[astro-ph/0507619] General Relativity Resolves Galactic Rotation Without Exotic Dark Matter

Authors:  F. I. Cooperstock, S. Tieu
Abstract:  A galaxy is modeled as a stationary axially symmetric pressure-free fluid in general relativity. For the weak gravitational fields under consideration, the field equations and the equations of motion ultimately lead to one linear and one nonlinear equation relating the angular velocity to the fluid density. It is shown that the rotation curves for the Milky Way, NGC 3031, NGC 3198 and NGC 7331 are consistent with the mass density distributions of the visible matter concentrated in flattened disks. Thus the need for a massive halo of exotic dark matter is removed. For these galaxies we determine the mass density for the luminous threshold as 10^{-21.75} kg.m$^{-3}.
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Discussion related to specific recent arXiv papers
Garth Antony Barber
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Re: [astro-ph/0507619] General Relativity Resolves Galactic

Post by Garth Antony Barber » March 30 2006

Tommy Anderberg wrote:Garth Antony Barber wrote:
Cluster DM has also been observed by gravitational lensing of distant quasars, do the GR non-linear effects achieve this effect without extra mass?
You are the relativist; you tell me. My intuitive answer would be that any GR effect which reduces the need for DM with regard to orbital motion should also mimic the effect of the replaced DM on test particles, zero mass ones included.

But suppose it didn't work out that way. If galaxies are 20% less massive than we thought, but we insist that Newtonian gravity is fine for clusters, the missing mass problem just got 20% worse for clusters. So we throw in - let me guess, 20% more dark matter at the cluster scale. What does that do to structure formation?

Questions, questions...
Well I was being rhetorical, C&L tried to explain away all DM as non-linear GR efects because in a galaxy the gravitational mass is itself in orbit. Even if this did work for the galactic rotaiton curve it would not work for a galaxy cluster as the dynamics are different and the inferred DM mass is so large. I do not see how the non-linear effect of a rotating galaxy could lens light, passing at a distance from its mass, through the cluster's IGM.

Garth

Daniel Grumiller
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[astro-ph/0507619] General Relativity Resolves Galactic Rota

Post by Daniel Grumiller » March 30 2006

Garth is of course correct - if CT would have worked for galaxy rotation curves, what about all the other hints for dark matter that we have, for instance cluster?

But since it did not work this is a "rhetorical" point now.

Whether or not the 30% effect is of relevance for available data concerning gravitational lensing I do not know.

Tommy Anderberg wrote:
My intuitive answer would be that any GR effect which reduces the need for DM with regard to orbital motion should also mimic the effect of the replaced DM on test particles, zero mass ones included.
I agree that it may sound plausible, but if there is one thing we can be sure about GR that intuition fails quite often. ;-)

Personally, I do not think that our result will have an effect on gravitational lensing, the physical situations are quite different: in lensing you have some light-like test-particles on some fixed background, whereas for rotation curves you have to take into account the full dynamics of the corotating perfect fluid.

But then again, this is just my intuition talking, so the same caveat applies...

Garth Antony Barber
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Re: [astro-ph/0507619] General Relativity Resolves Galactic

Post by Garth Antony Barber » March 30 2006

Daniel Grumiller wrote:Garth is of course correct - if CT would have worked for galaxy rotation curves, what about all the other hints for dark matter that we have, for instance cluster?

But since it did not work this is a "rhetorical" point now.

Whether or not the 30% effect is of relevance for available data concerning gravitational lensing I do not know.

.
The questions in GR pertinent to this problem are "1. How do we define mass and 2. how do we measure it?"

The definition of mass in motion, with a non-static gravitational field and possibly DE (i.e. with density and negative pressure) as well as DM, is problematic.

However to clear the air, would not one test be, find an unambiguous lensing galaxy/cluster, measure both the rotation profile Keplerian mass, the 'GR non-linear effect' mass, and the lensing mass and compare to see whether they are consistent or not?

Garth

Tommy Anderberg
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Re: [astro-ph/0507619] General Relativity Resolves Galactic

Post by Tommy Anderberg » April 01 2006

Daniel Grumiller wrote:Garth is of course correct - if CT would have worked for galaxy rotation curves, what about all the other hints for dark matter that we have, for instance cluster?
Just to recap the well-known argument, all those hints depend on two assumptions:

1) We have the correct theory of gravity.
2) We are applying it correctly.

C&T, and you, are questioning point (2). Others point to the fact that you can perform precision tests of GR up to the scale of the solar system (and even then, you have the unexplained Pioneer anomaly to contend with); beyond that scale, point (1) is just an assumption. When you see visible matter deviating from the predictions of GR, you can conclude that there must be invisible matter too, or you can conclude that GR needs to be modified at large scales, or you can be really evil and go for a combination of the two.

The last alternative wouldn't be beyond me. As you know, Garth is a much nicer person,

http://arxiv.org/abs/gr-qc/0405094

as are e.g. Brownstein and Moffat:

http://arxiv.org/abs/astro-ph/0506370
http://arxiv.org/abs/astro-ph/0507222

(there are others, many referenced in the last two papers).
Garth Antony Barber wrote: However to clear the air, would not one test be, find an unambiguous lensing galaxy/cluster, measure both the rotation profile Keplerian mass, the 'GR non-linear effect' mass, and the lensing mass and compare to see whether they are consistent or not?
It's not like I could tell a modern telescope from a coffee machine, but I did a bit of searching and almost immediately found what, to me at least, looks like a possible galactic candidate: Huchra's lens, an Einstein cross close enough to be studied in detail, and therefore very popular for this kind of thing. See for instance

http://arxiv.org/abs/astro-ph/0203196

What do you think?

Clusters look much more difficult. This paper seems to reflect the state of the art as far as modeling them goes:

http://arxiv.org/abs/astro-ph/0506171

I guess the N-body code they used is Newtonian. Anybody care to correct me?

Daniel Grumiller
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[astro-ph/0507619] General Relativity Resolves Galactic Rota

Post by Daniel Grumiller » April 07 2006

The questions raised by Garth are very relevant ones.

But if you have Killing vectors (as in stationary, axisymmetric solutions) the situation is not quite as desperate, so one can provide a meaningful mass definition.

How to measure it is an entirely different issue, of course...


Regarding Tommy Anderberg's two assumptions, I think we should be open-minded concerning both points. Assuming 1. is certainly conservative, but it has the advantage of more predictibility. Assuming 2. ... well, actually, one should not have to assume anything here, right? "Just" do the calculations correctly and check that the technical assumptions involved are meaningful from a physical point of view. Of course, the latter point may be the cause of some debates...

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