mitchell porter said:
A lot of theories and models are being discussed at once in this thread, but (in my opinion) without any clarity or precision.
Fair enough, although one of my purposes in posting the thread was to illustrate the overall state of the GR effects as DM literature which is quite a bit bigger than a lot of people realize, but apart from Deur and Ludwig, not very sustained and developed, in an effort to identify common themes and contradictions, if any, and also to demonstrate that this is not just one or two isolated individuals pursuing a research program that no one else is exploring (as well as to illustrate the concentration of the work on this research agenda in the time period since 2018 more or less).
I agree that the field itself is scattered and the people involved aren't listening to each other very much.
Deur's work is definitely the most developed line of scholarship in the GR effects cause DM phenomena research agenda, and unlike Ludwig, who is purportedly contradicted by Hanson and Ciotti, there isn't really any work out there engaging with his line of analysis for good or ill, despite the growing number of publications that Deur has made in the field.
Maybe this is because nobody inclined to do so has noticed him, but it also might be because those who have noticed intuitively believe that he must be wrong but haven't taken the time to work through the math because Deur is working with math inspired by QCD and familiar to people in that field but unfamiliar to most people in the heartland of GR theory and phenomenology. So, its a lot more work for them to dig into Deur's analysis than it is for them to work over GEM analysis that is far more familiar to them in Ludwig's papers.
mitchell porter said:
Regarding (1) and (2), Ciotti apparently carries out gravitomagnetic calculations in the context of ordinary textbook models, and obtains that the force is minuscule. But cautiously, he does not say that this refutes Ludwig, since he knows that Ludwig has a different starting point. He says only that it would be very surprising if a different kind of approximation led to such a different result from the textbook results, for weak fields.
So this raises the question that Robin Hanson tried to answer (#41, #42): exactly what is different about Ludwig's assumptions, that makes them capable of producing such a different result? Hanson proposed that it is the assumption of zero pressure, an assumption shared by several other papers cited in this thread. I am wondering if it's initial conditions: maybe if you start with large gravitomagnetic forces, they will continue to be generated, but if you don't, they won't become so strong? Surely, careful study of Ludwig's work, and careful comparison with the textbook models in Ciotti, can yield a definite answer to the question above.
Along that line, one of Ludwig's assumptions, also found in the paper in #1 that started this thread, is that the system is "rotationally supported" which goes to your initial conditions speculation. GEM may not provide a good source for revving up the spin from a dead halt, but could provide the field needed to sustain it once it is going.
Intuitively, it makes more sense that the rotationally supported assumption matters, than it does that it assumes zero pressure (even though zero pressure seems like a reasonable enough assumption at face value in a spiral galaxy system).
An earlier post also noted, and I don't think it should be dropped, the importance of assumptions about the geometry of the system (disk-like in Ludwig and the paper in #1 v. spherical in many other treatments) which is almost surely a material assumption.
mitchell porter said:
As for (3), Deur's work, it is being described in this thread (#43) as a model which takes into account the "self-interaction" of gravity in general relativity . . . I also want to understand the relationship between the classical and quantum parts of Deur's research. Hopefully all this can be disentangled with sufficient patience and care.
One important aspect of Deur's earlier quantum oriented work is that it is modeled in a static equilibrium model that explicitly disregards GEM effects that arise from the motion of the particles in the system. Systems not near equilibrium are expressly noted by Deur in those papers to be beyond the scope of applicability of his quantum oriented work.
(Incidentally, there is some MOND scholarship by Stacey McGaugh and others that also observes that MOND does not hold in systems not close to equilibrium and even uses a poor MOND fit as a flag that a system might be out of equilibrium. I won't cite it here as MOND itself is really off topic to this thread. This is notable, however, because, in the geometry of a spiral galaxy Deur's approach with pure GR closely approximates MOND, and Deur's approach could provide a solid GR theoretical basis for the MOND conclusions while expanding its domain of applicability in systems like galaxy clusters where MOND underperforms by resorting to the different geometry of the mass in these systems.)
In Deur's classical work, different simplifications, in addition to or in lieu of the static equilibrium assumption of the quantum work, are used in ways that less transparently differentiate gravitational field self-interaction from GEM effects. Crosta and Balasin in #2, for example, also make a static equilibrium analysis that cannot be due to GEM effects (and like Deur, have not triggered refutation papers.)
(I'm also not entirely convinced that the GEM effects aren't, through some back door in the equations, basically harnessing gravitational field self-interactions, particularly if the initial conditions in the GEM works turns out to be the key different assumption. Deur's quantum work makes it seem unlikely to me that the reverse, that his self-interaction effect is really a backdoor implicating GEM effects, is true).
Deur's recently published classical paper at #1, Alexandre Deur, "Relativistic corrections to the rotation curves of disk galaxies" (April 10, 2020) (lated updated February 8, 2021 in version accepted for publication in Eur. Phys. Jour. C)., uses a mean field approximation to do the GR analysis.
Some different methodological tools were used in the working paper, A. Deur, Corey Sargent, Balša Terzić, "
Significance of Gravitational Nonlinearities on the Dynamics of Disk Galaxies" (August 31, 2019, last revised January 11, 2020) (pre-print). Latest update May 18, 2020.
https://arxiv.org/abs/1909.00095v3
Some key points from the body text:
The rotation curves of several disk galaxies were computed in (Deur 2009) based on Eq. (1) and using numerical lattice calculations in the static limit (Deur 2017). . . . Although based directly on the GR’s Lagrangian, the lattice approach is limited since it is computationally costly and applies only to simple geometry, limiting the study to only a few late Hubble type galaxies at one time. To study the correlation from MLS2016 over the wide range of disk galaxy morphologies, we developed two models based on: 1) the 1/r gravitational force resulting from solving Eq. (1) for a disk of axisymmetrically distributed matter; and 2) the expectation that GR field self-interaction effects cancel for spherically symmetric distributions, such as that of a bulge, restoring the familiar 1/r 2 force.
and from the appendix:
The direct calculation of the effects of field self-interaction based on Eq. (1) employs the Feynman path integral formalism solved numerically on a lattice. While the method hails from quantum field theory, it is applied in the classical limit, see (Deur 2017). The first and main step is the calculation of the potential between two essentially static (v c) sources in the non-perturbative regime. Following the foremost non-perturbative method used in QCD, we employ a lattice technique using the Metropolis algorithm, a standard Monte-Carlo method (Deur 2009, 2017). The static calculations are performed on a 3-dimensional space lattice (in contrast to the usual 4-dimensional Euclidian spacetime lattice of QCD) using the 00 component of the gravitational field ϕµν. This implies that the results are taken to their classic limit, as it will be explained below. Furthermore, the dominance of ϕ00 over the other components of the gravitational field simplifies Eq (1) in which [ϕ n∂ϕ∂ϕ] → anϕ n 00∂ϕ00∂ϕ00, with an a set of proportionality constants. One has a0 ≡ 1 and one can show that a1 = 1 (Deur 2017).