines belong to different "linguistic groups" as far as notation, so that one has to be ready to be bilingual sometimes.

 

for now let's try to stick consistently to c hbar G and the units which they define because it is by far the more common

 

you are right to be using omega for ANGULAR frequency (radians of phase per unit time, or radians of rotation per unit time) since that is the frequency format which is compatible with using hbar.

 

E = hbar omega

 

there will always be advantages and disadvantages with whatever notation system

 

OK

 

BTW the Schwarzschild radius is only one distance associated with a standard BH. there is also the photosphere---photon orbit radius.

 

I believe that the basic length one should have in mind is

GM/c^2 (even though this length is ordinarily not given a special name)

 

the event horizon radius is TWO times this basic length: 2GM/c^2

and the photon orbit radius is THREE times this basic length 3GM/c^2

 

the photon orbit radius is very beautiful. at that distance from center a photon can circle the black hole at the speed of light in a circular orbit

like a little satellite

 

That seems interesting.

 

please Mr Skeptic remember that in German the word SCHILD means "shield" or "sign" like a shieldshaped sign that is hung outside an inn or workshop, for business. Black shield is SCHWARZ SCHILD

 

there is no "child" in the word.

 

Thanks, that will help me remember the name. I'm pretty bad with names. I thought it was something similar to the [iceland?] thing of adding -son to someone's name. I noticed the other thread is also mistitled. It should be illegal to have such a long name with only two vowels

[Fred56]

The thing I'm trying to get my head around is what “happens” at or to the singularity (in relativistic terms). Is a point of infinite spacetime density created? If it has infinite curvature then “where” is it and how did it “get” there? How satisfactory is it to say that it is a “point” “outside” of spacetime...?? There has to be both relativistic and quantum outcomes, but of course lots of people already know that. I think the problem just might have something to do with the deterministic flavour of GR. Matter is “remapped” somehow, but the parts haven't been swapped with some new kind of “spacetime stuff”. It's like a car that's been squished, or something, so it's not a car anymore but something more “basic”. Something that happens to spacetime, but doesn't make it something new, just maps it to a new (or more basic) topology.

[Martin]

I used h instead of hbar because I had already used h, and wasn't sure how to put hbar in LaTeX.

 

Just use

 

\hbar

 

the same way you would say

\omega

 

The thing I'm trying to get my head around is what “happens” at or to the singularity...

 

Singularities do not exist in nature as far as anyone knows. In other words, there is no singularity to get your head around.

 

Except of course there is a point at which a certain manmade theory (GR) breaks down or blows up----stops working---fails to give meaningful answers.

 

There will be nothing to understand until a satisfactory replacement for GR is found, which gives all the same good results that GR gives, where it works, and which continues working where GR fails.

 

Therefore there is nothing which you should be trying to "get your head around" until the replacement theory arrives.

 

=======================

If you want to get slightly ahead of the game you can, of course, read what highly-cited people at the forefront of quantum cosmology are saying about what replaces the bigbang singularity in current research---let me know if you want links. that's work in progress and it is going ahead rapidly at the moment. proceed at your own risk

[ydoaPs]

Singularities do not exist in nature as far as anyone knows.

 

I was under the impression that a black hole is a singularity.

[Martin]

I was under the impression that a black hole is a singularity.

 

A lot of people were. Do you know where you got that idea? Can you find an exact quote? I don't think any respectable scientist would have said that exact thing, but I could be wrong.

The usual thing to say was something like "In General Relativity the black hole has a singularity."

 

The lay reader would often not hear the important qualification (that the singularity was in the manmade model) and think that nature had a singularity. But on the contrary, the fact that General Relativity develops singularities is what tells us the limits to its applicability---in effect, that it is wrong.

 

Would you like stuff to read, Yourdad?

[Mr Skeptic]

Just use

 

\hbar

 

the same way you would say

\omega

 

OK, t[math]\hbar[/math]ank you.

 

Would you know if the situation I described, a photon with enough energy that its wavelength would be smaller than its Schwarzschild radius (treating [math]\frac{E}{c^2}[/math] as mass), become a black hole? Or does that only work with rest mass?

[Fred56]

If you want to get slightly ahead of the game you can, of course, read what highly-cited people at the forefront of quantum cosmology are saying about what replaces the bigbang singularity in current research---let me know if you want links. that's work in progress and it is going ahead rapidly at the moment. proceed at your own risk

No kidding. It certainly seems a fertile area 4 sure. Maybe since it might answer how relativity and QM are connected. I still remember when I got Laplace transforms. We had been studying the complex plane and the behaviours of reactive networks and how such can be reduced to an algebraic. Then the bulb came on, and I realised how the transform functions, in a complex plane are like a sort of magic view, where you get a much simpler picture which is then easier to “manipulate”. Then the transform inverts the view again and you've got your answer in the “real” world. Amazing.

[Mr Skeptic]

A lot of people were. Do you know where you got that idea? Can you find an exact quote? I don't think any respectable scientist would have said that exact thing, but I could be wrong.

The usual thing to say was something like "In General Relativity the black hole has a singularity."

 

The lay reader would often not hear the important qualification (that the singularity was in the manmade model) and think that nature had a singularity. But on the contrary, the fact that General Relativity develops singularities is what tells us the limits to its applicability---in effect, that it is wrong.

 

Would you like stuff to read, Yourdad?

 

The wikipedia article on black holes talks about a singularity (due to the breakdown of relativity equations) though also says that quantum mechanics would forbid that and that it would just be a superdense point. According to the wikipedia article, you could survive passing the event horizon, provided the black hole was really really big, but you would then inevitably fall into a singularity farther in?

 

That makes no sense to me. I thought that anything past the event horizon was not understood?

[Martin]

OK, t[math]\hbar[/math]ank you.

 

Would you know if the situation I described, a photon with enough energy that its wavelength would be smaller than its Schwarzschild radius (treating [math]\frac{E}{c^2}[/math] as mass), become a black hole? Or does that only work with rest mass?

 

Mr Skeptic, I have been enjoying your questions and discussion a lot, so I am truly sorry that I must disappoint you in this case and say NO I am not sure about that situation!

 

I have always assumed that you CAN'T get a photon to have Planck energy, in part for the very reason you name: a blackhole would form instead. But I don't actually know of an accepted model where that is proved.

I think it is more of a widely shared hunch. But somebody else may be able to say something more definite.

 

the Planck energy is about 2 Gigajoules. this is roughly the chemical energy in a tank of gasoline in your car. As mechanical energy, the Planck energy is on the order of 500 kilowatt hours or 1000 horsepower hours. Not trying to be precise.

 

When you start talking about a single photon delivering as much energy as a tankful of gasoline you are basically getting into the realm of quantum gravity. I am looking forward to the QG people developing a theoretical framework that can handle this kind of thing. It's exciting. But i don't think we are really there yet.

[timo]

I have always assumed that you CAN'T get a photon to have Planck energy, in part for the very reason you name: a blackhole would form instead.

As long as you assume relativity to be true, I would assume a photon with Planck energy is no problem. Two reasons:

1) You can have any energy you want (in (0,\infty), of course) by switching (Lorentz-boosting) to a suitable coordinate system (frame of reference).

2) The black-hole solutions that I am familiar are defined in the matter's frame of rest (or the closest one you get to that in case of oscillating or rotating mass distributions). I would assume conditions on black-hole formation to be implicitely meant in the center-of-mass frame.

[Mr Skeptic]

Mr Skeptic, I have been enjoying your questions and discussion a lot, so I am truly sorry that I must disappoint you in this case and say NO I am not sure about that situation!

 

I'm glad you're enjoying this as much as I do. I notice we (kind of) share avatars, which might hint at similar personalities. Be warned that I can be a bit crazy at times! (I'm sane enough to realize it though.)

 

I have always assumed that you CAN'T get a photon to have Planck energy, in part for the very reason you name: a blackhole would form instead. But I don't actually know of an accepted model where that is proved.

I think it is more of a widely shared hunch. But somebody else may be able to say something more definite.

 

Are you saying that rather than emit a photon of such unholy energy, the particles/whatever involved would turn into a black hole instead? I guess that would make more sense than somehow emitting such a photon and the photon collapsing afterward.

 

The other problem with the photon is that its energy would depend on frame of reference, so if it could collapse into a black hole, that would be rather unsettling in a different reference frame,

 

the Planck energy is about 2 Gigajoules. this is roughly the chemical energy in a tank of gasoline in your car. As mechanical energy, the Planck energy is on the order of 500 kilowatt hours or 1000 horsepower hours. Not trying to be precise.

 

I too did some rough estimating. Is one Planck energy more than the rest mass of every known particle?

 

When you start talking about a single photon delivering as much energy as a tankful of gasoline you are basically getting into the realm of quantum gravity. I am looking forward to the QG people developing a theoretical framework that can handle this kind of thing. It's exciting. But i don't think we are really there yet.

 

Yes, a photon's gravity was also bubbling around in my head but I wasn't sure where to ask about it. So I'll put it here:

If gravity moves at c, and a photon moves at c, and a photon has gravity, does that mean that a photon has a gravitational "sonic boom"? Also, how would such a "sonic boom" affect a photon's interactions?

[Fred56]

Planck's constant is an interesting thing to look at when you measure the deBroglie wavelength of "the" electron. He was the first (I think) to propose E=hv?

[Mr Skeptic]

Also, what about the Schwarzschild radius of the universe? Given an infinite universe with matter density [math]\rho[/math], the Schwarzschild radius would be

[math]r_s = \frac{2Gm}{c^2} = \frac{2G}{c^2} \rho \frac{4}{3} \pi r_s^3 = \sqrt{\frac{c^2}{2G}\frac{1}{\rho\frac{4}{3}\pi}} = \frac{1}{\sqrt{\rho}}\sqrt{\frac{c^2}{2G}\frac{1}{\frac{4}{3}\pi}}[/math]

 

[math]r_s[/math] can be made arbitrarily big for small enough density [math]\rho[/math], but for any infinite universe it would eventually reach that radius.

 

So how does this work? Does the Schwarzschild radius not work at this scale? Gravity work differently? Is the universe finite? Did I make a mistake? Is the universe's density zero, or even negative? Is this what is meant about the universe collapsing?

 

For our universe, estimating mass density at [math]3 X 10^{-39} kg/m^3[/math], the Schwarzschild radius would be [math]2.3 X 10^{32} meters[/math], which is farther than we can see (c times age of universe). Would this mean anything? My head hurts.

[Mr Skeptic]

Another one: how can things fall into a black hole? It may sound like a silly question, but here is how I understand it. Light always follows "straight" lines called geodesics. Light cannot escape a black hole, because the geodesics curve back on themselves. But if light can enter a black hole, then there is a geodesic from outside the black hole to inside, and if light were travelling the opposite direction it could escape. Therefore, there cannot be a geodesic from outside a black hole to inside, and light (and anything else, I suppose) cannot enter. The only way, then, that anything could get into a black hole would be if its event horizon expands.

 

Either that, or I don't understand something.

[Martin]

Another one: how can things fall into a black hole? It may sound like a silly question, but here is how I understand it. Light always follows "straight" lines called geodesics. Light cannot escape a black hole, because the geodesics curve back on themselves. But if light can enter a black hole, then there is a geodesic from outside the black hole to inside, and if light were travelling the opposite direction it could escape. Therefore, there cannot be a geodesic from outside a black hole to inside, and light (and anything else, I suppose) cannot enter. The only way, then, that anything could get into a black hole would be if its event horizon expands.

 

Either that, or I don't understand something.

 

Hi Mr Skeptic,

somehow I missed seeing all these questions over the past days and just came across them.

 

I will try to answer this last one. But you have raised so many that I don't know that I can find the time and energy to respond to all. I hope that Atheist and Swansont help out.

 

This last question, if I understand you, is not so hard. The geodesics are in spacetime. So you can have a ray of light going IN to the center, but not OUT.

inside the event horizon all the forward lightcones tilt so that they are inwards.

 

If the theory was just about spatial geodesics, in 3D spatial geometry, and a light particle could move either way along a geodesic, then you would be right----your intuition is right about that---light could get out along the same path that other light had fallen in

 

I apologize for delay in responding. As time permits I will look at some of the other questions you've raised.

 

Also, what about the Schwarzschild radius of the universe? Given an infinite universe with matter density [math]\rho[/math], the Schwarzschild radius would be

[math]r_s = \frac{2Gm}{c^2} = \frac{2G}{c^2} \rho \frac{4}{3} \pi r_s^3 = \sqrt{\frac{c^2}{2G}\frac{1}{\rho\frac{4}{3}\pi}} = \frac{1}{\sqrt{\rho}}\sqrt{\frac{c^2}{2G}\frac{1}{\frac{4}{3}\pi}}[/math]

 

[math]r_s[/math] can be made arbitrarily big for small enough density [math]\rho[/math], but for any infinite universe it would eventually reach that radius.

 

So how does this work? Does the Schwarzschild radius not work at this scale? Gravity work differently? Is the universe finite? Did I make a mistake? Is the universe's density zero, or even negative? Is this what is meant about the universe collapsing?

 

For our universe, estimating mass density at [math]3 X 10^{-39} kg/m^3[/math], the Schwarzschild radius would be [math]2.3 X 10^{32} meters[/math], which is farther than we can see (c times age of universe). Would this mean anything? My head hurts.

 

this is an interesting question.

didn't see it until just now or would have replied earlier.

 

the Schwarzschild solution to GR equations is a STATIC solution,

the standard Friedmann model universe starts at a very high density (often estimated at around Planck density roughly 10⁹³ times water.)

 

Your intuition is correct that if the universe did not have a running start, and merely consisted of a blob of matter with that huge density, surrounded by some empty space, then it would immediatly collapse to hole.

 

However that is not the picture that the Friedmann (1923) picture gives us----or the modern specialization of it called LambdaCDM. In the first place the model is not a blob of high density surrounded by empty space. It is a blob of uniform density with no larger surrounding space. The space itself expands and it does not expand "into" anything. Internal distances simply get larger. And the expansion has a running start---it is extremely rapid at the beginning (I am not talking about the inflation scenario but something more basic.)

 

the LCDM is what they all use, it is just the classic Friedmann with extra features like a positive cosmological constant Lambda and some cold dark matter DM. But the extra features can be ignored---don't make any essential difference.

 

The LCDM comes in two basic versions-----more common is the SPATIAL INFINITE version where space has no overall curvature. One reason they like it is ease of calculation. The other common version is SPATIAL FINITE version of LCDM where there is some average overall positive curvature and space looks like a three-sphere. finite but boundaryless. No other space surrounding it, just the 3-sphere (the 3D analog of familiar 2D sphere like surface of balloon)

 

It doesnt matter which you picture, the finite or the infinite. There is no surrounding space that our space expands out into. Our space starts out either infinite in extent with very high matter density. Or finite in extent, also with very high matter density.

And it starts out expanding very rapidly.

 

those are just the initial conditions. Quantum gravitists are working on an EXPLANATION of how those initial conditions came about, but in the classical model they are just what you get if you fit model to observation data and then run classical model back in time to nearly where it breaks down.

 

Intuitively, it is expanding so fast it never has a chance to form black holes

 

 

Although the early universe density is certainly high enough that if you could let a blob of it sit still for a moment it would collapse.

 

this is one helluvan informal explanation but it is the best you'll get from me at least for now.

 

the universe still has so much expansion that it continues to outrun any tendency to collapse.

there is something called the CRITICAL DENSITY which if we didnt have Lambda and the observed density was greater than that, then we would be scheduled to eventually stop expand and begin collapse.

 

But we have Lambda helping by accelerating expansion, and the observed density is NOT over the critical. so the universe has no Schw. radius and is not going to collapse-----there is no way the static Schw. model applies. We're SAFE.

 

Currently the value of the critical density, as I recall, is about 0.83 joules per cubic kilometer.

A joule is a small amount of energy----if I expressed it in (micro) nanograms of matter it would sound much smaller and be harder to remember----so I remember it as 0.83 joules. The actual observed density of detectable matter is only about 4 percent of that.

 

what I'm talking about is just the standard LCDM model-------there are all sorts of exotic gee-whiz models out there which one hears about and which may appeal to the imagination, but this is what is used because it fits the data surprisingly well and has kind of a minimum of assumptions (minimal extra baggage). With every model be skeptical (as your name) of course and only push it as far as it will go without breakdown.

 

the LCDM is due for replacement by a Quantum Gravity modified edition.

Bojowald just came out with a paper on Big Bang nucleosynthesis in the QG version of standard cosmology. Primordial abundances of elements. they are getting along with it.

[Norman Albers]

Nice overview, Martin. I read one interpretation recently that things will expand to the point where the matter field falls apart. I guess we're talking about the vacuum itself. . . . Yes, after rereading this reference: Documents and Settings\User\Local Settings\Temporary Internet Files\Content.IE5\01Y34563\UNC News release -- Endless universe made possible by new model.htmC:\ , I see they speak of an equation of state for dark energy. I wonder if they've seen my photon paper. The authors are Frampton and Baum.

 

No kidding. It certainly seems a fertile area 4 sure. Maybe since it might answer how relativity and QM are connected. I still remember when I got Laplace transforms. We had been studying the complex plane and the behaviours of reactive networks and how such can be reduced to an algebraic. Then the bulb came on, and I realised how the transform functions, in a complex plane are like a sort of magic view, where you get a much simpler picture which is then easier to “manipulate”. Then the transform inverts the view again and you've got your answer in the “real” world. Amazing.

Good stuff, Fred. This describes the regime in which my friend solidspin is constructing QFT.

[Mr Skeptic]

Hi Mr Skeptic,

somehow I missed seeing all these questions over the past days and just came across them.

 

I will try to answer this last one. But you have raised so many that I don't know that I can find the time and energy to respond to all. I hope that Atheist and Swansont help out.

 

Thank you for answering them. Your answers are very helpful and informative.

 

This last question, if I understand you, is not so hard. The geodesics are in spacetime. So you can have a ray of light going IN to the center, but not OUT.

inside the event horizon all the forward lightcones tilt so that they are inwards.

 

If the theory was just about spatial geodesics, in 3D spatial geometry, and a light particle could move either way along a geodesic, then you would be right----your intuition is right about that---light could get out along the same path that other light had fallen in

 

I think I get it. The path out of a black hole would require travel backwards in time, whereas the path in is forwards in time. So it really is like a one way street, you can go in but not out. Like you said, I had been thinking in terms of spatial dimensions.

 

the Schwarzschild solution to GR equations is a STATIC solution,

the standard Friedmann model universe starts at a very high density (often estimated at around Planck density roughly 10⁹³ times water.)

 

Ah, that question [about the Big Bang singularity collapsing into a black hole] was the very next thing I was going to ask about. I understand what you are saying, since everything is "moving" away from each other, the Schwartzschild radius doesn't apply because it is for static objects. That would also make sense of my calculation that the Schwartzschild radius of the universe would be farther away than c times the age of the universe.

 

[...]

this is one helluvan informal explanation but it is the best you'll get from me at least for now.

 

Oh, it is certainly good enough for me. My understanding of GR is rather limited, so a formal explanation might be over my head and give me a big tensor headache.

 

But we have Lambda helping by accelerating expansion, and the observed density is NOT over the critical. so the universe has no Schw. radius and is not going to collapse-----there is no way the static Schw. model applies. We're SAFE.

 

Well, safe from one thing. As I understand it, eventually the universe dies, be it by a Big Crunch, Big Rip, or Heat Death.

 

Currently the value of the critical density, as I recall, is about 0.83 joules per cubic kilometer.

A joule is a small amount of energy----if I expressed it in (micro) nanograms of matter it would sound much smaller and be harder to remember----so I remember it as 0.83 joules. The actual observed density of detectable matter is only about 4 percent of that.

 

Wow, that is incredibly small. Like 5 and a half hydrogen atoms per cubic meter. Except most of it would be dark matter and dark energy rather than regular matter, if I understand correctly from other places I read about that. If space itself has some intrinsic energy (like from where virtual particles come from), wouldn't that become a dominating factor if the universe continues to expand?

 

what I'm talking about is just the standard LCDM model-------there are all sorts of exotic gee-whiz models out there which one hears about and which may appeal to the imagination, but this is what is used because it fits the data surprisingly well and has kind of a minimum of assumptions (minimal extra baggage). With every model be skeptical (as your name) of course and only push it as far as it will go without breakdown.

 

I try to be careful, but I do like to entertain as many possibilities as possible. I am skeptical of anything I don't understand, and calculating the fate of the universe is way beyond me at the time. I do stick to the standard models whenever I am not busy being crazy though.

[Norman Albers]

Sorry if the reference above is not addressed. Try this: http://www.unc.edu/news/archives/jan07/newmodel012907.html

[Martin]

... I do stick to the standard models whenever I am not busy being crazy though.

 

Highly commendable balance. Moderation in all things including sanity.

[lakmilis]

It isn't a coincidence. You have discovered by yourself or come across somehow one of several rationales for introducing the Planck units.

There are various stories to tell that lead up to them and it is somewhat a matter of taste. Planck came to them by a different mental pathway.

 

Planck first published them in 1899 and they were the values for the units that you get using the hbar (reduced planck constant)

 

it is still generally customary to define them using hbar

 

although one sometimes sees them defined with h (but this is not so normal)

===================

 

the important thing is to be consistent. there is no god-given right way with units.

 

nowadays QG people (quantum gravitists) often use c, hbar, and 8 pi G

 

(instead of the more common c, hbar, G)

Don't worry about this! You will only see it if you are reading specialized technical papers. Just be alert to the fact that different research lines belong to different "linguistic groups" as far as notation, so that one has to be ready to be bilingual sometimes.

 

for now let's try to stick consistently to c hbar G and the units which they define because it is by far the more common

 

you are right to be using omega for ANGULAR frequency (radians of phase per unit time, or radians of rotation per unit time) since that is the frequency format which is compatible with using hbar.

 

E = hbar omega

 

there will always be advantages and disadvantages with whatever notation system

 

BTW the Schwarzschild radius is only one distance associated with a standard BH. there is also the photosphere---photon orbit radius.

 

I believe that the basic length one should have in mind is

GM/c^2 (even though this length is ordinarily not given a special name)

 

the event horizon radius is TWO times this basic length: 2GM/c^2

and the photon orbit radius is THREE times this basic length 3GM/c^2

 

the photon orbit radius is very beautiful. at that distance from center a photon can circle the black hole at the speed of light in a circular orbit

like a little satellite

 

==========

please Mr Skeptic remember that in German the word SCHILD means "shield" or "sign" like a shieldshaped sign that is hung outside an inn or workshop, for business. Black shield is SCHWARZ SCHILD

 

there is no "child" in the word.

 

great martin, I loved to see someone state this... although one thing... in reality the event horizon will be GM , the basic state as you said, rather than 2GM, no object in the universe which we know of has no angular momentum, and if a black hole was created from a celestial object collapsing it most certainly had a -'lot-' of angular momentum, making the event horizon at 2GM pretty impossible... of course GM is an extreme Kerr hole, this should be the case but then again, I completely missed the prediction of the frequencies of quasars, I thought they would be hitting 4-5 [kHz], fastes so afr observed is 1.1 or so? :/ but nonetheless, Schwarschild is just a useless metric, Kerr is the one to go for, or at least one of these general conditions with angular momentum

[Norman Albers]

Stellar collapses involve blasting off of outer layers, a significant fraction of the total original mass. What angular momentum transfers are possible here? If a "skater drawing in their arms" and thus moment of inertia, also tries to couple to another skater going outward, there will be transfer, no?

[lakmilis]

Stellar collapses involve blasting off of outer layers, a significant fraction of the total original mass. What angular momentum transfers are possible here? If a "skater drawing in their arms" and thus moment of inertia, also tries to couple to another skater going outward, there will be transfer, no?

 

Hmm. good point Albers.... but in that analogy , the outer skater if drew all momentum from the inner skater to stop the angular momentum to then let go... transferring it to a celestial object having a.. ok wait before I answer without thinking.. let me make some scribbles.. no let me rather just stick to the intuitivie initial thought I had... transferring the analogy back to a celestial object undegoing such a massive grav. collapse to actually become a black hole (and since you were trying to convince me a hole with no ang. momentum could be feasible..)... the blast would need to transfer as you say all angular momentum and yet escape whilst this object is collapsing to a non naked singularity???? hmm (as in to 'drop' enough mass to halt rotation entirely would have to mean the last lump to stick to analogies would have to be let loose at the time when the object becomes a black hole... in which it is sucked back in then?).

 

You are going to have to give me a better one than two skaters before I can go along with it albers...

 

 

mmm. Ok this is 10 minutes later or so... I can see one could claim it to be possible then... if (just for simplicity we say the explosion is 'instantaneous' and the excess mass is all let go in one lump)... ok so it would all explode off... taking away the angular momentum... the black hole is a SR. hole and ZIP it all gets sucked back in as its so close to this hole then ye... ? No external momentum to a black hole needs to increase its ang. momentum right(if not indeed that is the actualy case)?

 

Hmm any feedback please albers would be appreciated... if you are not around to read this old post. I'll pm you.

sorry I'm just abt to go to bed Albers and I am absoilutely knackered so I hope you can make out what I just tried to say with those incoherent sentences :/

 

lak

[Norman Albers]

Lakmilis I think you misinterpret me! I am not arguing significantly with you, but it is necessary to thoroughly understand the Schwarzschild solution before tackling the Kerr rotating source metric. I am just now completing my running of the Lense-Thirring analysis. I had to learn to crawl before walking here. Was it you who laid this term on me??? There is nothing easy about laying out and understanding all of this tensor analysis. If you can discuss degenerate metrics and the Kerr mathematics with me I will appreciate it. How much work has been done with the vision I have expressed? I am working with relativity at the particle scale. There, electromagnetics and spin greatly out weigh gravitation per se, but the synthesis I seek shows these as well as polar effects like Ahoronov-Bohm, as manifestations of a common source.