Dark Matter As Non-Newtonian Behaviour in Weak-Field GR

[Markus Hanke]

Interesting paper from back in July (how did I miss this?), co-authored by Giorgio Immirzi, one of the foremost experts on GR and quantum gravity:

https://arxiv.org/abs/2207.04279

This is just the latest paper within an increasingly large body of work that indicates that ‘dark matter’ as a separate phenomenon may be entirely superfluous. The basic idea here is that, under certain specific circumstances, even in the weak-field and low velocity regime, there may be non-negligible GR effects that aren’t found in Newtonian gravity. Hence, sometimes Newtonian gravity is not a valid approximation to GR in the weak field domain - which is the very assumption from which the idea of dark matter arises in the first place. What’s more, it turns out that under certain circumstances not even weak-field approximations of GR (such as GEM for example) are valid - specifically, this appears to be the case for rotating systems.

In other words, within this paradigm, dark matter would neither be some new exotic form of particulate matter, nor is it a modification of the laws of gravity; it’s quite simply an artefact of us not having applied standard GR correctly, because the assumption “weak field”=“Newtonian” does not always hold.

Small selection of other papers along the same lines:

https://arxiv.org/abs/2207.09736

https://link.springer.com/article/10.1140/epjc/s10052-021-08967-3

https://www.worldscientific.com/doi/abs/10.1142/S0218271808012140

https://arxiv.org/abs/astro-ph/0610370

https://academic.oup.com/mnras/article-abstract/496/2/2107/5850386?redirectedFrom=fulltext

https://arxiv.org/abs/1509.09288

https://arxiv.org/abs/2112.04116

https://arxiv.org/abs/2109.13515

https://arxiv.org/abs/2102.11282

[Genady]

Do I understand correctly that for this deviation from Newtonian approximation to be observed, large distances rather than strong fields or high velocities are required? Hence, the galactic scales of the phenomenon?

The plateau of rotational curves is not the only evidence for DM. Does this paradigm address the others?

[Markus Hanke]

27 minutes ago, Genady said:

Do I understand correctly that for this deviation from Newtonian approximation to be observed, large distances rather than strong fields or high velocities are required? Hence, the galactic scales of the phenomenon?

The distances are relevant for the original problem, being that galactic rotation curves flatten out at large radii, ie far from the galactic center. This is not what we’d expect based on ordinary Newtonian gravity, hence the ‘traditional’ need for Dark Matter.

The deviation between weak-field GR and Newtonian gravity seems to arise specifically for rotational systems, at least that’s the kind of systems almost all of these papers investigate. This is to say that within such systems, one cannot naively equate the weak-field regime to simple Newtonian gravity - the difference between the two (according to some of the above papers) amounts to as much as 30%.

IOW, there are circumstances were you can get very significant non-linear GR effects, even though the situation only deals with weak fields. Traditionally such systems have been treated as Newtonian, on the assumption that any GR effects would be minute and thus negligible; but now it might turn out that this was a fundamental error on our part. 

However, we need to be cautious here, because Dark Matter is also observationally relevant in systems without any significant rotation, for example the Bullet Cluster. So unless it can be shown that such weak-field non-linear effects also occur in more general systems, at least under some circumstances, then this whole thing may still not provide a good explanation for Dark Matter. But it’s an interesting line of research that’s well worth pursuing further. But it’s mathematically very challenging.

[Genady]

3 minutes ago, Markus Hanke said:

The distances are relevant for the original problem, being that galactic rotation curves flatten out at large radii, ie far from the galactic center. This is not what we’d expect based on ordinary Newtonian gravity, hence the ‘traditional’ need for Dark Matter.

The deviation between weak-field GR and Newtonian gravity seems to arise specifically for rotational systems, at least that’s the kind of systems almost all of these papers investigate. This is to say that within such systems, one cannot naively equate the weak-field regime to simple Newtonian gravity - the difference between the two (according to some of the above papers) amounts to as much as 30%.

IOW, there are circumstances were you can get very significant non-linear GR effects, even though the situation only deals with weak fields. Traditionally such systems have been treated as Newtonian, on the assumption that any GR effects would be minute and thus negligible; but now it might turn out that this was a fundamental error on our part. 

However, we need to be cautious here, because Dark Matter is also observationally relevant in systems without any significant rotation, for example the Bullet Cluster. So unless it can be shown that such weak-field non-linear effects also occur in more general systems, at least under some circumstances, then this whole thing may still not provide a good explanation for Dark Matter. But it’s an interesting line of research that’s well worth pursuing further. But it’s mathematically very challenging.

Thank you. Your last paragraph relates to the second question I've added above, i.e., regarding other evidence. I also want to point out that amounts of DM vary vastly from galaxy to galaxy and from cluster to cluster, and I don't know of a correlation between these amounts and other parameters such as angular momentum. Plus, DM is a crucial part of the standard cosmology. Is that role addressed?

Surely, it's refreshing to see a "third way out."

[joigus]

3 hours ago, Markus Hanke said:

Interesting paper from back in July (how did I miss this?), co-authored by Giorgio Immirzi, one of the foremost experts on GR and quantum gravity:

https://arxiv.org/abs/2207.04279

This is just the latest paper within an increasingly large body of work that indicates that ‘dark matter’ as a separate phenomenon may be entirely superfluous. The basic idea here is that, under certain specific circumstances, even in the weak-field and low velocity regime, there may be non-negligible GR effects that aren’t found in Newtonian gravity. Hence, sometimes Newtonian gravity is not a valid approximation to GR in the weak field domain - which is the very assumption from which the idea of dark matter arises in the first place. What’s more, it turns out that under certain circumstances not even weak-field approximations of GR (such as GEM for example) are valid - specifically, this appears to be the case for rotating systems.

In other words, within this paradigm, dark matter would neither be some new exotic form of particulate matter, nor is it a modification of the laws of gravity; it’s quite simply an artefact of us not having applied standard GR correctly, because the assumption “weak field”=“Newtonian” does not always hold.

Small selection of other papers along the same lines:

https://arxiv.org/abs/2207.09736

https://link.springer.com/article/10.1140/epjc/s10052-021-08967-3

https://www.worldscientific.com/doi/abs/10.1142/S0218271808012140

https://arxiv.org/abs/astro-ph/0610370

https://academic.oup.com/mnras/article-abstract/496/2/2107/5850386?redirectedFrom=fulltext

https://arxiv.org/abs/1509.09288

https://arxiv.org/abs/2112.04116

https://arxiv.org/abs/2109.13515

https://arxiv.org/abs/2102.11282

Very interesting. I'm familiar with Immirzi from the "Immirzi parameter" in topological GR. I'm assuming it's the same Immirzi.

I'll probably take a second and a third read of this.

Thank you. +1

[Markus Hanke]

24 minutes ago, Genady said:

and I don't know of a correlation between these amounts and other parameters such as angular momentum

The extra effects here are highly non-linear, so there wouldn’t be any straightforward correlation - what it comes down to is that for some systems, it is in fact necessary to use exact solutions to the full Einstein equations, rather than linearised approximations, even though such systems are not ordinarily considered generally relativistic. To put it differently, within such systems, the error introduced by treating gravity as a linear perturbation of flat spacetime is much larger than is naively expected, due to additional non-linear effects in the full non-perturbative EFE.

The big question is what characteristics must be present within a given system for this to be the case, and that question is still very much open. It appears that it being rotational may contribute to it, but it may also be down to other things.

Within non-linear systems, it is very difficult to tell how much error margin you introduce (relative to the full non-perturbative solution) by linearising it locally, and then cutting off higher-order terms in the expansion to make it computationally accessible. Which is essentially what is happening here, since complex systems such as galaxies can only ever be simulated using simplifying approximations.

[MigL]

Seems to me that if there can be as much as a 30% discrepancy between GR and the Newtonian limit for rotational systems like galaxies, the effect should be detectable in the case of the Solar System, where we have done fly-bys of Pluto using the Newtonian 'approximation'.
Still, very interesting.

[joigus]

4 hours ago, Markus Hanke said:

Within non-linear systems, it is very difficult to tell how much error margin you introduce (relative to the full non-perturbative solution) by linearising it locally, and then cutting off higher-order terms in the expansion to make it computationally accessible. Which is essentially what is happening here, since complex systems such as galaxies can only ever be simulated using simplifying approximations.

I'm thinking that, in particular, the Weyl solution extends this rotational velocity field to infinity --I'm not clear about assymptotic behaviour, but paper seems to suggest radiation-like, so 1/r. So it's probably not realistic to describe a distribution of galaxies. At some point near the intergalactic distance it's bound to stop being accurate.

Even so, it's interesting that the picture of an axially-symmetric rotating galaxy already produces deviations from the Newtonian approximations for reasons that, OTOH, are very physical --a Lense-Thirring-like effect.

I'm reminded of techniques that are used to deal with condensed-matter systems like, eg, the mean-field approximation. Usually, when I read about numerical relativity, it's always colliding BHs and the like. Extrapolation to clusters of galaxies, and the metric "looking Weyl" near any particular galaxy?

I'm trying to dash-off some thoughts, but I still haven't made up my mind, one way or the other.

[Mordred]

Interesting article, even if it allows for compensating for the Non Kepler curve in galaxy rotation it doesn't address other indicators of DM such as early large scale structure formation or gravitational lenses without the presence of baryonic matter.

Think I may have forgotten a rule on the inverse of a tensor. In so far as the signature doesn't match up from  II.1. Likely just me forgetting the inverse tensor rules will have to look into that.

 

Edited December 19, 2022 by Mordred

[Markus Hanke]

14 hours ago, joigus said:

Extrapolation to clusters of galaxies, and the metric "looking Weyl" near any particular galaxy?

I know very little about numerical GR, but from what I do know, this type of simulation is prohibitive expense in computational terms. It a shame that a model like GR, which is conceptually so simple, is so hard to actually solve!

6 hours ago, Mordred said:

it doesn't address other indicators of DM such as early large scale structure formation or gravitational lenses without the presence of baryonic matter.

Yes, very true. A lot of investigative work still needs to be done here.