New study shows Dark Matter isn't needed? Relativty explains it?

[SimonA]

It seems maybe I posted this on the wrong board ?

https://www.physicsforums.com/showthread.php?t=94351

 

[Lapin Dormant]

Sorry a bit 'off thread' but

No, that's a measurable effect. In science, we're only concerned with measurable effects. If that's not what you mean by what we can "see", then I can assure that the distinction you're making is scientifically uninteresting.

What I mean by 'See' is simply that you cannot see {Visualy} that gravity is acting in an on-going-persistent-incessant fashion-manner as to keep that car attached to the ground, Unmoving, and you cannot "see" it doing that, "see" as in OBSERVE {Visually} the energy at work.

If you have a Problem with the idea of "invisible things" {'things' like energy} you cannot see radiation either, so use a gieger counter and be scientific.

That you personally express that as something that you find "scientifically uninteresting" is to me more your loss then anything else.

The noun form of "elemental" is not used in that way, so please use the word "element" in the future if you want people to understand you. Nobody is going to think that you're unintelligent if you use the standard meanings of words.

Now you are making me laugh, forgive me, but I find this rather condescending, in tone. {Langauge instructions?}

No idea what you're trying to say. The same applies to your other posts, which read more like a philosophy text than a scientific query. You need to be more precise if you wish to understand something scientific. For example, sentences like the following:

Firstly what leads you to believe that I am making only 'queries'? nevermind you seem to miss that all science is Philosophically based, from it's outset, as it is a System of 'beliefs-theories' that attempts to use certain standards, scientific Methodology, as proof of those beliefs-theories. Concensus to that 'belief' {Theory} is acknowledged when evidenced by the ability of Observational-testable-repetitively experimentation concords from readings of 'Physical' things, like atoms.

After that, as you admit you have "NO idea" of what I am saying, I'll re-iterate it, with some additions as to endevour to Make it clear to you

No need of time variation in the laws of physics, simply the notation that what is Observed, 13.5 Billion Light years away, is also that NEW.
Means that what we currently see is "New" in the sense that it is the Beginning of the Universe from a Point of View of 'Time'.[/color]

Therefore perhaps operating on-in a manner that is yet not understood, from this perspective, as this perspective is where we have taken all of our Known {current} 'rules of physics' from, not from "there".
All of what we currently know is from Local Space respective of Having Tested the Properties of Physical Space, Light speed might be Different Just outside of the Local Vicinity, we have not yet, and can not, yet, test that. That would Change Many things.[/color]

Could be some {very} Slight Differences we don't realize just yet, the View has some obscuring factors to it, doesn't it.

In the one page, you referred me to, respective of the Conversation you had with Turbot, you mentioned that (1+z) that z=1000 and-or z=1200 would not be observed, here, locally, as it has become obscured, right?
That is what I am referring to, that, and some other 'notions' that apply.[/color]

Now, you follow up with this

What is there" {Liqid-solid-gas} is just as important, if not moreso, to "how it is functioning" as 'How it is functioning' is Based upon What is there!

This would be completely ignored by most scientists if asked to them. I'm willing to make an attempt at answering your question, but you need to be more specific. The one question that sort of makes sense is the following:

Please look, and read, what I had posted as a "quotation of Myself" Above, and your responce, as it is not a question, it is a Statement. That you cannot find the 'sense' in it, not my fault, also the Idea that you seem to think that you can respond in the stead of "Most scientists, well rather assumptive of you, isn't it? perhaps condescending again?

Which chemical element(al) it actually is} expand it's r value, so does it's potential G/r value change, as well?

<Quite a partiallity of citation of what I had written, and with 'no name' ascribed, that is simply lazy.

If a cloud of constant mass and density expands to a larger radius, then yes, its potential energy increases (all of the elements expand in approximately the same way). If you mean the gravitational potential on the surface, then your formula is correct. If you mean the total potential energy of the cloud, then it's given by:

Sorry but I have emboldened your words as I now need Clarification from you, as you State that, "If a cloud of constant mass and density expands to a larger radius, then yes," [/color] Please tell me how a Cloud can retain a CONSTANT DENSITY and CONSTANT MASS and expand, in VOLUME? cause I am at a COMPLETE loss as to how that works.

Then you tell me "If you mean the gravitational potential on the surface, then your formula is correct." [/color] It would, otherwise be amusing, but laughing at you now would be rude, BECAUSE the "Formula" that you Claim I am Using, please remember, I asked you a QUESTION, is not the Right answer, as increasing the radius of the Cloud will space out the Atoms and their gravitational Interactivety as per the measure of "Gravitational Action at a Distance" therefore the Activity dropping off at the SQUARE of the Distance, so the Proportionate Amount of Negation of the Superficial Gravitational Effect would be FOUR TIMES, or x 4 or Gm/4r

Thereafter, I had NOT queried you for this responce " If you mean the total potential energy of the cloud, then it's given by:"[/color]

Not the Total Potential energy of the cloud, but the measure of it's gravitational effect on any other given Mass, as measured from it's "surface" I HAD been Specific, as you seemed to be seeking.

SO, I 'googled' your equation, something like this u = (3/5)(GM^2/r)
and Found a website Merlyn.demon.Co-Uk wherein under this title "Binding Energy" we find your equation derived as thus:

The binding energy, U, of a sphere (of mass M and radius R) is the energy required to move all of its particles to infinity in different directions; it is given by U = 3/5GM2/R.

To calculate U, one can dismantle the sphere shell by shell and integrate; from the above, the energy dU required to move a shell of thickness dr and mass dm to infinity from a surface at radius r and local gravity g is given by dU = g r dm. We have g = GM(r/R)3/r2 and dm = M×3r2dr/R3 (volume increases thrice as fast as radius, relatively). Thus
U = ò0R [ GM(r/R)3/r2 × r × 3Mr2dr/R3 ]
U = 3 G M 2 / R6 × ò0R [ r4dr ] = 3/5 GM2/R

So we read what the gentleman writes and we find that he seems to think that; "(volume increases thrice as fast as radius, relatively)" so I go to this website W³ .aaamath. com to verify that I have the Correct formula for the calculations of the Volume of Spheres, do the Math using 4/3πr³ such that, at an r value of 20 the answer works out to 33510.3216, and at an r value double that, 40 the answer is 33510.3216 which is an eightfold change in volume.

Can you see a problem there? {and My Apologies to Dr J R Stockton, just that}

Although I can clearly see that you can type well, as in this thread CMB it would appear that typing the Words "I Do Not {currently} Know the Answer to that Question" doesn't seem to flow, from your mind, to your fingers, and it would seem that even the attempt at evading the Correct responce by pointing at a Power metric, was founded in Flawed Information, so it would seem that your not a thorough on your "references" either.

As you may be able to tell, saying "I didn't know" is what you were supposed to write in that last post.

If you would like to measure, as a "Dynamic measure" the 'Force' acting upon the parked car, then simply get yourself a Michaelson Morely Interferometer, and Point the "Two light pathways" perpendicular to the Ground, you will get a Quite Dynamic reading of the Invisible force, of Gravity, as it is Acting.

Perhaps, after that, you will do me a small favor, and not respond, to anything, I write, any further.

Good thing I agreed "Not to" a priori.

LD
.....walks...off...head down...saddened...[/color]

 

[matt.o]

ever heard of private messaging?

 

[SpaceTiger]

What I mean by 'See' is simply that you cannot see {Visualy} that gravity is acting in an on-going-persistent-incessant fashion-manner as to keep that car attached to the ground, Unmoving, and you cannot "see" it doing that, "see" as in OBSERVE {Visually} the energy at work.

See my first response. This is basically equivalent to hypothesizing a correction to gravity (or perhaps another force). In order to achieve the balance you're describing, gravity and electromagnetism are inducing equal and opposite forces on the car. In the case of a star, the only force we know of that can act on it in any significant way is gravity... and we have a law for how that behaves.

If you have a Problem with the idea of "invisible things" {'things' like energy} you cannot see radiation either, so use a gieger counter and be scientific.

Read what I said again:

In science, we're only concerned with measurable effects. If that's not what you mean by what we can "see", then I can assure that the distinction you're making is scientifically uninteresting.

Both energy and radiation are measurable, so no, I wouldn't find them scientifically uninteresting.

also the Idea that you seem to think that you can respond in the stead of "Most scientists, well rather assumptive of you, isn't it? perhaps condescending again?

Unless you're a scientist, how would you know? Perhaps if you were, the statement would be plainly obvious.
If you were to walk onto a construction site, would you be upset if the workers lectured you on the use of their equipment? Would it be condescending that they assumed you weren't as familiar as they in their area of expertise?

Sorry but I have emboldened your words as I now need Clarification from you, as you State that, "If a cloud of constant mass and density expands to a larger radius, then yes," [/color] Please tell me how a Cloud can retain a CONSTANT DENSITY and CONSTANT MASS and expand, in VOLUME? cause I am at a COMPLETE loss as to how that works.

Constant density in space, not time. That is, the cloud has one spatially constant density before expanding and another afterwards. This is only to simplify the computation of the potential/binding energy. Other spatial dependences of density will give a different constant out front, but will be of the same character (proportional to M² and 1/R).

Then you tell me "If you mean the gravitational potential on the surface, then your formula is correct." [/color] It would, otherwise be amusing, but laughing at you now would be rude, BECAUSE the "Formula" that you Claim I am Using, please remember, I asked you a QUESTION, is not the Right answer, as increasing the radius of the Cloud will space out the Atoms and their gravitational Interactivety as per the measure of "Gravitational Action at a Distance" therefore the Activity dropping off at the SQUARE of the Distance, so the Proportionate Amount of Negation of the Superficial Gravitational Effect would be FOUR TIMES, or x 4 or Gm/4r

Let's review the basic gravitational formulae:

F=\frac{GMm}{r^2}
\Phi=\frac{GM}{r}
U=\frac{3}{5}\frac{GM^2}{R}

The first is the magnitude of the force on a mass, m, a distance r from the cloud center. The second (which is what you had in your post), is the magnitude of the gravitational potential at a distance, r, from the cloud center. The last is the magnitude of the potential/binding energy of the cloud, where I substituted R to represent the total radius of the cloud. Please note that r=R only if you're evaluating the the force or potential at the surface of the cloud.

If you double the radius of the cloud, the first and second quantities stay the same unless you're moving the point at which you evaluate them. If you evaluate them both at the surface, the force will fall by a factor of a quarter, the potential by a factor of a half. The last equation is a property of the cloud itself, so it does not have a point of evaluation. Doubling the radius will then reduce that quantity by a factor of a half.

Hopefully this will clear up your misunderstanding.

 

[Lapin Dormant]

ever heard of private messaging?

Yes, I have!

 

[Lapin Dormant]

ever heard of private messaging?

And if you read the Guidelines you will know that it is NOT private, Not at all.

Funny too, your public profile wouldn't let me read any of your other postings, just a Ruse/psyeudonymforamentor name, are you?

LD
Don't Bother .. .. .. .. .. .. ThinksThanks .. .. .. .., ,.. .. .. I lept .. Figures, NOW it does .. .. .., ,.. .. .. lept again[/color]

 

[Garth]

Bringing this thread back on topic...

I'm going to hide behind the skirt here, Garth... Can we say with any confidence what disc model might work? I think the observational evidence is really thin. Another objection: since when did CERN jump into the fray? I don't think that is even relevant to this conversation.

No, we cannot say at the moment what disk model might work with pure GR, though I do think the infinitely thin disk of Cooperstock & Tieu is a workable rough approximation to the real situation.

The point is that until a proper GR analysis is done noboby will know whether any model might work.

However, as I posted in the S&GR forum "Overturning GR contest" thread, given that the mass in a galaxy is in orbit, rather than concentrated at the centre, GR's non-linear effects might well be significant. The orbiting mass's 'kinetic energy' contributes to the density and angular momentum terms of the stress-energy-momentum tensor T_uv which then generates more gravity (curvature) in a way that does not happen in Newtonian theory.

The onus is therefore on those who want to analyse galactic rotation profiles in the Newtonian approximation to prove that the non-linear terms are not significant.

AFAIK this has not been done. As I asked in the "Overturning GR contest" thread: "does anybody know of any previous work" where this has been published?
Garth

 

[EL]

No, we cannot say at the moment what disk model might work with pure GR, though I do think the infinitely thin disk of Cooperstock & Tieu is a workable rough approximation to the real situation.

But, still the thing is that C&T happened to include a singular disk which they didn't mean to, i.e. their model includes an ADDITIONAL source of gravity APART FROM the ordinary matter in the galaxy.
If you would model the galaxy as simply an infinitely thin disk, you would not end up with the same rotation curves as they get in their paper.

Their additional thin disk acts as dark matter, and hence it is not that strange they get the correct rotation curves. They included DM without knowing it...

 

[Garth]

But, still the thing is that C&T happened to include a singular disk which they didn't mean to, i.e. their model includes an ADDITIONAL source of gravity APART FROM the ordinary matter in the galaxy.
If you would model the galaxy as simply an infinitely thin disk, you would not end up with the same rotation curves as they get in their paper.
Their additional thin disk acts as dark matter, and hence it is not that strange they get the correct rotation curves. They included DM without knowing it...

Hi EL! Thank you for your comment.

Yes I do understand what Korzynski is saying. He does not, however, indicate the total mass of this additional thin disk. I cannot believe it is as massive as the DM halo it replaces, 10X the baryonic mass, as it is all within the visible galaxy outer radius and it would affect stellar orbital periods too much. If it is only a small additional component to the total galaxy mass (Cooperstock's value 2.1 x 10¹¹ M_solar) then it might be a reasonable model of the thin galactic disk observed (6 x 10¹⁰ M_solar).

My main point, however, is notwithstanding Cooperstock & Tieu model's validity, the non-linear GR effects may well be significant in galactic rotation profiles and should be investigated thoroughly.

Garth

 

[Garth]

But if you notice the Cooperstock Appendix you'll see their solution for density is
\rho=5.64 . 10^{-14}\frac{(N_r^2+N_z^2)}{r^2} kg/m³
so they are back to the old 1/r² Newtonian flat rotation solution!
Garth

 

[SpaceTiger]

But if you notice the Cooperstock Appendix you'll see their solution for density is
\rho=5.64 . 10^{-14}\frac{(N_r^2+N_z^2)}{r^2} kg/m³
so they are back to the old 1/r² Newtonian flat rotation solution!

It's not obvious to me that the above equation is even a close approximation to a 1/r^2 dependence, since N depends non-trivially on radius. Did you check this numerically?

 

[Garth]

It's not obvious to me that the above equation is even a close approximation to a 1/r^2 dependence, since N depends non-trivially on radius. Did you check this numerically?

I was using a 'wand waving' OOM approximation:
As V(r, z)=\frac{3.10^8}{r}N(r, z) is more or less constant on the flat part of the rotation curve therefore approximately we can take
N(r, z) = A.V(r,z).r
and at constant z
\rho=5.64 . 10^{-14}\frac{(N_r^2+N_z^2)}{r^2} kg/m³
becomes
\rho=A_1 + A_2\frac{N_z^2}{r^2}
more or less the Newtonian model with appropriate values for the constants A₁ and A₂.
I hope this helps.
Garth

 

[SpaceTiger]

I was using a 'wand waving' OOM approximation:
As V(r, z)=\frac{3.10^8}{r}N(r, z) is more or less constant on the flat part of the rotation curve therefore approximately we can take
N(r, z) = A.V(r,z).r
and at constant z
\rho=5.64 . 10^{-14}\frac{(N_r^2+N_z^2)}{r^2} kg/m³
becomes
\rho=A_1 + A_2\frac{N_z^2}{r^2}
more or less the Newtonian model with appropriate values for the constants A₁ and A₂.
I hope this helps.

Well, firstly, take another look at your final equation. It says that the density approaches a constant value as the radius approaches infinity. This should give you a hint that something is wrong. The basic rotation curve that results from that equation is flat towards the center and then rises linearly as the first term becomes larger than the second term.

What it would seem you did is misinterpret the N_r^2 and N_z^2[/tex]. They&#039;re partial derivatives, so to take advantage of the flat rotation curve simplification, you have to differentiate V with respect to r like:<br /> <br /> \frac{dV}{dr}=AN_rr+AN_zr+AN(r,z)=0<br /> <br /> which leads to:<br /> <br /> N_r^2=(-N_z-\frac{V}{Ar^2})^2<br /> <br /> Plugging this into your density equation will still give you something non-trivial, I&#039;m afraid. Try reading the density profiles from their plots instead.<br /> <br /> Edit: Replaced V_r with \frac{dV}{dr} to make it clear that I was taking a total derivative, not a partial.

 

[Garth]

Well, firstly, take another look at your final equation. It says that the density approaches a constant value as the radius approaches infinity. This should give you a hint that something is wrong.

The Newtonian density function that delivers the flat rotation curve is:
\rho(r)=\frac{C_0}{(a^2+r^2)}
where C₀=4.6x10⁸M_solar and a = 2.8 kpc. of course the density distribution has to be truncated at some radius r = a₀ otherwise the total galactic mass would be infinite. This is basic theory.

Cooperstock &Tieu discuss the matter quite extensively: “It is unknown how far the galactic disks extend. More data points beyond those provided thus far by observational astronomers would enable us to extend the velocity curves further. Presumably a point (let us call it r_f ) is reached where we can set rho to zero. At this point, (2) no longer applies as there are no longer co-rotating fluid elements being tracked. As a result, (9) no longer applies and the w function is no longer constant. Beyond r_f, no further mass is accumulated.“

There is also a change of regime as r tends to zero.

All I did was to give a very ‘rough and ready’ comparison, taking z to be a constant, therefore N becomes N(r), and also taking V to be a constant then N becomes linear in r and N_r a constant..

I was considering only the central ranges to show that \rho varies as r^-2. The complete numerical calculation was done by Cooperstock & Tieu.

As I said the main question is whether the non-linear GR effects are significant in galactic rotation, and if so then what of galactic halo DM?

Garth

 

[SpaceTiger]

The Newtonian density function that delivers the flat rotation curve is:
\rho(r)=\frac{C_0}{(a^2+r^2)}
where C₀=4.6x10⁸M_solar and a = 2.8 kpc. of course the density distribution has to be truncated at some radius r = a₀ otherwise the total galactic mass would be infinite. This is basic theory.

Come on Garth, you're just making this worse. First of all, that's not the relation you got in your above calculation:

A_1+\frac{A_2}{r^2} \ne \frac{B_1}{B_2+r^2}

for any constants A and B. You can see this by again looking at its limits. Your first expression goes to a constant density at infinity, while this new one goes to zero.

Secondly, that is not the expression to generate a flat rotation curve in Newtonian gravity, it's an expression for which the rotation curve asymptotes to flatness at infinity. A completely flat rotation curve comes from an isothermal sphere:

\rho=\frac{A}{r^2}

All I did was to give a very ‘rough and ready’ comparison, taking z to be a constant, therefore N becomes N(r), and also taking V to be a constant then N becomes linear in r and N_r a constant..

If this was what you did, it would be inconsistent with your result. That gives:

\rho = \frac{const.+N_z^2}{r^2}

Now, this is the Newtonian result if N_z is a constant with radius, but there's no reason to assume this should be the case. Taking the radial partial derivative at a constant z does not mean that partial of z is constant with r.

 

[Garth]

\rho(r)=\frac{C_0}{(a^2+r^2)}

that is not the expression to generate a flat rotation curve in Newtonian gravity, it's an expression for which the rotation curve asymptotes to flatness at infinity.

It's the standard expression that delivers a flat velocity profile at large
r >> a, but modifies the isothermal sphere to give rigid-body rotation at small r << a.

A completely flat rotation curve comes from an isothermal sphere:
\rho=\frac{A}{r^2}

Which is what I was saying, I know that N_z is not constant in general - however it is zero if in a certain regime in the Cooperstock & Tieu relationship the orbital velocity is taken to be constant.
V (r, z) =\frac{3.10^8}{r}N(r, z)=constant

so N(r,z) = C.r

therefore N_r = C and N_z = 0,

my A₁ should have been in fact zero (I answered the post hurriedly - thank you for correcting me) so the density expression does approximate to the isothermal sphere,
\rho=\frac{A}{r^2}

As I have been saying this is only my first approximation to the exact Cooperstock & Tieu equation, 'reverse engineering' it to see how it works and that it is consistent with the standard Newtonian theory. As I said, the equation must be solved properly as in fact they did. And they got that result without a massive external halo - just (with the Korzynski correction) of an extra infinitely thin disk, which might be modelling the observed thin galactic disk.

This diversion has taken attention away from the main question: as I have now raised several times:"Are the non-linear GR effects significant in galactic rotation, and if so, then what of galactic halo DM?"

Garth

 

[EL]

"Are the non-linear GR effects significant in galactic rotation, and if so, then what of galactic halo DM?"

I would love to see this actually worked out in detail. My impression is that almost everyone (including myself) "feels" that the non-linear corrections would be unimportant, or at least not able to replace the dark matter, but that's of course not a reason why they should be so.

 

[Garth]

Thank you EL, what do you think of the Cooperstock and Tieu approach to the problem? I am at a disadvantage in not being able to get a copy of their reference 6 - van Stockum, W.J., 1937. Proc. R. Soc. Edin. 57, 135, which appears to be quite important; does anybody know where it might be downloaded?

Having been rebutted maybe they will present a revised paper for publication during the refereeing process, but it would be unfortunate if such a paper were not accepted and the question of non-linear effects were simply forgotten.

Garth

 

[Turbot]

van Stockum's work is cited all over the 'net in the context of frame dragging, temporal anomalies, etc, but it does not appear that anybody has transcribed or scanned the original work for download.

Here's a paper that might be interesting to people studying DM distribution.

http://www.csun.edu/~vcphy00d/PDFPublications/2004 FDARB.pdf

We give examples of axially symmetric solutions to the field equations in which zero angular momentum test particles, with respect to nonrotating coordinate systems, acquire angular velocities in the opposite direction of rotation from the sources of the metrics. We refer to this phenomenon as “negative frame dragging.”

 

[pervect]

I'm finding the Cooperstock and Tieu paper very hard to follow. The rebuttal paper is much clearer.

Assuming the rebutal paper is correct about the expression for N(r,z), it's very clear that
N_{z,z} is not well behaved at z=0, which leads me to believe the rebuttal paper. (That's the second partial of N(r,z) with respect to z, in case the notation isn't clear).

At this point, though, I am getting different results for the Einstein equation than Cooperstock and Tieu. I've tried a couple of different approaches

1) Ignore C&T's remarks about \bar{\Phi} and just find the Einstein equations for zero pressure in the coordinate basis.

2) Set up an orthonormal basis of one-forms that creates a diagonal metric, and calculate G with respect to this orthonormal basis. I *think* this is most likely what C&T means by a "local" transform. Unfortunately, I still get different results for the Einstein equation.

In the group of equations given in (5) in

http://arxiv.org/PS_cache/astro-ph/pdf/0507/0507619.pdf

the fourth equation follows from the first two, however I get a different result for the third equation.

<br /> (3 N^2+r^2)(N_r^2+N_z^2) + 2(N^2-r^2)(V_{r,r}+V_{z,z})<br />

It could easily be a mistake on my part. Then Van Stockum paper might help clear up what's going on (but I don't have easy access to it).

 

[SpaceTiger]

As I have been saying this is only my first approximation to the exact Cooperstock & Tieu equation, 'reverse engineering' it to see how it works and that it is consistent with the standard Newtonian theory.

We haven't even started on the fact that their galaxy model is not spherically symmetric, which is what is assumed in those various Newtonian limits you (and I) cited.

I don't know why you're pushing this point, though. If their equations reduce to the Newtonian limit, it means their paper is even more wrong than we already thought.

This diversion has taken attention away from the main question: as I have now raised several times:"Are the non-linear GR effects significant in galactic rotation, and if so, then what of galactic halo DM?"

If you're so curious, do the calculation yourself. My intuition tells me that it's not significant enough to solve the dark matter problem in galaxies, so I wouldn't be prone to waste my time on it. If you feel otherwise, then go for it. If you can show it to be significant, you'll be famous.

 

[Mike2]

My intuition tells me that it's not significant enough to solve the dark matter problem in galaxies, so I wouldn't be prone to waste my time on it. If you feel otherwise, then go for it. If you can show it to be significant, you'll be famous.

If the calculation reveals more mass than otherwise thought, than does that mean the process needs to be iterated to now accommodate the added mass of the previous calculation? Would this series of additional iterations converge quickly or would it eventually add up? Thanks.

 

[Garth]

We haven't even started on the fact that their galaxy model is not spherically symmetric, which is what is assumed in those various Newtonian limits you (and I) cited.
I don't know why you're pushing this point, though. If their equations reduce to the Newtonian limit, it means their paper is even more wrong than we already thought.
If you're so curious, do the calculation yourself. My intuition tells me that it's not significant enough to solve the dark matter problem in galaxies, so I wouldn't be prone to waste my time on it. If you feel otherwise, then go for it. If you can show it to be significant, you'll be famous.

As we, perfect as well as myself, have been saying its not so easy to do. But the question stands, and raises an interesting possibility. That is why we have been trying to understand C&T more deeply. Who knows? The solution might even require a scalar field in addition to the matter field to replace the singular disk!

Garth

 

[Garth]

If the calculation reveals more mass than otherwise thought, than does that mean the process needs to be iterated to now accommodate the added mass of the previous calculation? Would this series of additional iterations converge quickly or would it eventually add up? Thanks.

Its not just the extra mass (kinetic energy) that you have to worry about but also time dilation, angular momentum and frame-dragging as well. Even though orbital velocities are only 10^-3c it is not so obvious that the non-linear accumulative effect can be ignored.

Garth

 

[pervect]

The rebuttal paper by Korzynski

http://arxiv.org/PS_cache/astro-ph/pdf/0508/0508377.pdf

does a pretty good job of setting up the problem. They find there is no solution which is both asymptotically flat and static. This puzzled me for a bit, but I think I may see what's going on.

The problem is attempting to find a static solution for a disk of finite thickness with no pressure. This is indeed not possible.

The 4-acceleration of any point above z=0 must have a downward component. The only way to support a static disk of finite thickness is to have pressure in the z-direction.

Probably the best approach would be to try an analysis similar to that by Korzynski, but in 2 dimensions, not three, and keep the zero-pressure assumption.

 

[EL]

Thank you EL, what do you think of the Cooperstock and Tieu approach to the problem?
Having been rebutted maybe they will present a revised paper for publication during the refereeing process, but it would be unfortunate if such a paper were not accepted and the question of non-linear effects were simply forgotten.

I must admit I'm not enough into GR to say in what way one should approach the problem.
Personaly, my intuition tells me the non-linear effects will turn out to be very small, so I don't feel for digging to deep into the problem either. (Probably I will go for SUSY DM instead.) However, I would of course be happy if someone else finally cleared this out! If you decide to give it a try, I wish you all luck, and I'll look forward to the result.

 

[Garth]

The problem is attempting to find a static solution for a disk of finite thickness with no pressure. This is indeed not possible.

The 4-acceleration of any point above z=0 must have a downward component. The only way to support a static disk of finite thickness is to have pressure in the z-direction.

Probably the best approach would be to try an analysis similar to that by Korzynski, but in 2 dimensions, not three, and keep the zero-pressure assumption.

That makes a lot of sense, although it is not altogether immediately clear why the need for pressure in the z-direction is resolved by adding a singular disk at z = 0!

Garth

 

[pervect]

The sign of the contribution from the delta-function density singularity hasn't been explicitly determined in anything I've read. If it turns out to be repulsive, this would explain the finite thickness, but then one wonders why the solution models galactic rotation which requires more (not less) matter.

 

[Chronos]

My admittedly crude intuition insists a rotating, roughly spherical mass will naturally flatten out into a disc-like structure. Deriving the observed features of galaxies appears almost incomprehensively difficult. I see all kinds of complications - classical physics, turbulence, tidal forces, electromagnetism, backreactions and relativistic corrections. Perhaps dark matter represents an approximation of these combined effects.

 

[Garth]

We haven't even started on the fact that their galaxy model is not spherically symmetric, which is what is assumed in those various Newtonian limits you (and I) cited.
I don't know why you're pushing this point, though. If their equations reduce to the Newtonian limit, it means their paper is even more wrong than we already thought.

Yes, that is where the non-linear effects kick in, its not Newtonian.

Newton delivers flat rotation with a spherically symmetric distribution, whereas GR (if C&T are more or less correct) delivers it with a thin axially symmetric distribution both with an r dependence of:

\rho(r)=\frac{a}{r^2}.

Garth