Cooperstock and Tieu Respond to Criticisms

[George Jones]

I just noticed that Cooperstock and Tieu have http://arxiv.org/abs/astro-ph/0512048" (last Friday) on arxiv a reponse (which I haven't actually read) to the criticisms leveled against their proposed solution to the problem of dark matter.

Any comments?

Regards,
George

 

[EL]

Up on nine! The battle continues!
At least one more round...

 

[pervect]

If I'm following what C&T are doing, they are creating an orthonormal basis of one-forms

> [r/sqrt(r^2-N(r,z)^2),0,0,0];
> [0,exp(-v(r,z)/2),0,0];
> [0,0,exp(-v(r,z)/2),0,0];
> [ N(r,z)/sqrt( r^2-N(r,z)^2 ) ,0,0,sqrt(r^2-N(r,z)^2)];

which can be plugged directly into GRtII to give their metric. They are then finding the einstein tensor G in terms of the orthonormal basis, and equating all the pressure terms to zero.

This gives me the first two of their equations in (6). But I can't quite figure out how they are getting the third.

This is sort of a moot point, because I don't think C&T have really thought about the issue of the Komar mass being non-zero for a very short cylinder at z=0. C&T seem to actually admit that this happens, but don't seem to recognize properly the physical significance of this result.

 

[Garth]

The debate continues!

Comments on "Perspectives on Galactic Dynamics via General Relativity" by Vogt & Letelier.

Abstract
In this comment we question some arguments presented in http://arxiv.org/abs/astro-ph/0512048 to refuse the presence of an singular mass surface layer. In particular, incorrect expressions are used for the disk’s surface mass density. We also point out that the procedure of removing the descontinuity on the z = 0 plane with a region of continuous density gradient generates other two regions of descontinuities with singular mass surface layers making the model unrealistic.

Garth

 

[EL]

And here is another one:
http://www.arxiv.org/abs/astro-ph/0601191

The recently proposed Cooperstock-Tieu galaxy model claims to explain the flat rotation curves without dark matter. The purpose of this note is to show that this model is internally inconsistent and thus cannot be considered a valid solution. Moreover, by making the solution consistent the ability to explain the flat rotation curves is lost.

 

[Garth]

And that paper concludes:

However, the flat rotation curves seem to imply a large inertial induction effect, where the rotating inner matter boosts the rotation of the outer matter, leveling off the rotation curve, which is what the Cooperstock-Tieu model attempts to describe within general relativity. Since their solution predicts a matter density well within visible limits it is quite possible that their solution represents an alternative, more Machian, gravitational theory where inertial induction effects are much larger than in General Relativity.

A more Machian alternative anybody?

Garth

 

[Garth]

Another approach by Cooperstock & Lieu in today's ArXiv: General relativistic velocity: the alternative to dark matter.

We consider the gravitational collapse of a spherically symmetric ball of dust in the general relativistic weak gravity regime. The velocity of the matter as viewed by external observers is compared to the velocity gauged by local observers. While the comparison in the case of very strong gravity is seen to follow the pattern familiar from studies of test particles falling towards a concentrated mass, the case of weak gravity is very different. The velocity of the dust that is witnessed by external observers is derived for the critically open case and is seen to differ markedly from the expectations based upon Newtonian gravity theory. Viewed as an idealized model for a cluster of galaxies, we find that with the general relativistic velocity expression, the higher-than-expected constituent velocities observed can be readily correlated with the solely baryonic measure of the mass, obviating the need to introduce extraneous dark matter. Hitherto unexplained and subject-to-reinterpretation astrophysical phenomena could also be considered within this context. It is suggested that an attempt be made to formulate an experimental design at smaller scales simulating or realizing a collapse with the aim of implementing a new test of general relativity.

They note:

Various critics have claimed that our results stemmed from a singular surface layer of mass but we have shown that the singularity actually represents the benign incorporation of a discontinuity in density gradient. As well, a different approach [3] largely supported our central thesis.

That reference [3] was to: Significant reduction of galactic dark matter by general relativity by Daniel Grumiller & H. Balasin, they say:

Exact stationary axially symmetric solutions of the 4D Einstein equations with co-rotating pressureless perfect fluid sources are studied. A particular solution with approximately flat rotation curve is discussed in some detail. We find that simple Newtonian arguments over-estimate the amount of matter needed to explain these curves by more than 30%. The crucial insight gained by this model is that the Newtonian approximation breaks down globally, even though it is valid locally everywhere.

.

Any thoughts, is DM to explain galactic rotation curves really not required?

Garth

 

[Wallace]

I found the original C&T proposal very interesting but at the time was not sufficiently versed in GR to make a genuine appraisal of the validity in light of the criticism it received.

I think this latest work is clever from both a purely scientific view as well as a more sociological one. They really aren't doing all that much new maths, but rather thinking about the observer dependent nature of an existing solution (collapsing spherical dust cloud) from none other than the most sacred of physics tomes, Landau and Lif****z (EDIT: PF won't let me write Lif$hitz, it thinks I'm trying to swear). There can be no argument this time about the validity of the solution, no one would dare publicly criticize L&L!

Of course by their own admission, the collapsing dust cloud is not a reasonable physical analog of a cluster or galaxy, so this latest paper doesn't conclusively argue against DM in these systems, however they have (as long as there analysis is correct) shown that the central idea of the original proposal is somewhat vindicated. The idea (as I understand it) is that while the weak field limit of GR very closely matches the Newtonian result for a single point mass, the non-linear effects of GR (which means the fact that the effect of a sum of particles is not simply the sum of their individual potentials) are still important in the weak-field regime.

The collapsing dust cloud example they go through is such a 'weak field' system and they demonstrate the significant departure of the GR result from the Newtonian result. This paves the way for, as they suggest, a true 'General Relativistic Virial Thereom' that would allow the true GR calculation for the expected velocity dispersion of a virialised object (such as a galaxy or cluster) for an object of a given mass.

I haven't gone through the analysis in the paper in great detail yet, but at first glance it seems reasonable. I'm sure we haven't heard the last of this either way!