Explaining Galaxy Rotation Speed Discrepancies with GR & Gravitic Fields

[Sagittarius A-Star]

TL;DR Summary

From Kepler's Second Law, it is expected that the rotation velocities will decrease with distance from the center of a Galaxy, similar to the Solar System. This is not observed. Can this be explained with rotational frame-dragging (the Lense–Thirring effect)?

The speed of the ends of the galaxies is higher than what it should be. Current solution: This could be explained by hypothetical "dark matter", which was not found up to now, or by a MOND theory (MOdified Newtonian Dynamics).

Can this be explained instead with rotational frame-dragging (Lense–Thirring effect) by the rotating Galaxy?

This is suggested in the following paper:

In our study, we will try a third way of explanation of these discrepancies. This explanation doesn’t modify the quantities of observed matter and doesn’t modify general relativity. To demonstrate the capacity of the general relativity to explain dark matter, we are going to use, in our paper, the native metric of linearized general relativity (also called gravitoelectromagnetism) in agreement with the expected domain of validity of our study ... It doesn’t modify the gravity field of Newtonian approximation but defines a better approximation by adding a component (called gravitic field, similar to magnetic field of Maxwell idealization) correcting some imperfections of the Newtonian idealization (in particular the infinite propagation speed of gravitation). ... The only assumption that will be made in this paper is that there are some large astrophysical structures that can generate a significant value of gravitic field. And we will see that the galaxies’ cluster can generate it.

Source:
https://arxiv.org/ftp/arxiv/papers/1503/1503.07440.pdf

 

[anuttarasammyak]

I read https://en.wikipedia.org/wiki/Galaxy_rotation_curve and I do not think Lense-Thirring effect matters because mass of galaxy is heavily concentrated around the core and mass of rotating "cylinder" apart from the core seems not so much.

 

[Vanadium 50]

That paper is low quality, and after 5 years unpublished, and uncited. It also fails to do what you say it does: show that DM is from the Lense-Thirring Effect.

I recommend you calculate the size of the effect and compare it with the size of the observation.

 

[vanhees71]

I also think that the Lense-Thirring effect is too weak to explain the discrepancy between the velocity curves of the stars and Kepler's Law taking into account only the visible matter as the source of gravity for their motion.

 

[Sagittarius A-Star]

I read https://en.wikipedia.org/wiki/Galaxy_rotation_curve and I do not think Lense-Thirring effect matters because mass of galaxy is heavily concentrated around the core and mass of rotating "cylinder" apart from the core seems not so much.

But in the last sentence of this Wikipedia article stands also:

Alternatives to dark matter
...
According to a 2020 analysis of the data produced by the Gaia spacecraft , it would seem possible to explain at least the Milky Way's rotation curve without requiring any dark matter if instead of a Newtonian approximation the entire set of equations of general relativity is adopted. [39].

The cited paper [39] says in it's abstract:

This supports the ansatz that a weak gravitational contribution due to the off-diagonal term of the metric, by explaining the observed flatness of MW’s RC, could fill the gap in a baryons-only MW, thus rendering the Newtonian-origin DM a general relativity-like effect.

Source:
https://academic.oup.com/mnras/article-abstract/496/2/2107/5850386

see also:

Basically, frame dragging arises out of the off-diagonal terms in the Kerr metric.

Source:
https://physics.stackexchange.com/q...strate-frame-dragging-through-the-kerr-metric

 

[Vanadium 50]

The cited paper [39] does not say it's the Lense-Thirring Effect.
That's two papers you have pointed us to that don't say what you say they do.

 

[Sagittarius A-Star]

The cited paper [39] does not say it's the Lense-Thirring Effect.

A one year earlier paper by all 4 authors, which is freely available, says:

Applying the same reasoning to a conjectural metric for the Galaxy weak gravitational fields away from its center, the non-diagonal contribution is of $∼(v_{Gal}/c)^3 ≈ 100μas$, already within the error level of Gaia’s DR2. The GR small curvature limit may not coincide with the Newtonian regime, as it is the case of the Lense-Thirring effect [8]. The situation appears similar to what was needed to explain the advancement of Mercury’s perihelion: instead of correcting the dynamics by adding a ”dark planet” (Vulcano), GR cured the anomalous precession by accounting for the weak non-linear gravitational fields overlapping nearby the Sun.

Source:
https://arxiv.org/pdf/1810.04445.pdf

 

[Vanadium 50]

Yes, they mention it. Once. But they do not show - or even attempt to show - that this is the cause of rotation curves.

This misinformation has to stop if we have any hope of intelligent discussion.

 

[Sagittarius A-Star]

But they do not show - or even attempt to show - that this is the cause of rotation curves.

In the further text they call it several times "gravitational dragging effect". Don't they mean by this the "Lense-Thirring effect"?

Example:

5 Final remarks
...
By proving our relativistic ansatz on a gravitational dragging effect driving the Galaxy velocity rotation curve, we suggest that geometry - unseen but perceived as manifestation of gravity according to Einstein’s equation - is responsible of the flatness at large Galactic radii.

Source:
https://arxiv.org/pdf/1810.04445.pdf

 

[PeterDonis]

This is suggested in the following paper

As far as I can tell, this paper never actually calculates what the magnitude of what it calls the "gravitic field" (by which it appears to mean the magnetic part of gravitoelectromagnetism, a weak field approximation to a certain class of solutions of the Einstein Field Equation) would be given the actual distribution of mass that is observed. It just calculates what the magnitude of the "gravitic field" would need to be to account for galaxy rotation curves, and then assumes that it has that magnitude, without ever justifying that assumption in terms of the distribution of visible matter.

The cited paper [39]

A one year earlier paper by all 4 authors

Both of these papers appear to be doing basically the same thing as the one above--they are calculating what the spacetime geometry would need to be in order for gravitomagnetic effects to account for the observed galaxy rotation curves, but they never actually calculate what the spacetime geometry due to the distribution of visible matter would be.

In the further text they call it several times "gravitational dragging effect". Don't they mean by this the "Lense-Thirring effect"?

It's somewhat unclear exactly what effect these papers are referring to. The 2018 paper, for example, mentions the precession of Mercury's perihelion, and appears to be implying that the effect it is going to talk about is the same one that is responsible for that precession. But the precession of Mercury's perihelion is not due to the Lense-Thirring effect; it is not due to "frame dragging" by the rotation of the Sun (which is the central mass in question in this example). The precession of Mercury's perihelion can be derived using Schwarzschild spacetime, which has zero "frame dragging" and zero Lense-Thirring effect.

In short, as far as these papers are concerned, the answer to the title question of this thread still appears to be "no".

 

[Vanadium 50]

It just calculates what the magnitude of the "gravitic field" would need to be to account for galaxy rotation curves, and then assumes that it has that magnitude, without ever justifying that assumption in terms of the distribution of visible matter.

Yes.

--they are calculating what the spacetime geometry would need to be in order for gravitomagnetic effects to account for the observed galaxy rotation curves, but they never actually calculate what the spacetime geometry due to the distribution of visible matter would be.

Yes.

In short, as far as these papers are concerned, the answer to the title question of this thread still appears to be "no".

Yes.

They seem to take one additional step. They seem to be saying you can make this work by adding more non-interacting "dust" (in the GR sense) to the galaxy. That may be so, but non-interacting "dust" sounds a lot like "dark matter". Maybe I misunderstood their argument.

My suggestion in post #3 was to calculate the magnitude of the effect. I believe the effect goes as $M\omega^2/r$. GPB sees an effect of order 1 turn per 1000 years. Going from Earth to the galaxy, you get a 10¹⁷ in mass, a 10¹⁴ in radius and 10^-11 in angular velocity, so you need to square that. So the effect is 10¹⁶ years or about 10^-8 on the rotational velocity, when we need a number that is comparable.

It's not even close.

That's why I suggested the OP do the calculation. Before claiming one has discovered something everyone else has missed, it's worth doing an order-of-magnitude estimate.

 

[PeterDonis]

My suggestion in post #3 was to calculate the magnitude of the effect.

We would first have to decide which effect we are interested in. Your numbers are for the Lense-Thirring precession, but it's not clear to me that the Lense-Thirring precession is even relevant; we are not talking about precession of gyroscopes but about orbital velocities. As I noted, the papers themselves don't seem to be entirely clear on what effect they are talking about.

A relevant calculation, it seems to me, would be of prograde free-fall orbital velocities in something like the weak field approximation to the Kerr metric, as compared with the Schwarzschild metric, for a given distance from center. I would expect any such effects to be small for a galaxy, since we are talking about distances from center many orders of magnitude larger than the mass (in geometric units), and it is only for distances from center of the same order of magnitude as the mass (in geometric units) that any effects of Kerr spacetime on orbital velocities become significant.

 

[Vanadium 50]

Your numbers are for the Lense-Thirring precession

Yes, because...

Can this be explained instead with rotational frame-dragging (Lense–Thirring effect)

 

[Vanadium 50]

If you want to say "Well, this question was bad and overly narrow. Could any angular GR effect replace DM?" That would be very unlikely. The DM effect has to be comparable to (actually, about 5x larger than) g00 gravitational effects. The next order down has one power of β, which is of order 0.002 for the galaxy. So you need terms of order 1 to somehow work out to 2500. This is not unprecedented (I know of one example that's 192π³, but I remember it not because it is common but because it is rare) but it is very, very unusual.

 

[PeterDonis]

If you want to say "Well, this question was bad and overly narrow. Could any angular GR effect replace DM?" That would be very unlikely.

Yes, agreed. That is basically what the last part of my post #12 is getting at: any corrections due to the effects of rotating matter on the spacetime geometry are going to be much too small.

 

[Sagittarius A-Star]

Yes, agreed. That is basically what the last part of my post #12 is getting at: any corrections due to the effects of rotating matter on the spacetime geometry are going to be much too small.

O.K. That answers my question. Thanks!

 

[PeterDonis]

That answers my question.

Ok, good.

 

[BruceAW]

I believe the graph in the wiki link posted above, that shows the velocities of stellar objects increasing with distance from galactic center, is erroneous.
I believe the correct graph. https://www.ippp.dur.ac.uk/~dcerdeno/Dark_Matter_Lab_files/DM.pdf
Does not show much, if any, increase in velocity with distance.
It just shows velocity, that increasingly exceeds the velocities they expect to decrease with distance. Based on calculations of the gravity from known matter in the galaxy.

 

[PeterDonis]

I believe the graph in the wiki link posted above, that shows the velocities of stellar objects increasing with distance from galactic center, is erroneous.
I believe the correct graph. https://www.ippp.dur.ac.uk/~dcerdeno/Dark_Matter_Lab_files/DM.pdf

There isn't just one graph. It's different for different galaxies. The Wikipedia one is for the galaxy M33. The one in Fig 1.1 of the PDF you linked to is for NGC 3198. You should not expect the curves to be identical.

 

[BruceAW]

PeterDonis said
"There isn't just one graph. It's different for different galaxies."
Yes. Apologies . I will try to be more careful.

 

[alantheastronomer]

Summary:: From Kepler's Second Law, it is expected that the rotation velocities will decrease with distance from the center of a Galaxy, similar to the Solar System. This is not observed. Can this be explained with rotational frame-dragging (the Lense–Thirring effect)?

The speed of the ends of the galaxies is higher than what it should be. Current solution: This could be explained by hypothetical "dark matter", which was not found up to now, or by a MOND theory (MOdified Newtonian Dynamics).

Can this be explained instead with rotational frame-dragging?

The Lense-Thirring effect falls off with distance even more severely than Keplerian motion, so frame-dragging wouldn't be able to sustain flat rotation curves over thousands of light years. So no, but interesting idea though...

 

[BoraxZ]

TL;DR Summary: From Kepler's Second Law, it is expected that the rotation velocities will decrease with distance from the center of a Galaxy, similar to the Solar System. This is not observed. Can this be explained with rotational frame-dragging (the Lense–Thirring effect)?

The speed of the ends of the galaxies is higher than what it should be. Current solution: This could be explained by hypothetical "dark matter", which was not found up to now, or by a MOND theory (MOdified Newtonian Dynamics).

Can this be explained instead with rotational frame-dragging (Lense–Thirring effect) by the rotating Galaxy?

This is suggested in the following paper:

Source:
https://arxiv.org/ftp/arxiv/papers/1503/1503.07440.pdf

Is the following question about the same stuff you introduce here?
This question:

"LQG Legend Writes Paper Claiming GR Explains Dark Matter Phenomena | Page 6 | Physics Forums" https://www.physicsforums.com/threa...-matter-phenomena.1016800/page-6#post-6865041

 

[PeterDonis]

Is the following question about the same stuff you introduce here?
This question:

"LQG Legend Writes Paper Claiming GR Explains Dark Matter Phenomena | Page 6 | Physics Forums" https://www.physicsforums.com/threa...-matter-phenomena.1016800/page-6#post-6865041

No.