More about the Cooperstock and Tieu model


by EL
Tags: cooperstock, model, tieu
Garth
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Oct27-05, 05:56 AM
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Yes I was just reading the same paper by Vogt & Letelier.
We analyze the presence of an additional singular thin disk in the recent General Relativistic model of galactic gravitational field proposed by Cooperstock and Tieu. The physical variables of the disk’s energy-momentum tensor are calculated. We show that the disk is made of exotic matter, either cosmic strings or struts with negative energy density.
They make the same point that I did in the thread new study shows Dark Matter isn't needed? Relativty explains it? "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?""

From their paper
Although the proposed galactic model does not really resolve galactic rotation without the presence of exotic matter, we believe that the idea of treating the non-linear galactic dynamical problem in the context of General Relativity is quite interesting and should be further investigated, specially the rotating models where we have the non-Newtonian effect of dragging of inertial frames; a modest step in this direction is presented in [9].
And that reference 9 was to their earlier paper: Relativistic Models of Galaxies
Rotation is also incorporated to the models and the effects of the source rotation on the rotation profile are calculated as first order corrections by using an approximate form of the Kerr metric in isotropic coordinates.
- As I suggested. So the problem has been worked on for some time!

That latter paper has many references to such work and concludes:
As an example of application of the models, we have numerically calculated some geodesic orbits for one of the potentials and compared them with the Newtonian orbits with the same energy and angular momentum. Near the central regions where the gravitational fields are strong, the motion of particles is considerably altered by General Relativistic effects.

We also calculated the first order effects of galactic rotation on the tangential velocity of circular orbits on the galactic plane using an approximate form of the Kerr metric expressed in cylindrical isotropic coordinates. In general, rotation increases the progade tangential velocity and has an opposite effect on the retrogade tangential velocity.

It should be mentioned that the stability study of the models presented based on the extension of Rayleigh criteria of stability is very limited. A more realistic stability analysis should rely on the first order perturbed General Relativistic fluid equations taking into account two spatial coordinates, which may be not a trivial task (see, for instance, Ujevic & Letelier (2004) for the one dimensional case). This will be subject of further investigation.
(emphasis mine)

The case is by no means closed!

Garth
EL
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Oct27-05, 06:38 AM
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Quote Quote by Garth
The case is by no means closed!
Of course we need to clear these non-linear effects out, just because it is something interesting in itself. However, could you agree on that it probably won't solve the dark matter problem in any way?
At least this attempt by C&T has been debunked, and I can hardly see that any other attempts would succeed. I mean, there's a lot of other stuff that DM particles solves, which we then must find new explanations for if GR could explain the rotation curves.

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Oct27-05, 07:30 AM
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More about the Cooperstock and Tieu model


Quote Quote by EL
However, could you agree on that it probably won't solve the dark matter problem in any way?
Several points: First, there are several DM problems, that needed to resolve galactic rotation curves as discussed in this thread, that needed to gravitationally bind galactic clusters, especially rich cluster DM, and that detected through analysis of the WMAP data. It is also required to explain large-scale structure formation in the early universe given the near isotropy of the CMB at z ~ 1100.

All these observations are theory dependent. C&L suggested that it all might be explained away by GR non-linear effects, that is not my position. These different observations of DM may have different explanations, each has to be analysed separately and not just lumped together.

The galactic halo DM is particularly troublesome in that the gravitational source itself is in orbit and non-linear effects may be significant. C&L may be onto something, they are not idiots (Professor Cooperstock, Department of Physics and Astronomy, University of Victoria), even if their analysis has been criticised - that is par for the game. Before I can "agree on that it probably won't solve the dark matter problem in any way" Voigt & Letelier's This will be subject of further investigation will have to be completed first!

My own personal agenda? To explore a hunch that C&L's singular disk might just in fact be the non-minimally connected scalar field of SCC which would substantially explain the need for spiral galaxies to have massive haloes. However I conjecture that the rich and not-so-rich cluster DM is in the form of IMBH's, the relics of a dense population of (not-so-massive) Pop III stars. At the moment that is only a guess, so I'll shut up before being closed down!

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Oct27-05, 08:51 AM
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If the need for galactic haloes can be substantially explained by non-linear GR effects, whereas cluster DM is real, then this hypothesis may be tested.
Individual galaxies should lens distant quasars less effectively than a cluster. IOW the lensing mass of a spiral galaxy should agree with its baryonic mass, whereas the lensing (and virial) mass of a cluster should be much larger than the sum total of its visible component parts. The latter part is true, but what of the former - what data do we have on the gravitational lensing by an individual spiral galaxy?

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EL
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Oct27-05, 08:56 AM
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Quote Quote by Garth
All these observations are theory dependent. C&L suggested that it all might be explained away by GR non-linear effects
Well, they said like this:
Quote Quote by astro-ph/0510750 Cooperstock & Tieu
Moreover, it will be of interest to extend this general relativistic approach to the other relevant areas of astrophysics with the aim of determining whether there is any scope remaining for the presence of any exotic dark matter in the universe. Clearly the absence of such exotic dark matter would have considerable significance.
So they really don't offer any hints of HOW general relativity would solve the other problems.


These different observations of DM may have different explanations, each has to be analysed separately and not just lumped together.
But here is where the beauty of particle DM comes in! It may solve a bunch of, at least at first site, unrelated problems!


C&L may be onto something, they are not idiots
Of course not. I'm sure they are great physicists. And I'm also sure they will accept that they have made some errors.
EL
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Oct27-05, 09:03 AM
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Quote Quote by Garth
If the need for galactic haloes can be substantially explained by non-linear GR effects, whereas cluster DM is real, then this hypothesis may be tested.
Individual galaxies should lens distant quasars less effectively than a cluster. IOW the lensing mass of a spiral galaxy should agree with its baryonic mass, whereas the lensing (and virial) mass of a cluster should be much larger than the sum total of its visible component parts. The latter part is true, but what of the former - what data do we have on the gravitational lensing by an individual spiral galaxy?
Garth
Nice thought! (Unfortunately I don't have any data here right now.)
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Oct27-05, 09:06 AM
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Quote Quote by EL
But here is where the beauty of particle DM comes in! It may solve a bunch of, at least at first site, unrelated problems!
Show me the particle and I'll agree with you!

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EL
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Oct27-05, 09:08 AM
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Quote Quote by Garth
Show me the particle and I'll agree with you!
Garth
Well, eh, give me some minutes...
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Oct27-05, 10:04 AM
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Quote Quote by Garth
Several points: First, there are several DM problems, that needed to resolve galactic rotation curves as discussed in this thread, that needed to gravitationally bind galactic clusters, especially rich cluster DM, and that detected through analysis of the WMAP data. It is also required to explain large-scale structure formation in the early universe given the near isotropy of the CMB at z ~ 1100.
All these observations are theory dependent. C&L suggested that it all might be explained away by GR non-linear effects, that is not my position. These different observations of DM may have different explanations, each has to be analysed separately and not just lumped together.
It might be helpful to lump them together but take DM entirely out of the equation. Then ask "why does the GR gravititational model fail to accurately predict the behavior of visible matter at galactic, cluster, and cosmological scales?" Blind faith in the infallibility of GR gravitation necessitated the invention of DM - simply because GR could not be allowed to fail. Back when GR was developed, physicists "knew" things about the universe that later observations have shown to be absolutely wrong. Is this 90-year old theory of gravitation so sacred that we cannot allow observations to falsify it?

If gravitation does not follow an inverse square law on large scales or in complex systems, this is a strong clue that gravitation is an emergent force and not a fundamental one. Many smart fellows, including Sakharov and Feynman, believed that the "fundamental" properties of matter arise from interaction and are not innate to the material body. Others today like Puthoff, Rueda and Haisch are exploring this, as well.


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