19 Aug 2005 3:27:55 UTC

Topic 189714

(moderation:

Since Dark Matter seems to interact with baryonic matter only through gravity, would not gravity waves serve as a probe of the dark matter between the source of the GW's and the detectors here on Earth?

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## A Probe for Dark Matter?

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Hi, jlass --

It's possible that the 'dark matter' is baryonic, e.g., brown dwarfs, in which case gravitational lensing might work, and lensing also if the 'dark matter' is composed of supermassive black holes, but these could be possible sources of GW radiation too, I suppose. If the 'dark matter' isn't baryonic, (e.g., WIMPs) who knows?

I just learned that a probe, floating peacefully at L2 and measuring anisotropy of the microwave background radiation with great precision, has been used to place strong constraints on both the geometry and composition of the universe: it's flat (rather than open or closed), with 73% dark energy, 23% cold dark matter, and 4% atoms. See Wilkinson Microwave Anisotropy Probe

## The strongest argument for

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The strongest argument for dark matter is that galaxies rotate to fast to be held together by just heir "visiable" matter. So something unseen must be providing a lot of additional gravational attraction. The fields that create gravational lens and einstien rings should do the same thing for gravity waves. However such gravity waves would usually come from enormous distances and be extremely hard to detect. It would also be very difficult separate the effects of normal matter from those of dark matter.

## Jlass, It sounds like

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Jlass,

It sounds like you're thinking of something like lensing through the stuff in between a "normal" source and the detector. That's not a good prospect for LIGO.

But depending on what the dark matter is, it might emit gravitational waves itself. Chipper Q mentioned supermassive black holes. Actually, numerous smaller black holes are a better candidate. Our sensitivity to these isn't great yet (partly because the data analysis problems are huge), but we're looking.

Hope this helps,

Ben

## Chipper – Just an update to

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Chipper – Just an update to the thread, concerning the existence of "dark matter", which might be of interest to you and the others.

Take Care,

Tom

Theory of Gravitational Waves & LIGO

Laser Interferometer Space Antenna - LISA

JPL-Caltech

## For those innterested in dark

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For those innterested in dark matter it could also be worth mentioning that there are now several projects working on dark matter detectors:

Germany

UK

US

## RE: Just an update to the

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Thanks, Tom – after seeing how difficult astrometrics can be, it wouldn't be too surprising if Cooperstock is right about 0% dark matter. But what is the “nonlinearity” in GR that he's referring to, that others didn't include?

Quoting some wise words from Ben, this looks like another 'fast-moving topic'.

## Hello all, There is a

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Hello all,

There is a pretty effective, IMO, rebuttal to this idea posted on the BAUT formerly BABB) bulletin board, in this thread, specifically, this post.

From Korzynski's paper referred to there:

"We argue that in this model the gravitational field is generated not only by the galaxy matter, but by a thin, singular disk as well. The model should therefore be considered unphysical."

Now, the paper is mathematically beyond me, but I assume that "singular" is used here in a technical sense: a discontinuity. A disk of arbitrarily small thickness in the galaxy's plane which nevertheless generates gravity seems wrong, to say the least.

Of course, there is a singularity at the center of galaxies, the black hole, which is a source of lots of gravity, but that doesn't help reduce the need for dark matter: You need a source of gravity away from the center to account for the rotation curves. Dark matter halos provide that, and so would this mysterious singular disk, except for the fact that it probably can't exist.

Ken G's comment toward the end of the thread also seems like good sense, again, just IMO:

"Newtonian gravity works fine for all systems with velocities that are way below that of the speed of light, and the last time I checked, that includes the rotation curves of galaxies!"

Ken

## Thanks for those links, Ken –

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Thanks for those links, Ken – some very sharp minds also in the BAUT forum (nicked myself on a couple of the posts :))

For anyone familiar with the math, I have a couple questions on the basics:

1)With regard to calculating the rotation rates (at the heart of the matter), are both

and

T = (T_0)(gamma)

in

?

2)When going from Newtonian mechanics to GR,

in ,

does the exponent for the “r” term need to be generalized, or is the rigid geometry of the Inverse Square Law also accounted for, in G_mu nu?

## ChipperQ: I don't know of any

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ChipperQ:

I don't know of any direct link between your first two links. The first equation describes the relation between the clock rate at R-sub-c and the clock rate at R->infinity (in the traditional form of a Schwarzschild black hole). The second equation is Einstein's stress energy tensor in terms of its differential geometry components. The first is very specific the second is general (and equal to 0 in the Schwarzschild case).

The third link does not apply in the GR. It is replace by sum of terms involving Christoffel Symbols of the Second Kind and the generalized velocity vector of the world line (check out equation 45).In the Newtonian approximation of the Schwarzschild case you can get back the equation of the third link.

I the case of spherically symmetrical solution such as the Schwarzschild solution you can define the radial coordinate in such a way that link 4 is valid.

But relationship between this radial coordinate and the Newtonian approximation of force may not match the equation of link 3.

## Thanks, Mark. I'm still

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Thanks, Mark. I'm still having trouble attaching physical interpretations to equations, and am grateful for all the help I can get. I should have been asking about the geodesic instead of the metric, I think...

Presuming a relativistic framework, I see at least two non-linearities that must be considered when calculating the rotation rates of stars in galaxies, that have nothing to do with the non-relativistic velocities of the individual stars themselves. One is the gravitational field of the galaxy itself, making the “galaxy's clock” appear to run slower (1st link in previous post), and the other is the rate at which the observed galaxy is receding (where T = (T_0)(gamma), gamma = 1 / sqr(1 – v^2/c^2)). How are these two different times, T, added together, or otherwise reconciled? While the former may play a larger role than the latter, are these the 'well known non-linearities' mentioned in the article about Cooperstock's work? Is there another non-linearity I'm overlooking?