Ultimately, I am confident that dark matter phenomena will be explained entirely as a gravitational effect.

Quite possibly, simply correctly considering standard general relativity effects beyond Newtonian gravity is all that is required. The alternative is that the correct theory of gravity is a gravitational theory very similar to standard general relativity, that is almost indistinguishable in strong gravitational field settings, but differs from it in some subtle respect that is primarily observable only in weak fields as a lower order effect.

Many researchers have explored this idea and tentatively shown that it is feasible in the last decade and a half or so, although most of them are outsiders of the astronomy and general relativity research specialty, their papers have not received a lot of attention from leading specialists in this field, their approaches are somewhat varied (and it isn't clear if they are consistent with each other despite all matching the same observational data), and they have not gelled to form an interacting community of scholars taking on a common project in a collective manner that allows their contributions to be rigorously vetted and refined. Some of the more notable papers along this line are collected below.

One of the latest of these papers, published in a peer reviewed academic journal, is G.O. Ludwig, a Brazilian physicist whose background in primarily in the design of nuclear fusion reactors, in the article below, makes a convincing argument that dark matter phenomena are a result of non-Newtonian aspects of general relativity that conventional modeling of galactic dynamics neglects. Ludwig's paper and its abstract are as follows:

Historically, the existence of dark matter has been postulated to resolve discrepancies between astrophysical observations and accepted theories of gravity. In particular, the measured rotation curve of galaxies provided much experimental support to the dark matter concept. However,most theories used to explain the rotation curve have been restricted to the Newtonian potential framework, disregarding the general relativistic corrections associated with mass currents. In this paper it is shown that the gravitomagnetic field produced by the currents modifies the galactic rotation curve, notably at large distances. The coupling between the Newtonian potential and the gravitomagnetic flux function results in a nonlinear differential equation that relates the rotation velocity to the mass density. The solution of this equation reproduces the galactic rotation curve without recourse to obscure dark matter components, as exemplified by three characteristic cases.A bi-dimensional model is developed that allows to estimate the total mass, the central mass density, and the overall shape of the galaxies, while fitting the measured luminosity and rotation curves. The effects attributed to dark matter can be simply explained by the gravitomagnetic field produced by the mass currents.

This is similar to the approach of Deur (whose work I have advocated at this blog in the past):

Our present understanding of the universe requires the existence of dark matter and dark energy. We describe here a natural mechanism that could make exotic dark matter and possibly dark energy unnecessary.Graviton-graviton interactions increase the gravitational binding of matter. This increase, for large massive systems such as galaxies, may be large enough to make exotic dark matter superfluous. Within a weak field approximation we compute the effect on the rotation curves of galaxies and find the correct magnitude and distribution without need for arbitrary parameters or additional exotic particles. The Tully-Fisher relation also emerges naturally from this framework. The computations are further applied to galaxy clusters.

We consider the consequences of applying general relativity to the description of the dynamics of a galaxy, given the observed flattened rotation curves. The galaxy is modeled as a stationary axially symmetric pressure-free fluid. In spite of the weak gravitational field and the non-relativistic source velocities, the mathematical system is still seen to be non-linear. It is shown thatthe rotation curves for various galaxies as examples are consistent with the mass density distributions of the visible matter within essentially flattened disks. This obviates the need for a massive halo of exotic dark matter.We determine that the mass density for the luminous threshold as tracked in the radial direction is 10^−21.75 kg⋅m^−3 for these galaxies and conjecture that this will be the case for other galaxies yet to be analyzed. We present a velocity dispersion test to determine the extent, if of any significance, of matter that may lie beyond the visible/HI region. Various comments and criticisms from colleagues are addressed.

*See also*follow up papers in 2007, in 2011, and 2015.

Exact stationary axially symmetric solutions to the four-dimensional Einstein equations with corotating pressureless perfect fluid sources are studied. A particular solution with an approximately flat rotation curve is discussed in some detail. We find thatsimple Newtonian arguments overestimate the amount of matter needed to explain such curves by more than 30%. The crucial insight gained by this model is that the Newtonian approximation breaks down in an extended rotating region, even though it is valid locally everywhere. No conflict with solar system tests arises.

Flat rotation curves (RCs) in disc galaxies provide the main observational support to the hypothesis of surrounding dark matter (DM). Despite of the difficulty in identifying the DM contribution to the total mass density in our Galaxy, stellar kinematics, as tracer of gravitational potential, is the most reliable observable for gauging different matter components. 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. This is the angular momentum supported population of the Milky Way (MW) that better traces its observed RC.

We fitted such data to both a classical, i.e. including a DM halo, velocity profile model, and a general relativistic one derived from a stationary axisymmetric galaxy-scale metric.The general relativistic MW RC results statistically indistinguishable from its state-of-the-art DM analogue.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. In the context of Local Cosmology, our findings are suggestive of the Galaxy’s phase space as the exterior gravitational field in equilibrium far from a Kerr-like inner source, possibly with no need for extra matter to account for the disc kinematics.

In Newtonian gravity, mass is an intrinsic property of matter while in general relativity (GR), mass is a contextual property of matter, i.e., matter can simultaneously possess two different values of mass when it is responsible for two different spatiotemporal geometries. Herein, we explore the possibility thatthe astrophysical missing mass attributed to non-baryonic dark matter (DM) actually obtains because we have been assuming the Newtonian view of mass rather than the GR view. Since an exact GR solution for realistic astrophysical situations is not feasible, we explore GR-motivated ansatzes relating proper mass and dynamic mass for one and the same baryonic matter, as justified by GR contextuality. We consider four GR alternatives and find that the GR ansatz motivated by metric perturbation theory works well in fitting galactic rotation curves (THINGS data), the mass profiles of X-ray clusters (ROSAT and ASCA data) and the angular power spectrum of the cosmic microwave background (CMB, Planck 2015 data) without DM. We compare our galactic rotation curve fits to modified Newtonian dynamics (MOND), Burkett halo DM and Navarro-Frenk-White (NFW) halo DM. We compare our X-ray cluster mass profile fits to metric skew-tensor gravity (MSTG) and core-modified NFW DM. We compare our CMB angular power spectrum fit to scalar-tensor-vector gravity (STVG) and ΛCDM. Overall, we find our fits to be comparable to those of MOND, MSTG, STVG, ΛCDM, Burkett, and NFW.We present and discuss correlations and trends for the best fit values of our fitting parameters. For the most part, the correlations are consistent with well-established results at all scales, which is perhaps surprising given the simple functional form of the GR ansatz.

We push ahead the idea developed in [24], thatsome fraction of the dark matter and the dark energy can be explained as a relativistic effect.The inhomogeneity matter generates gravitational distortions, which are general relativistically retarded. These combine in a magnification effect since the past matter density, which generated the distortion we feel now, is greater than the present one. The non negligible effect on the averaged expansion of the universe contributes both to the estimations of the dark matter and to the dark energy, so that the parameters of the Cosmological Standard Model need some corrections.

In this second work we apply the previously developed framework to relativistic models of the universe. It results that one parameter remain free, so that more solutions are possible, as function of inhomogeneity. One of these fully explains the dark energy, but requires more dark matter than the Cosmological Standard Model (91% of the total matter). Another solution fully explains the dark matter, but requires more dark energy than the Cosmological Standard Model (15% more). A third noteworthy solution explains a consistent part of the dark matter (it would be 63% of the total matter) and also some of the dark energy (4%).

## 9 comments:

G.O. Ludwig, is a plasma physicist, his paper actually have several blog posts and again it was just published February 23, 2021 so it might take time

one question I have is this, since gravitomagnetic flux function is in analogy to standard magnetism and GEM is in analogy to E&M

could you build a E&M simulated "galaxy" with charged particles (ions, electrons) and do they behave, with standard magnetism to produce same type of rotation curves as we see in galaxies.

if they do I'd say this is persuasive evidence G.O. Ludwig is on the right track.

as well as galaxy and large scale structure formation (which is said to require cold dark matter)

presumably galaxy clusters also have gravitomagnetic mass currents, which MOND is unable to correct (MOND still requires additional matter)

i also wonder if gravitomagnetic mass currents could explain the CMB third peak without dark matter.

btw here is quite a bit of discussion on G.O. Ludwig paper

https://news.ycombinator.com/item?id=26442021

gravity probe B established gravitomagnetism to within experimental measurement

"By August 2008, the frame-dragging effect had been confirmed to within 15% of the expected result,[6] and the December 2008 NASA report indicated that the geodetic effect was confirmed to better than 0.5%.[7]

In an article published in the journal Physical Review Letters in 2011, the authors reported analysis of the data from all four gyroscopes results in a geodetic drift rate of −6601.8±18.3 mas/yr and a frame-dragging drift rate of −37.2±7.2 mas/yr, in good agreement with the general relativity predictions of −6606.1±0.28% mas/yr and −39.2±0.19% mas/yr, respectively.[8] "

Gravitomagnetic is a well established general relativistic effect that really no one disputes (MOND supporters included), although it isn't exact, it is an approximation of an important subset of distinctions between GR and Newtonian gravity. The form of the equations is very similar to that of Maxwell's equations, and the first efforts at what we would now call a TOE, in which Einstein and many of his contemporaries participated actively, we to develop a unification of GR and Maxwell's equations.

The difficulty involved in using physical electromagnetic systems to model Newtonian + Gravitomagnetic effects is that the coupling constants, the charge/masses, and the distances in the systems described by very similar classical equations are so different from each other. Basically, the inputs into the analogous equations are so different that it is hard to make a physical analog.

It is not akin to the situation in which condensed matter physics in systems governed by equations very similar to those of QCD can be used to provide a physical analog to QCD physics (which are too microscope to observe in a useful way directly the way that one can in a condense matter system).

The difficulty is that you can't model a system with as many points as a galaxy (even if you had one point per star) using full GR or even a close simplified approximation of it that doesn't just reduce to Newtonian gravity) in an N-body simulation, even with massive computing power. So, you need to figure out how to balance the practical need to do calculations with available computational resources (which requires massive simplification of the problem) without losing GR features that are important at a macro-level even if they are negligible, for example, at a solar system level, and furthermore, how to be confident that you have done so correctly and not missed something important.

One of the reasons that you are seeing so many non-GR specialists attempt this is that they have mathematical tools in their toolbox that are better suited to the kind of mathematical analysis needed than most people trained as GR specialists.

For example, GR specialists show unreasonable preference for analysis of highly symmetric systems (which works great for black holes and neutron stars in strong fields), because it is mathematically much easier to manage and no one is banging on their door to try something different, while nuclear and QCD physicists out of necessity have had to develop methods to cope with asymmetric distributions of force sources and matter which are common place in the real world universe.

Newtonian gravity + Gravitomagnetic effect still misses important GR effects, and it isn't at all obvious is GR effects that might explain the CMB third peak without dark matter, or cluster dynamics are the same ones that are important in explaining disk-like galaxies. Deur's work is attractive because, while some of his work is very back of napkin, he has developed his GR inspired approach to address issues like cluster dynamics and cosmology issues that investigators in other approaches haven't yet gotten around to examining and developing.

btw https://twitter.com/robinhanson/status/1370113520998699013

Sabine's doesn't like it, but Robin Hanson says he has reviewed it and seems solid.

Sabine complains it doesn't explain everything but Robin says it seems to explain galactic rotation curves just fine.

given it is just a first paper I think Sabine is unreasonable

do you think black holes can explain the third peak of the CMB, or to put it another way,

what kind of black holes, in terms of mass and size and quantity, could explain the third peak of the CMB? and what effects do standard model neutrinos play in the third peak of the CMB

Locklin and posters on this link https://news.ycombinator.com/item?id=26442021 suggested G.O. Ludwig should get the nobel prize in physics if this paper pans out.

how does GEM compare with MOND? Sabine in her twitter claims galaxy rotation can be done with MOND, but GEM seems a much better theoretical basis, it already has a relativistic generation, namely GR

Garrett Lisi did a quick calculation and concluded that galactic gravitomagnetism is something like one millionth of what it needs to be, to account for the rotation curves.

Robin Hanson thinks he has identified a specific error in Ludwig and similar papers - approximating the galactic disk of stars as a zero-pressure dust because stars hardly ever collide. He argues that "pressure" here should instead count the number of stars passing through a given cross-sectional area per unit time.

https://www.overcomingbias.com/2021/03/what-holds-up-a-north-pole-of-dust.html

It would mean that Ludwig and similar authors are using the wrong equation of state - they need to have a nonzero pressure component.

It seems unlikely to me that "gravitomagnetism from ordinary matter alone" is going to work. But instead I am wondering now, could you get the rotation curves from the gravitomagnetism of the right kind of dark matter? Like the virtual dust of RelMOND (whatever that actually is):

http://dispatchesfromturtleisland.blogspot.com/2021/03/dark-matter-and-dark-energy-as-general.html

@neo "what kind of black holes, in terms of mass and size and quantity, could explain the third peak of the CMB? and what effects do standard model neutrinos play in the third peak of the CMB"

I don't think that either black holes or standard model neutrinos can play a significant part in the third peak of the CMB.

The standard model neutrino hypothesis has been modeled expensively by the scientists behind Planck and other collaborations with CMB measuring telescopes.

The Black Hole hypothesis has been pretty much ruled out at this point through a patchwork of evidence from different kinds of observations.

@neo

"G.O. Ludwig should get the nobel prize in physics if this paper pans out.

how does GEM compare with MOND? Sabine in her twitter claims galaxy rotation can be done with MOND, but GEM seems a much better theoretical basis, it already has a relativistic generation, namely GR."

G.O. Ludwig is late to the party as his own paper acknowledges. GEM, MOND and lots of other modified/unconventionally applied gravity proposals can get you to flat rotation curves, and is has yet to be determined if his proposal is the right one among the many cited in this post (also MOG by Moffatt and Conformal Gravity and some kinds of f(R) gravity). Normally, Nobel prizes go to the first to come up with an idea.

MOND was never meant to be an accurate, theoretically grounded description of the universe. But Milgrom deserves a lot of credit for being really the first to establish in a proof of concept that some sort of simple gravitational modification can explain dark matter phenomena over a wide domain of applicability and describing it with enough specificity to make a lot of successful ex ante predictions.

Ludwig may very well be right that non-Newtonian elements of GR explain DM components. But gravitomagnetism (like MOND) almost certainly can't explain DM in clusters, or many cosmology issues attributed to DM, or wide binary stars. Deur's approach does manage to do those things and make additional predictions not found in prior approaches that bear out, and explains dark energy in a way that removes one experimental constant from GR with a cosmological constant, while also naturally solving the cosmic coincidence problem, the 21 cm problem, and the global conservation of mass-energy in GR problem with the cosmological constant doesn't. And, he's earlier. So I'd count him as more deserving. But credit in the fundamental sciences is always a tricky thing.

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