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

 

[Garth]

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.

Hi pervect - is that the rebuttal correction compared to C&T or C&Tcompared to Newtonian?

The C&T solution requires less matter (no DM halo) than the Newtonian.

Garth

 

[Garth]

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.

Thanks Chronos obviously a detailed model able to explain the spiral arms, the central bulge, the warp in the disk and the contribution of the globular clusters and anything else out there in the form of a DM halo is going to be horribly complicated - not a 'back of the envelope' type of calculation!

However it would be good to get the basic flat rotation profile sorted.

Garth

 

[Chronos]

Agreed, Garth. Would you concede that even the 'simple' model is anything but simple? I think if we could get that much right, the details would be mostly easier.

 

[pervect]

Hi pervect - is that the rebuttal correction compared to C&T or C&Tcompared to Newtonian?
The C&T solution requires less matter (no DM halo) than the Newtonian.
Garth

The article in question is http://arxiv.org/abs/astro-ph/0508377

They first point out that the second derivative of N with respect to z is undefined at z=0 because the first derivative changes sign. Their argument that the disk must contains a "shell" of matter is based on the Komar integral - this is equivalent to the Komar mass, which is mass defined in terms of a Killing vector (this concept of mass is valid in any static space-times). They take the limit of the Komar integral (which gives the enclosed mass) for a cylinder which approaches zero volume (by shrinking the height 'a' of the cyliner to zero), and find that the resulting limit as the height a->0 is non-zero

I don't know offhand whether non-zero means positive, or negative. I see a minus sign in (20), but it's easy to lose track of signs.

BTW the concept of Komar mass is the one found on pg 298 of Wald - I've posted about it before, but never under that name - I didn't realize it had a name until just now (it's handy to know it's name).

 

[Garth]

Thank you, yes I have read the rebuttal paper, its good to have it explained so clearly.

Garth

 

[SpaceTiger]

Interesting sidenote. The speaker at my seminar today used this paper as an example of "How not to do GR."

 

[Garth]

Concur - what is needed is an equivalent to the Kerr metric.

Garth

 

[Garth]

And now it seems spiral galaxy rotation curves are not even flat - as C&L were assuming! Comment on "Scalar-tensor gravity coupled to a global monopole and flat rotation curves" by Lee and Lee

Garth