Deur Gravitational self-interaction Doesn't Explain Galaxy Rotation Curves

[kodama]

TL;DR Summary

Gravitational self-interaction cannot replace dark matter

Deur Gravitational self-interaction Doesn't Explain Galaxy Rotation Curves

this paper

A. N. Lasenby, M. P. Hobson, W. E. V. Barker, "Gravitomagnetism and galaxy rotation curves: a cautionary tale" arXiv:2303.06115 (March 10, 2023).

We investigate recent claims that gravitomagnetic effects in linearised general relativity can explain flat and rising rotation curves, such as those observed in galaxies, without the need for dark matter.

If one models a galaxy as an axisymmetric, stationary, rotating, non-relativistic and pressureless 'dust' of stars in the gravitoelectromagnetic (GEM) formalism, we show that GEM effects on the circular velocity v of a star are O(10^−6) smaller than the standard Newtonian (gravitoelectric) effects.

Moreover, we find that gravitomagnetic effects are O(10^−6) too small to provide the vertical support necessary to maintain the dynamical equilibrium assumed.

These issues are obscured if one constructs a single equation for v, as considered previously. We nevertheless solve this equation for a galaxy having a Miyamoto--Nagai density profile. We show that for the values of the mass, M, and semi-major and semi-minor axes, a and b, typical for a dwarf galaxy, the rotation curve depends only very weakly on M. Moreover, for aspect ratios a/b>2, the rotation curves are concave over their entire range, which does not match observations in any galaxy.

Most importantly, we show that for the poloidal gravitomagnetic flux ψ to provide the necessary vertical support, it must become singular at the origin. This originates from the unwitting, but forbidden, inclusion of free-space solutions of the Poisson-like equation that determines ψ, hence ruling out the methodology as a means of explaining flat galaxy rotation curves.

We further show that recent deliberate attempts to leverage such free-space solutions against the rotation curve problem yield no deterministic modification outside the thin disk approximation, and that, in any case, the homogeneous contributions to ψ are ruled out by the boundary value problem posed by any physical axisymmetric galaxy.

Directly comments on Deur's theory of self-interaction

the question is why if Deur is correct why has his results been missed by numerical general relativity and other approximations by highly qualified GR experts

these GR experts found NO support for Deur's claims, including use of super computers.


authors state

​

Can dark matter in galaxies be explained by relativistic corrections?​

Mikołaj Korzyński1 Published 6 June 2007 • 2007 IOP Publishing Ltd
Journal of Physics A: Mathematical and Theoretical, Volume 40, Number 25 Citation Mikołaj Korzyński 2007 J. Phys. A: Math. Theor. 40 7087 DOI 10.1088/1751-8113/40/25/S66

Abstract​

Cooperstock and Tieu proposed a model of galaxy, based on ordinary GR, in which no exotic dark matter is needed to explain the flat rotation curves in galaxies. I will present the arguments against this model. In particular, I will show that in their model the gravitational field is generated not only by the ordinary matter distribution, but by a infinitely thin, massive and rotating disc as well. This is a serious and incurable flaw and makes the Cooperstock–Tieu metric unphysical as a galaxy model.So Deur's claims Gravitational self-interaction can replace dark matter with just ordinary GR + ideas from QCD that are non-viable, the authors go on to show that GEM also does not work as too weak by a factor of 10-6neither Gravitational self-interaction per Deur nor GEM and standard GR can replace dark matter (or MOND)

time to move on. perhaps refracted gravity is a better approach

Dark Coincidences: Small-Scale Solutions with Refracted Gravity and MOND​

Valentina Cesare

General relativity and its Newtonian weak field limit are not sufficient to explain the observed phenomenology in the Universe, from the formation of large-scale structures to the dynamics of galaxies, with the only presence of baryonic matter. The most investigated cosmological model, the ΛCDM, accounts for the majority of observations by introducing two dark components, dark energy and dark matter, which represent ∼95% of the mass-energy budget of the Universe. Nevertheless, the ΛCDM model faces important challenges on the scale of galaxies. For example, some very tight relations between the properties of dark and baryonic matters in disk galaxies, such as the baryonic Tully-Fisher relation (BTFR), the mass discrepancy-acceleration relation (MDAR), and the radial acceleration relation (RAR), which see the emergence of the acceleration scale a0≃1.2×10−10 m s−2, cannot be intuitively explained by the CDM paradigm, where cosmic structures form through a stochastic merging process. An even more outstanding coincidence is due to the fact that the acceleration scale a0, emerging from galaxy dynamics, also seems to be related to the cosmological constant Λ. Another challenge is provided by dwarf galaxies, which are darker than what is expected in their innermost regions. These pieces of evidence can be more naturally explained, or sometimes even predicted, by modified theories of gravity, that do not introduce any dark fluid. I illustrate possible solutions to these problems with the modified theory of gravity MOND, which departs from Newtonian gravity for accelerations smaller than a0, and with Refracted Gravity, a novel classical theory of gravity introduced in 2016, where the modification of the law of gravity is instead regulated by a density scale.

Comments:	34 pages, 7 figures, published on 16th January 2023 in Universe 2023, 9(1), 56, in the Special Issue "Modified Gravity and Dark Matter at the Scale of Galaxies"; accepted for publication on 12th January 2023
Subjects:	Astrophysics of Galaxies (astro-ph.GA)
Cite as:	arXiv:2301.07115 [astro-ph.GA]

 

[ohwilleke]

Citation #27 addresses Cooperstock–Tieu and not Deur. It isn't breaking news.

Citation #26 isn't available in preprint so the jury is out on it. Nothing in the rest of the paper discusses Deur - the rest of the paper discusses GR GEM effects (which I agree don't get it done).

Cooperstock-Tieu and Deur are closer in method to each other than GEM approaches, but they are far from identical and are not even all that similar.

Nothing published even in preprint form let alone a peer reviewed journal article has actually shown Deur is wrong, although a preprint may be out soon to look at and I welcome that. Presumably it would assert that the GR Lagrangian was done in the wrong way or that the effects with a parameter calculated from first principles rather than empirically determined is too weak.

If his empirically fitted new parameter that he assumes can be derived from Newton's constant without actually doing so is too large and that is the only problem, it would imply the gravitons in weak fields couple to each other more strongly than to other particles with equivalent mass-energy, which I've never seen proposed by anyone before explicitly, but which wouldn't be an insurmountable feature to incorporate rigorously into a modified gravity theory.

Deur discusses in multiple papers the choices he made in expressing the GR Lagrangian the way that he does and why it captures aspects of GR assumed away, for example, in linearized theories and the Post-Newtonian approximation and in spherically symmetric approximations, but can be captured in a lattice calculation comparable to lattice QCD that are not spherically symmetric, and he also discusses why the effects are present in large mass systems (like galaxies) but implicitly are not in small mass systems (like wide binary star systems).

Often early critics find that a theory is invalid (which it may or may not be) because they misunderstand the new theory. Since Deur is relying on mathematical approaches widely used in QCD (his day job) and little used in astrophysics, it wouldn't be surprising if an astrophysicists criticism of the math got some of the QCD based methods that Deur relies upon wrong.

But, ultimately, suppose that it turns out the Deur is a subtle modification of GR rather than the genuine article, but his equations and methods (which are not actually true GR) still explain all dark matter and dark energy phenomena and do it without the mass-energy conservation issues of LambdaCDM and GR with a cosmological constant.

Who cares?

It could be that he's actually identified a purely quantum gravity effect and made a mistake in his classical analysis papers, or it could be that his theory is just an outright modification that abridges a GR axiom in some subtle way. I've always been unsure over whether his approach really is truly GR but not as conventionally operationalized, as opposed to being a GR modification.

But, if it works in the complete domain of applicability of all evidence about gravity, which it appears to so far, makes novel predictions so far confirmed by new astronomy data, does it without dark matter or dark energy, and isn't mathematically pathological (there has never been a hint that it is), and can do it with a tensor theory rather than the tensor scalar of LambdaCDM and GR with a cosmological constant (which also makes generalization to quantum gravity easier), and possibly has one less free parameter (which Deur has claimed but not proven by deriving an additional parameter that is used on the assumption that it could be derived), then that's still great, Nobel prize class stuff, even if he inaccurately assumed that it was equivalent to GR and even if it actually has an additional free parameter.

It could be that quantum gravity has been so hard to devise because standard GR isn't quite the right theory to quantize.

Still, any realistic GR modification that explains dark matter phenomena and dark energy phenomena is still going to look a whole lot like GR, because of all of the places where GR works and is proven to work (especially in strong gravitational fields). Likewise, even toy-model MOND implicitly assumes GR in gravitational fields stronger than its a₀ physical constant and in terms of gravitational fields affecting photons and not just baryonic matter.

The material below until the arXiv abstract and citation, is a self-quotation from a blog post I made elsewhere, which I have given myself permission to make here:

My first impressions of refracted gravity are that it has issues, although I welcome all new serious efforts to find gravitational solutions to dark matter phenomena and possibly also dark energy phenomena (which LambdaCDM does explain in the GR gravitational equation not with a new substance):

(1) the shape of the matter distribution doesn't seem to be important and it doesn't seem to have a source of isotropy violation, which are both problematic;

(2) like GR with a cosmological constant and many other gravity modifications, it is a scalar-tensor theory (Deur's GR-SI is a pure tensor theory as is GR without a cosmological constant) - an important downside of a scalar-tensor v. a tensor theory is that it makes generalization to a quantum gravity theory harder;

(3) unlike Deur's approach, it doesn't appear to resolve the conservation of energy issues associated with the lion's share of gravity theories with a dark energy component, but this calls for closer inspection and isn't entirely clear from the abstract;

(4) further inspection of the permittivity-mass density relationship proposed is necessary for me to really understand it;

(5) it appears to have one more experimentally fixed parameter than GR with a cosmological constant, similar to relativistic MOND with a cosmological constant;

(6) there are lots of key areas (early galaxy formation, CMB peaks, cluster dynamics, Bullet cluster, cluster collision rate expectations, tendency of satellite galaxies to line up in planes, Hubble tension) where it isn't clear what is predicted although other papers may develop the theory more fully;

(7) all development of gravity based solutions to dark matter and dark energy phenomena are a welcome change, even though I'm skeptical that this will get the job done and the core assumption about permittivity isn't very well motivated (at least in the abstract).

(8) Refracted gravity (with apologies to Sabine Hoffenfelder) is a fairly ugly theory (worse than toy model MOND). Deur's GR-SI (for GR self interaction) methods are very beautiful and elegant. That counts for something.

The abstract and paper on refracted gravity that I've read is as follows, although I am aware that there are several more out there.

We propose a covariant formulation of refracted gravity (RG), a classical theory of gravity based on the introduction of the gravitational permittivity -- a monotonic function of the local mass density -- in the standard Poisson equation.

The gravitational permittivity mimics the dark matter phenomenology. Our covariant formulation of RG (CRG) belongs to the class of scalar-tensor theories, where the scalar field φ has a self-interaction potential (φ)=−Ξφ, with Ξ a normalization constant. We show that the scalar field is twice the gravitational permittivity in the weak-field limit.

Far from a spherical source of density ρs(r), the transition between the Newtonian and the RG regime appears below the acceleration scale aΞ=(2Ξ−8πGρ/φ)1/2, with ρ=ρs+ρbg and ρbg an isotropic and homogeneous background.

In the limit 2Ξ≫8πGρ/φ, we obtain aΞ∼10−10~m~s−2. This acceleration is comparable to the acceleration a0 originally introduced in Modified Newtonian Dynamics (MOND).

From CRG, we also derive the modified Friedmann equations for an expanding, homogeneous, and isotropic universe. We find that the same scalar field that mimics dark matter also drives the accelerated expansion of the Universe. Since Ξ plays a role roughly similar to the cosmological constant Λ in the standard model and has a comparable value, CRG suggests a natural explanation of the known relation a0∼Λ1/2.

CRG thus appears to describe both the dynamics of cosmic structure and the expanding Universe with a single scalar field, and falls within the family of models that unify the two dark sectors, highlighting a possible deep connection between phenomena currently attributed to dark matter and dark energy separately.

Andrea Pierfrancesco Sanna, Titos Matsakos, Antonaldo Diaferio, "Covariant Formulation of refracted gravity" arXiv:2109.11217 (September 25, 2021) (submitted to Physical Review D).

 

[kodama]

Again,

Deur's claims are highly implausible on the fact that despite over the long history of GR, including use of super computers, they have found nothing to support Deur's conclusions.

numerical relativity is analyzing GR via super computers by highly qualified experts in multiple specialties over decades, which did not find any evidence of Deur's self-interactions strong enough to explain or replace dark matter

Can you explain why GR experts have missed such important effects after decades of study as identified by Deur, and why numerical relativity has over decades completely missed such important effects Deur has claimed? (or others such as nonlinear effects of GR or GEM?)

Galactic Dynamics via General Relativity: A Compilation and New Developments​

F. I. Cooperstock, S. Tieu

In spite of the weak gravitational field and the non-relativistic source velocities, the mathematical system is still seen to be non-linear.
arXiv:astro-ph/0610370

and Deur both claim non-linear effects in GR not present in Newtonian gravity can replace dark matter.

This has been shown to be incorrect.

 

[ohwilleke]

Again,

View attachment 323747

Deur's claims are highly implausible on the fact that despite over the long history of GR, including use of super computers, they have found nothing to support Deur's conclusions.

numerical relativity is analyzing GR via super computers by highly qualified experts in multiple specialties over decades, which did not find any evidence of Deur's self-interactions strong enough to explain or replace dark matter

Can you explain why GR experts have missed such important effects after decades of study as identified by Deur, and why numerical relativity has over decades completely missed such important effects Deur has claimed? (or others such as nonlinear effects of GR or GEM?)

Galactic Dynamics via General Relativity: A Compilation and New Developments​

F. I. Cooperstock, S. Tieu

In spite of the weak gravitational field and the non-relativistic source velocities, the mathematical system is still seen to be non-linear.
arXiv:astro-ph/0610370

and Deur both claim non-linear effects in GR not present in Newtonian gravity can replace dark matter.

This has been shown to be incorrect.

Deur has expressly addressed the Post-Newtonian formalism which assumes at the outset that the self-interaction effect he is utilizing is negligible without rigorously confirming that this is so (and in many contexts where it is used, like close binary star systems, that is a reasonable assumption and it performs closer to the reality and full GR than you would expect naively).

The issue in numerical general relativity boils down to what simplifying assumptions are made in the models and what kind of situations they are used in. Lattice methods are also numerical GR approaches and Deur has replicated the GR-SI effects he has claimed using lattice methods.

I personally am not familiar enough with numerical GR to have any insight into the question at this time. If your numerical methods are using the simplifying assumptions of linearized GR, for example, as some do, or working with the assumption of spherically symmetric mass distributions (which are much less processor intensive and a good substitute in many cases) you're going to miss self-interaction effects in GR. Likewise, since self-interactions are a weak field only second order effect, if you are using numerical GR to study only strong field GR effects (and that is precisely where conventional wisdom would tell you to look for non-linear GR effects justifying the effort), you are going to miss it.

It is a fact that the vast majority of astronomy, cosmology, and astrophysics modeling done at scales of less than the entire universe and away from ultracompact objects like black holes and neutron stars or close binary stars, is done with plain old Newtonian gravity on the assumption that the GR deviations from Newtonian gravity are absent in weak gravitational fields, assuming away any possible GR effects in that regime without acting testing to see what the GR effects are there. If there is a flaw in that assumption, a lot of very competent astrophysicists and astronomers and cosmologists following standard practices in their field would never catch it.

The "nobody saw it before" despite the fact that they have PhDs in GR doesn't carry a whole lot of weight, because whole disciplines can be subject to group think, or make common assumptions, that someone from outside the same discipline wouldn't take for granted. Usually the common assumptions of experts are good ones, but sometimes those common assumptions have blind spots. I've discussed in the past at the Physics Forums (and won't reiterate now) how some statements made in at least on leading GR textbook overstate the case that some effects in GR which are often negligible can never have an effect that are at best misleading. The bottom line is that arguments from authority or collective conventional wisdom aren't very strong ones in my book. If everyone trained in the field assumes a direction of inquiry is futile, they stop looking there, even if it isn't actually futile.

Mathematically, as a non-abelian theory, GR is a lot closer to QCD than it is to Newtonian gravity or electromagnetism (which are Abelian). Indeed, in most circumstances, you can calculate something in QCD, square it, and get a correct result in GR mimicking quantum gravity.

So, looking at QCD phenomena for analogs in GR phenomena is a very sound approach to generating hypotheses to test that depart from questions that are standard fare for GR specialist scientists to investigate because the questions that seem most natural to ask from the perspective of working with GR formulated with Einstein's equations and the questions that seem most natural to ask from the perspective of GR considered in light of QCD squared are not the same. But since we can easily run QCD experiments by the millions day after day and generate data about them that needs to be explained, QCD scientists have had to get out of their comfort zone to try to make sense to mathematically inconvenient to deal with configurations in a non-abelian gauge theory in a way that astrophysicists feel less pressure to do. So, I wouldn't discount the comparative advantage in the area of intuition about what is likely to work in a non-abelian gauge theory that Deur might benefit from.

 

[kodama]

I personally am not familiar enough with numerical GR to have any insight into the question at this time. I

Numerical Relativity: Solving Einstein's Equations on the Computer Illustrated Edition​

Aimed at students and researchers entering the field, this pedagogical introduction to numerical relativity will also interest scientists seeking a broad survey of its challenges and achievements. Assuming only a basic knowledge of classical general relativity, the book develops the mathematical formalism from first principles, and then highlights some of the pioneering simulations involving black holes and neutron stars, gravitational collapse and gravitational waves. The book contains 300 exercises to help readers master new material as it is presented. Numerous illustrations, many in color, assist in visualizing new geometric concepts and highlighting the results of computer simulations. Summary boxes encapsulate some of the most important results for quick reference. Applications covered include calculations of coalescing binary black holes and binary neutron stars, rotating stars, colliding star clusters, gravitational and magnetorotational collapse, critical phenomena, the generation of gravitational waves, and other topics of current physical and astrophysical significance.

https://www.amazon.com/dp/052151407X/?tag=pfamazon01-20

Introduction to Numerical Relativity​

Carlos Palenzuela

Numerical Relativity is a multidisciplinary field including relativity, magneto-hydrodynamics, astrophysics and computational methods, among others, with the aim of solving numerically highly-dynamical, strong-gravity scenarios where no other approximations are available. Here we describe some of the foundations of the field, starting from the covariant Einstein equations and how to write them as a well-posed system of evolution equations, discussing the different formalisms, coordinate conditions and numerical methods commonly employed nowadays for the modeling of gravitational wave sources.

Comments:	Accepted by Frontiers Astronomy and Space Sciences, invited review for the Research Topic "Gravitational Waves: A New Window to the Universe"
Subjects:	General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO)
Cite as:	arXiv:2008.12931 [gr-qc]

Binary Merger Observations and Numerical Relativity​

The goal of this Max Planck Independent Research Group is to decipher gravitational-wave observations of merging black holes and neutron stars with the help of our most sophisticated theoretical tool: large-scale numerical simulations of these violent collisions.

Knowing what to look for​

When the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) detected gravitational waves for the first time on September 14, 2015, we were able to understand what we had seen because theoretical predictions told us what to look for. These theoretical prediction come from solutions of Einstein’s equations that tell us how colliding black holes warp the spacetime around them and thus emit gravitational waves that can be observed with ultra-sensitive instruments such as LIGO. However, the equations are so complicated that the most violent (and possibly most interesting) part of the collision can only be understood by large-scale simulations on supercomputers.

https://www.aei.mpg.de/BinaryObservationsNR

What would be a reason Numerical Relativity has been very successful in correctly number crunching via computer and correctly using GR + Computer as input, a very wide variety of observations of the real world over its long history as mention above, but completely failed to support any deviations from Newtonian physics, whether GEM, self-interactions, or nonlinear effects to replace dark matter solely with GR?

 

[ohwilleke]

What would be a reason Numerical Relativity has been very successful in correctly number crunching via computer and correctly using GR + Computer as input, a very wide variety of observations of the real world over its long history as mention above, but completely failed to support any deviations from Newtonian physics, whether GEM, self-interactions, or nonlinear effects to replace dark matter solely with GR?

Because, as the material you quote states: "Numerical Relativity is a multidisciplinary field . . . with the aim of solving numerically highly-dynamical, strong-gravity scenarios where no other approximations are available."

This tool is used in strong-gravity scenarios, but the effect claimed, because it is a second order effect, is only discernible in weak-gravity scenarios in which the strong-first order gravitational effects don't overwhelm it. But, in those circumstances, approximations other than numerical relativity are used. Those approximations, however, expressly ignore gravitational field self-interactions on the mistaken assumption that they don't matter in that context.

What do we mean when we say that dark matter phenomena (as MOND nicely illustrates) only becomes noticeable when the local gravitational fields are very weak? (And, for what it is worth, dark energy effects only show up relative to other gravitational effects when gravitational fields are much weaker than that).

The material below is a self-quotation which I have granted myself permission to reproduce.

The gravitational field of the Sun alone falls to the strength where modified gravity/dark matter effects become noticeable at a distance of about 1,052 billion km (about 7000 astronomical units (AU). An AU, which is 149.6 million km, is the average distance of the Earth from the Sun.

This is about 1/9th of the light year from the Sun, which is about 175 times the average distance of Pluto from the Sun. Pluto's average distance from the Sun is about 6 billion km).

This is about 58 times more distant from the Sun that the heliosphere, which is a functional definition of where the solar system ends and deep interstellar space begins, that is about 18 billion km (120 astronomical units) from the Sun.

As of February 2018, Voyager 1, the most distant man made object from Earth, was about 21 billion km from Earth, and Voyager 2, the second most distant man made object from Earth is about 17 billion km from Earth. Both were launched in 1977. These probes (which will run about of power around the year 2025), will reach this distance from the Sun about 2000 years from now in around 4000 CE.

 

[kodama]

The book contains 300 exercises to help readers master new material as it is presented. Numerous illustrations, many in color, assist in visualizing new geometric concepts and highlighting the results of computer simulations. Summary boxes encapsulate some of the most important results for quick reference. Applications covered include calculations of coalescing binary black holes and binary neutron stars, rotating stars, colliding star clusters, gravitational and magnetorotational collapse, critical phenomena, the generation of gravitational waves, and other topics of current physical and astrophysical significance.

https://www.amazon.com/dp/052151407X/?tag=pfamazon01-20

critical phenomena, the generation of gravitational waves, and other topics of current physical and astrophysical significance.

that includes weak-gravity scenarios in galaxies

 

[timmdeeg]

This discussion is about a claim in Citation [26] W. E. V. Barker, M. P. Hobson, and A. N. Lasenby, (2020), manuscript in preparation

Can you explain why GR experts have missed such important effects after decades of study as identified by Deur, and why numerical relativity has over decades completely missed such important effects Deur has claimed? (or others such as nonlinear effects of GR or GEM?)

Supposed experts haven't "missed such important effects" why then is this manuscript in preparation since 2020? It's just an idea, would it make sense to ask the authors for clarification? As a non-expert myself I can't do it. Perhaps someone else around here?

 

[kodama]

This discussion is about a claim in Citation [26] W. E. V. Barker, M. P. Hobson, and A. N. Lasenby, (2020), manuscript in preparationSupposed experts haven't "missed such important effects" why then is this manuscript in preparation since 2020? It's just an idea, would it make sense to ask the authors for clarification? As a non-expert myself I can't do it. Perhaps someone else around here?

read it again

 

[renormalize]

This discussion is about a claim in Citation [26] W. E. V. Barker, M. P. Hobson, and A. N. Lasenby, (2020), manuscript in preparation

Supposed experts haven't "missed such important effects" why then is this manuscript in preparation since 2020? It's just an idea, would it make sense to ask the authors for clarification? As a non-expert myself I can't do it. Perhaps someone else around here?

This preprint is now online at https://arxiv.org/abs/2303.11094.

Does gravitational confinement sustain flat galactic rotation curves without dark matter?​

W. E. V. Barker, M. P. Hobson, A. N. Lasenby
I quote an excerpt from the abstract:
"The short answer is probably no. ...
In summary, whilst it may be interesting to consider the possibility of confinement-type effects in gravity,
such an investigation should be done thoroughly, without relying on heuristics: that task is neither attempted in
this work nor accomplished by the key works referenced. Pending such analysis, we may at least conclude here
that confinement-type effects cannot play any significant part in explaining flat or rising galactic rotation curves
without paradigmatic dark matter halos." (Emphasis in original.)

 

[timmdeeg]

This preprint is now online at https://arxiv.org/abs/2303.11094.

Thanks, very helpful! I will have to study that.

 

[Madeleine Birchfield]

Coincidentally, prompted by the latest Deur article on the Hubble tension, a few weeks ago I emailed Anthony Lasenby asking him about whether general relativity and by extension his gauge theory gravity has a confinement effect similar to that found in QCD. He hasn't responded to the email yet but it seems like I've found the answer I'm looking for in Lasenby's latest preprint.

 

[timmdeeg]

Does gravitational confinement sustain flat galactic rotation curves without dark matter?

This article addresses Deur's claim very seriously that taking field self-interaction into account there is no necessity to assume dark energy and dark matter.

The authors are concerned by asking "But do gravitons carry the GEM mass-energy charge, as gluons carry colour? They do, but only at the expense of general covariance. In developing a GEFC picture of ‘heavy flux’, it seems hard to avoid an appeal to gravitational energy, for which there is no preferred, generally-applicable localisation scheme [24, 27]." but at the same time they are cautious by answering the title question: The short answer is probably no. and by stressing "However, some caveats are in order.", see below.

Having performed numerical calculations one of the conclusion is:

Now this looks like a big discrepancy, and a possible source of why GEFC/[7] says that the rays become parallel near the galaxy disc edge, whereas as we have seen, this would require densities about 1000 times larger than typical galactic densities. However, some caveats are in order.

One can be eager if and how Deur will comment on this.

 

[Madeleine Birchfield]

Does gravitational confinement sustain flat galactic rotation curves without dark matter?

This article addresses Deur's claim very seriously that taking field self-interaction into account there is no necessity to assume dark energy and dark matter.

The authors are concerned by asking "But do gravitons carry the GEM mass-energy charge, as gluons carry colour? They do, but only at the expense of general covariance. In developing a GEFC picture of ‘heavy flux’, it seems hard to avoid an appeal to gravitational energy, for which there is no preferred, generally-applicable localisation scheme [24, 27]." but at the same time they are cautious by answering the title question: The short answer is probably no. and by stressing "However, some caveats are in order.", see below.

Having performed numerical calculations one of the conclusion is:

Now this looks like a big discrepancy, and a possible source of why GEFC/[7] says that the rays become parallel near the galaxy disc edge, whereas as we have seen, this would require densities about 1000 times larger than typical galactic densities. However, some caveats are in order.

One can be eager if and how Deur will comment on this.

The Acknowledgements section has this paragraph:

We are grateful to Alexandre Deur for rapid, thorough replies and vital clarifications at several junctures. We are also grateful to Craig Mackay and Amel Duraković for several useful discussions, and to John Donoghue and Subodh Patil for helpful correspondence.

 

[timmdeeg]

The Acknowledgements section has this paragraph:

The discrepancy amounts to 3 orders of magnitude which hopefully will be commented by Deur sometime.

 

[Vanadium 50]

This thread seems to be a hodgepodge of people cheerleading for their favorite theories of modified gravity. Lets go back to the thread titie: Deur Gravitational self-interaction Doesn't Explain Galaxy Rotation Curves

It can't, and it should be obvious.

Grabitational self-interaction will of of order the gravitational potential energy (I am ignoring factors of 2 or pi or whatever, or $GM^2/r$ this has to exceed $Nc^2r$ by around a factor of 5:
$$\frac{GM^2}{r} > Mc^2$$
$$\frac{GM}{rc^2} > 1$$
The left hand side needs to be about a million times bigger. It's not even close.

 

[timmdeeg]

It can't, and it should be obvious.

Grabitational self-interaction will of of order the gravitational potential energy (I am ignoring factors of 2 or pi or whatever, or $GM^2/r$ this has to exceed $Nc^2r$ by around a factor of 5:
$$\frac{GM^2}{r} > Mc^2$$
$$\frac{GM}{rc^2} > 1$$
The left hand side needs to be about a million times bigger. It's not even close.

If this disproves Deur why then this paper with 33 pages?

 

[Vanadium 50]

How shoiuld I know. People write all sorts of things.

 

[timmdeeg]

Perhaps because they think it makes sense to investigate the non-linearities of the lagrangian?
Which seems unavoidable if one examines field self-interaction.

 

[Adrian59]

It has been a while since I last contributed to this forum. However, it is good to see that Ohwilleke is still providing high quality interventions.

The "nobody saw it before" despite the fact that they have PhDs in GR doesn't carry a whole lot of weight, because whole disciplines can be subject to group think, or make common assumptions, that someone from outside the same discipline wouldn't take for granted. Usually the common assumptions of experts are good ones, but sometimes those common assumptions have blind spots. I've discussed in the past at the Physics Forums (and won't reiterate now) how some statements made in at least on leading GR textbook overstate the case that some effects in GR which are often negligible can never have an effect that are at best misleading. The bottom line is that arguments from authority or collective conventional wisdom aren't very strong ones in my book. If everyone trained in the field assumes a direction of inquiry is futile, they stop looking there, even if it isn't actually futile.

I have often thought that the phenomenon of 'group think' is at the heart of many issues in science, but I doubted many scientists were even aware of this term, how wrong was I!

I have commented before about Cooperstock, and I have had a copy of Deur's paper for some time.

TL;DR Summary: Gravitational self-interaction cannot replace dark matter

Deur Gravitational self-interaction Doesn't Explain Galaxy Rotation Curves

Kodama makes this claim about Deur's work, but as Ohwilleke correctly points out:

Nothing in the rest of the paper discusses Deur - the rest of the paper discusses GR GEM effects (which I agree don't get it done).

However, claims that there are no alternatives to ΛCDM or for that matter MOG are somewhat derailed by the fact that there are several approaches (Cooperstock -2005, Deur - 2017 and Jalocha - 2008) that get the right answer without speculative physics. In fact it appears the only way to get the wrong answer is use the approach that initially led to the idea of dark matter.

So that I find all these attempts to disprove these alternative approaches questionable, I think they doth protest too much.

 

[strangerep]

So that I find all these attempts to disprove these alternative approaches questionable, I think they doth protest too much.

Have you actually tried to reproduce the detailed math of Deur's approximation scheme? I have, but I couldn't get it to make sense. He seems to introduce an arbitrary $M$ parameter at the start, rather than having it emerge as an integration constant as happens when obtaining the Schwarzschild solution.

Nowhere (afaik) does Deur give a detailed account of his math. If you know of such, please tell me.

(So yes, I do protest against his lack of mathematical detail.)

 

[Adrian59]

We may be at slight cross purposes by reading different papers - admittedly I should have given to whole reference for the paper I was eluding to. The reference is:

Deur, A. (2019). ‘An explanation for dark matter and dark energy consistent with the standard model of particle physics and General Relativity’. Eur. Phys. J. C; 79: 883.

I certainly can follow his argument in this paper. If you find this lacking in rigour, you may have to contact Deur himself. He is a particle physicist so I am sure he could furnish any level of mathematical detail.

However, are you happy with the Cooperstock approach, ref:

Carrick J. and Cooperstock, F. (2012). ‘General Relativistic Dynamics Applied to the Rotation Curves of Galaxies’. Astrophysics and Space Science; 337, Iss. 1: pp 321–329

or even my other reference:

Jalocha, J., Bratek, L. and Kutschera, M. (2008). ‘Is Dark Matter Present in NGC 4736? An Iterative Spectral Method for Finding Mass Distribution in Spiral Galaxies.’ Astrophysical Journal, 679, pp 373–378

The point I am trying to make is there are multiple approaches that give the right answer without dark matter:
can they all be in error!

 

[Vanadium 50]

think they doth protest too much.

You could make the same argument about perpetual motion. Every time someone claims it to work, someone complains and the thread is shut down.

 

[Adrian59]

TL;DR Summary: Gravitational self-interaction cannot replace dark matter

Deur Gravitational self-interaction Doesn't Explain Galaxy Rotation Curves

As I have mentioned above it has been a while since I have contributed to this forum, so I did not realize there was a similar thread from 12/7/22 entitled: LQG Legend Writes Paper Claiming GR Explains Dark Matter Phenomena. In this thread there was a discussion about Deur's papers.

Deur is relying on mathematical approaches widely used in QCD (his day job) and little used in astrophysics, it wouldn't be surprising if an astrophysicists criticism of the math got some of the QCD based methods that Deur relies upon wrong.

The interesting reference from this thread was:

M. Crosta, M. Giammaria, M.G. Lattanzi, E. Poggio, "On testing CDM and geometry-driven Milky Way rotation curve models with Gaia DR2." 496 Mon. Not. R. Astron. Soc. 2107–2122 (2020) (open access).

The authors state: 'from the Gaia second data release catalogue, we extracted parallaxes, proper motions, and line-of-sight velocities of unprecedented accuracy for a carefully selected sample of disc stars.'

I have been a supporter of alternative theories of galaxy rotation curves for several years, and even before this paper was published I considered that the Gaia data could resolve this issue.

That a large data set does indeed support these alternatives like Cooperstock and Deur is notable.

 

[mitchell porter]

From a critique of Cooperstock and Tieu:

It has been shown that the Cooperstock-Tieu galaxy model is inconsistent as a general relativistic model and that a proper model fails to account for the flatness of the rotation curves without the dark-matter hypothesis. This failure is due to the weakness of the metric coupling to the angular momentum of the galaxy.

However, the flat rotation curves seem to imply a large inertial induction effect, where the rotating inner matter boosts the rotation of the outer matter, leveling off the rotation curve, which is what the Cooperstock-Tieu model attempts to describe within general relativity. Since their solution predicts a matter density well within visible limits it is quite possible that their solution represents an alternative, more Machian, gravitational theory where inertial induction effects are much larger than in General Relativity.

In our discussions of Deur, we have also speculated that his results might be obtained from a modification of GR.

 

[kodama]

From a critique of Cooperstock and Tieu:

In our discussions of Deur, we have also speculated that his results might be obtained from a modification of GR.

with a scalar ?

 

[strangerep]

From a critique of Cooperstock and Tieu:
[...]

The arxiv version of this critique by Cross is here.

I have just now become aware of Cooperstock's book:
"General Relativistic Dynamics", 2009, ISBN-13 978-981-4271-16-5.

In ch9 he presents his theory of the motion of stars in galaxies in a more pedestrian manner. In ch10, he presents his version for clusters. I haven't yet had time to study it properly, but will do so in the near future.

In appendix A of that book, Cooperstock responds to various criticisms of his method, including those of Cross.

Unfortunately, I gather that Prof Cooperstock died in 2018. (?)

The point I am trying to make is there are multiple approaches that give the right answer without dark matter: can they all be in error!

This group-think type of attitude is not good for scientific research, imho.

 

[ohwilleke]

with a scalar ?

Deur does a lot of his math using a scalar field approximation of a tensor gravitational field because the mathematics is so much easier.

One of the key points of contention is whether that approximation is a reasonable one for the purposes for which it is used.

He takes the position that it is equivalent to a static approximation of GR that ignores dynamic components of the stress-energy tensor like electromagnetic flux, linear momentum, and angular momentum, which are typically small enough in the context of the galaxy and galaxy cluster and large scale structure determinations being made that they can be safely ignored.

In the same vein, the Newtonian gravity approximation of GR typically used in galaxy and larger scale astronomy and cosmology applications (in circumstances remote from the Big Bang where dark energy is also irrelevant) is also a scalar field approximation of GR. But, unlike Deur's scalar approximation, the Lagrangian of Newtonian gravity has no self-interaction term for the gravitational field.

This is different from scalar-tensor theories which have two fields - typically a tensor field which is the same as or similar to the GR tensor, and a separate scalar field.

 

[Structure seeker]

This group-think type of attitude is not good for scientific research,

The attitude not, indeed. I'm of the opinion that Deur's approach is very interesting for the sole reason that it completely preserves that all forces alike are each mediated by the quanta of one gauge field. That means an easily understandable and generic analytic framework for all forces and elementary particles at once, like the quantized states of atoms completely describe all possible non-nuclear chemical reactions and all stable chemical elements. And at the same time, if his calculations are right, it features MOND dynamics with possibly an upgrade (clusters) to the set of data it explains.

 

[kodama]

Deur does a lot of his math using a scalar field approximation of a tensor gravitational field because the mathematics is so much easier.

One of the key points of contention is whether that approximation is a reasonable one for the purposes for which it is used.

He takes the position that it is equivalent to a static approximation of GR that ignores dynamic components of the stress-energy tensor like electromagnetic flux, linear momentum, and angular momentum, which are typically small enough in the context of the galaxy and galaxy cluster and large scale structure determinations being made that they can be safely ignored.

In the same vein, the Newtonian gravity approximation of GR typically used in galaxy and larger scale astronomy and cosmology applications (in circumstances remote from the Big Bang where dark energy is also irrelevant) is also a scalar field approximation of GR. But, unlike Deur's scalar approximation, the Lagrangian of Newtonian gravity has no self-interaction term for the gravitational field.

This is different from scalar-tensor theories which have two fields - typically a tensor field which is the same as or similar to the GR tensor, and a separate scalar field.

It seems clear Deur ideas are wrong #16 and arxiv.org/abs/2303.11094.

are you ready to move on?

 

[strangerep]

Gravitational self-interaction will of of order the gravitational potential energy (I am ignoring factors of 2 or pi or whatever, or $GM^2/r$ this has to exceed $Nc^2r$ by around a factor of 5:
$$\frac{GM^2}{r} > Mc^2$$
$$\frac{GM}{rc^2} > 1$$
The left hand side needs to be about a million times bigger. It's not even close.

Could you please elaborate your calculation? It's not obvious (to me at least) where/how you're getting these expressions and inequalities.

 

[ohwilleke]

It seems clear Deur ideas are wrong #16 and arxiv.org/abs/2303.11094.

are you ready to move on?

The linked article doesn't even claim more than "probably" wrong. Also, it is only concluding that the conclusion is not pure GR not that it doesn't match the observational evidence.

I also don't agree with the analysis in #16.

Any method with success with a broad range of applicability is worth attention and the fact that a single article disagrees with a theory doesn't automatically make it invalid. I'll keep an open mind.

So far, every alternative has some issues.

 

[kodama]

The linked article doesn't even claim more than "probably" wrong. Also, it is only concluding that the conclusion is not pure GR not that it doesn't match the observational evidence.

I also don't agree with the analysis in #16.

Any method with success with a broad range of applicability is worth attention and the fact that a single article disagrees with a theory doesn't automatically make it invalid. I'll keep an open mind.

So far, every alternative has some issues.

what is wrong with

#16.

 

[timmdeeg]

According to Deur's cosmological model "Gravitational Non-Linearities" have to be considered.

Significance of Gravitational Nonlinearities on the Dynamics of Disk Galaxies​

#16 doesn't seem to take gravitational non-linearities into account, as already mentioned in #19.​

 

[renormalize]

According to Deur's cosmological model "Gravitational Non-Linearities" have to be considered.

Significance of Gravitational Nonlinearities on the Dynamics of Disk Galaxies​

#16 doesn't seem to take gravitational non-linearities into account, as already mentioned in #19.​

No, but the recent preprint by Barker et.al. https://arxiv.org/abs/2303.11094 cited in post #10 above does purport to take non-linearities into account (and employs actual General Relativity (GR) rather than some scalar approximation to boot!). The authors refer to Deur's proposed confinement mechanism by the acronym GEFC ("gravitoelectric flux collapse"). You should read the full paper yourself, but I quote a relevant portion (with footnote and reference numbers dropped for readability):

"We also address the outstanding phenomenological claims of GEFC, insofar as they pertain to galactic rotation curves in GEFC. We attempt to ‘steel-man’ the GEFC hypothesis by discarding the faulty scalar model, and directly probing nonlinear GR for the claimed phenomena in the presence of reasonable, lenticular baryon profiles. We are disappointed to find no such phenomena at next-to-leading order, though we consider a range of gauges and perturbation schemes. In GEFC the effect of graviton self-interaction on rotation curves is actually modelled by considering the gravitoelectric field lines as the trajectories of massless gravitons, which are then gravitationally lensed by the galactic density distribution in the same way as photon trajectories; that the paths of electric field lines in GR follow precisely those of null geodesics has been discussed previously by Padmanahban. The modified gravitoelectric field at any point, and hence the force on a test particle, is then determined by calculating the flux of the lensed field lines through a small surface at that point. Based on this interesting method, however, our own calculations will indicate lensing effects three orders of magnitude smaller than those claimed in GEFC." (Emphasis in original.)

Off by three orders of magnitude is not quite as dramatic as Vanadium 50's estimate of a factor of a million, but still far too small to mimic dark matter.