LQG Legend Writes Paper Claiming GR Explains Dark Matter Phenomena

[ohwilleke]

TL;DR Summary

A new paper with corresponding author is Giorgio Immirzi, the person after whom the somewhat mysterious Immirzi parameter of Loop Quantum Gravity is named claims to explain DM with GR.

A new group of investigators are attempting something similar to Deur's work, which seeks to explain dark matter phenomena with general relativity corrections to Newtonian gravity is systems like galaxies. Deur's most similar publication to this one along these lines was:

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).

One thing that makes this new paper notable is that the corresponding author is Giorgio Immirzi, the person after whom the somewhat mysterious Immirzi parameter of Loop Quantum Gravity is named.

I will be reviewing the paper more carefully later, but quickly reviewing the citations, I was struck by the over reliance on Ludwig whose effort to explain dark matter phenomena with GR using the gravito-magnetic effect was quickly debunked as too weak, and by the somewhat disappointing as is the lack of citation of Deur who has published multiple papers on exactly this topic since publishing:

A. Deur, “Implications of Graviton-Graviton Interaction to Dark Matter” (May 6, 2009) (published at 676 Phys. Lett. B 21 (2009)).

Still, the new paper did produce the following graph which is consistent with the Milky Way galaxy rotation curve without using dark matter or modified gravity, which is worthwhile in and of itself, regardless of who is cited and who gets credit.

The paper and its abstract are as follows:

A very general class of axially-symmetric metrics in general relativity (GR) that includes rotations is used to discuss the dynamics of rotationally-supported galaxies. The exact vacuum solutions of the Einstein equations for this extended Weyl class of metrics allow us to deduce rigorously the following: (i) GR rotational velocity always exceeds the Newtonian velocity (thanks to Lenz's law in GR); (ii) A non-vanishing intrinsic angular momentum (J) for a galaxy demands the asymptotic constancy of the Weyl (vectorial) length parameter (a) -a behavior identical to that found for the Kerr metric; (iii) Asymptotic constancy of the same parameter also demands a plateau in the rotational velocity.

Unlike the Kerr metric, the extended Weyl metric can and has been continued within the galaxy and it has been shown under what conditions Gauß & Ampére laws emerge along with Ludwig's extended GEM theory with its attendant non-linear rate equations for the velocity field.

Better estimates (than that from the Newtonian theory) for the escape velocity of the Sun and a reasonable rotation curve for our own galaxy has been presented.

Yogendra Srivastava, Giorgio Immirzi, John Swain, Orland Panella, Simone Pacetti, "General Relativity versus Dark Matter for rotating galaxies" arXiv:2207.04279 (July 9, 2022).

Given the five co-authors of the paper including high profile Giorgio Immirzi, this could be the paper that finally gains traction for the argument that the Newtonian approximation of gravity used predominantly in galaxy and galaxy cluster scale astrophysics is materially flawed and that these flaws account for much or all of the phenomena attributed to dark matter, even though the argument has been made in many articles by lower profile authors over the last fifteen years or so.

Notably, this paper stands by the dust model of baryonic matter in galaxies that was seriously questioned when previously advanced by Ludwig.

 

[ohwilleke]

Other papers by people other than the authors of this paper and Deur pursuing the same basic agenda of explaining Dark Matter phenomena with unmodified General Relativity rather than a Newtonian approximation include the following (nine of which date to 2018 or later, reflecting a recent surge of activity in this research agenda):

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.

G. O. Ludwig, "Galactic rotation curve and dark matter according to gravitomagnetism" 81 The European Physical Journal C 186 (February 23, 2021) (open access).

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 that the 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.

F.I. Cooperstock, S. Tieu, "Galactic dynamics via general relativity: a compilation and new developments." 22 Int. J. Mod. Phys. A 2293–2325 (2007). arXiv:astro-ph/0610370 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 that simple 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.

H. Balasin, D. Grumiller, "Non-Newtonian behavior in weak field general relativity for extended rotating sources." 17 Int. J. Mod. Phys. D 475–488 (2008) (arXiv version here).

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.

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).

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 possesses two different values of mass when it is responsible for two different spatiotemporal geometries. Herein, we explore the possibility that the 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.

W.M. Stuckey, Timothy McDevitt, A.K. Sten, Michael Silberstein, "The Missing Mass Problem as a Manifestation of GR Contextuality" 27(14) International Journal of Modern Physics D 1847018 (2018). DOI: 10.1142/S0218271818470181.

We push ahead the idea developed in [24], that some 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%).

Federico Re, "Fake dark matter from retarded distortions" (May 30, 2020).

We show that Einstein's conformal gravity is able to explain simply on the geometric ground the galactic rotation curves without need to introduce any modification in both the gravitational as well as in the matter sector of the theory.

The geometry of each galaxy is described by a metric obtained making a singular rescaling of the Schwarzschild's spacetime. The new exact solution, which is asymptotically Anti-de Sitter, manifests an unattainable singularity at infinity that can not be reached in finite proper time, namely, the spacetime is geodetically complete. It deserves to be notice that we here think different from the usual. Indeed, instead of making the metric singularity-free, we make it apparently but harmlessly even more singular then the Schwarzschild's one.

Finally, it is crucial to point that the Weyl's conformal symmetry is spontaneously broken to the new singular vacuum rather then the asymptotically flat Schwarzschild's one. The metric, is unique according to: the null energy condition, the zero acceleration for photons in the Newtonian regime, and the homogeneity of the Universe at large scales.

Once the matter is conformally coupled to gravity, the orbital velocity for a probe star in the galaxy turns out to be asymptotically constant consistently with the observations and the Tully-Fisher relation. Therefore, we compare our model with a sample of 175 galaxies and we show that our velocity profile very well interpolates the galactic rotation-curves for a proper choice of the only free parameter in the metric and the the mass to luminosity ratios, which turn out to be close to 1 consistently with the absence of dark matter.

Leonardo Modesto, Tian Zhou, Qiang Li, "Geometric origin of the galaxies' dark side" arXiv:2112.04116 (December 8, 2021).

The metric tensor in the four dimensional flat space-time is represented as the matrix form and then the transformation is performed for successive Lorentz boost. After extending or more generalizations the transformation of metric is derived for the curved space-time, manifested after the synergy of different sources of mass. The transformed metric in linear perturbation interestingly reveals a shift from Newtonian gravity for two or more than two body system.

Shubhen Biswas, "The metric transformations and modified Newtonian gravity" arXiv:2109.13515 (September 28, 2021) (note that this not a "MOND" paper, as used in the title "modified Newtonian gravity" means Newtonian gravity with GR based adjustments).

The flattening of spiral-galaxy rotation curves is unnatural in view of the expectations from Kepler's third law and a central mass. It is interesting, however, that the radius-independence velocity is what one expects in one less dimension. In our three-dimensional space, the rotation curve is natural if, outside the galaxy's center, the gravitational potential corresponds to that of a very prolate ellipsoid, filament, string, or otherwise cylindrical structure perpendicular to the galactic plane. While there is observational evidence (and numerical simulations) for filamentary structure at large scales, this has not been discussed at scales commensurable with galactic sizes. If, nevertheless, the hypothesis is tentatively adopted, the scaling exponent of the baryonic Tully--Fisher relation due to accretion of visible matter by the halo comes out to reasonably be 4. At a minimum, this analytical limit would suggest that simulations yielding prolate haloes would provide a better overall fit to small-scale galaxy data.

Felipe J. Llanes-Estrada, "Elongated Gravity Sources as an Analytical Limit for Flat Galaxy Rotation Curves" 7(9) Universe 346 arXiv:2109.08505 (September 16, 2021) DOI: 10.3390/universe7090346

Inspired by the statistical mechanics of an ensemble of interacting particles (BBGKY hierarchy), we propose to account for small-scale inhomogeneities in self-gravitating astrophysical fluids by deriving a non-ideal Virial theorem and non-ideal NavierStokes equations. These equations involve the pair radial distribution function (similar to the two-point correlation function used to characterize the large-scale structures of the Universe), similarly to the interaction energy and equation of state in liquids. Within this framework, small-scale correlations lead to a non-ideal amplification of the gravitational interaction energy, whose omission leads to a missing mass problem, e.g., in galaxies and galaxy clusters.

We propose to use a decomposition of the gravitational potential into a near- and far-field component in order to account for the gravitational force and correlations in the thermodynamics properties of the fluid. Based on the non-ideal Virial theorem, we also propose an extension of the Friedmann equations in the non-ideal regime and use numerical simulations to constrain the contribution of these correlations to the expansion and acceleration of the Universe.

We estimate the non-ideal amplification factor of the gravitational interaction energy of the baryons to lie between 5 and 20, potentially explaining the observed value of the Hubble parameter (since the uncorrelated energy account for ∼ 5%). Within this framework, the acceleration of the expansion emerges naturally because of the increasing number of sub-structures induced by gravitational collapse, which increases their contribution to the total gravitational energy. A simple estimate predicts a non-ideal deceleration parameter qni ' -1; this is potentially the first determination of the observed value based on an intuitively physical argument. We show that another consequence of the small-scale gravitational interactions in bound structures (spiral arms or local clustering) yields a transition to a viscous regime that can lead to flat rotation curves. This transition can also explain the dichotomy between (Keplerian) LSB elliptical galaxy and (non-Keplerian) spiral galaxy rotation profiles. Overall, our results demonstrate that non-ideal effects induced by inhomogeneities must be taken into account, potentially with our formalism, in order to properly determine the gravitational dynamics of galaxies and the larger scale universe.

P. Tremblin, et al., "Non-ideal self-gravity and cosmology: the importance of correlations in the dynamics of the large-scale structures of the Universe" arXiv:2109.09087 (September 19, 2021) (submitted to A&A, original version submitted in 2019).

Honorable mention goes to Lorenzo Posti, S. Michael Fall "Dynamical evidence for a morphology-dependent relation between the stellar and halo masses of galaxies" Accepted for publication in A&A. arXiv:2102.11282 [astro-ph.GA] (February 22, 2021) which notes the relationship at the center of Deur's framework which is the relationship between a system's shape and the dark matter phenomena which it exhibits.

 

[kodama]

gravitomagnetic is very weak effect and probably too weak to replace Dark Matter phenomena

Gravity Probe B confirm with 1% but it is extremely small

 

[malawi_glenn]

Can gravitoelectromagnetism also explain galactic gravitational lensing?

(ill stated question, see my reply in post #6 for a longer, more precise question)

 

[phinds]

Can gravitoelectromagnetism also explain galactic gravitational lensing?

Not necessary. GR explains gravitational lensing perfectly well as an effect of the geometry of spacetime.

 

[malawi_glenn]

GR explains gravitational lensing perfectly

i know that...

I should have phrased my question better:

We all know that galaxies cause gravitational lensing, BUT, the observed effect is too big for the "visible" mass of the galaxy. This is also taken as an evidence for the Dark Matter hypothesis https://royalsocietypublishing.org/doi/10.1098/rsta.2009.0209

Now, can gravitoelectromagnetism also explain this excessive gravitational lensing of galaxies?
@ohwilleke the paper claims to "rule out" DM, but the Dark Matter hypothesis does not stand or die with rotating galaxy curves. So, that is my question, can their work also explain this Dark Matter "pillar"?

 

[phinds]

Now, can gravitoelectromagnetism also explain this excessive gravitational lensing of galaxies?

How would it do that? Photons have no charge.

 

[malawi_glenn]

How would it do that? Photons have no charge.

https://en.wikipedia.org/wiki/Gravitoelectromagnetism

Gravitoelectromagnetism, abbreviated GEM, refers to a set of formal analogies between the equations for electromagnetism and relativistic gravitation; specifically: between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity. Gravitomagnetism is a widely used term referring specifically to the kinetic effects of gravity, in analogy to the magnetic effects of moving electric charge

-------------------------------------------------------------------------------------

https://sergf.ru/gmen.htm

Gravitoelectromagnetism (sometimes Gravitomagnetism, Gravimagnetism, abbreviated GEM), refers to a set of formal analogies between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity. The most common version of GEM is valid only far from isolated sources, and for slowly moving test particles.

--------------------------------------------------------------------------------------

Why did you mention "photons"?

 

[ohwilleke]

We all know that galaxies cause gravitational lensing, BUT, the observed effect is too big for the "visible" mass of the galaxy. This is also taken as an evidence for the Dark Matter hypothesis https://royalsocietypublishing.org/doi/10.1098/rsta.2009.0209

Now, can gravitoelectromagnetism also explain this excessive gravitational lensing of galaxies?
@ohwilleke the paper claims to "rule out" DM, but the Dark Matter hypothesis does not stand or die with rotating galaxy curves. So, that is my question, can their work also explain this Dark Matter "pillar"?

Lensing is a product of the strength of the gravitational field (or in a geometric characterization the curvature of space-time) in the vicinity of the photon.

In Newtonian gravity, the strength of a gravitational field is a linear function of the amount of mass that is the source of the field, and of distance.

In General Relativity, the gravitational field a.k.a. curvature of space-time arising from gravity, doesn't necessarily arise from the stationary rest mass of nearby matter. It can arise from anything that goes into the stress-energy tensor, and the relationship between the source and the field strength (curvature magnitude) can have a non-linear relationship to the size of the mass-energy that is the source of the field (curvature).

In other words, if non-linear and non-mass sourced components of gravitational fields make it appear that a galaxy has dark matter, the lensing effects will be the same as they would be if it did.

 

[malawi_glenn]

In other words, if non-linear and non-mass sourced components of gravitational fields make it appear that a galaxy has dark matter, the lensing effects will be the same as they would be if it did.

I will take this as a "yes". Even for elliptical galaxies, and galaxy clusters?

and the bullet cluster too I guess.

 

[ohwilleke]

I will take this as a "yes". Even for elliptical galaxies, and galaxy clusters?

View attachment 304151
and the bullet cluster too I guess.

Yes. Lensing really isn't a distinct problem in modified gravity or GR based theories.

 

[kodama]

I suspect Deur wasn't cited since this paper is based on Ludwig GEM proposal rather than GR self-interaction. I asked Stacy McGaugh about Ludwig proposal and he regarded it as rubbish, while GEM is real and experimentally verified by Gravity probe B, it's far too weak to explain dark matter phenomena on his blog by orders of magnitude. I'm surprised 5 physicists have taken up on Ludwig's proposal.

I recall a MOND paper that explains MOND in terms of the contribution the cosmological constant to standard GR stress energy tensor, but I don't recall it now. The paper idea was that the energy in empty space itself gravitates as it has energy. I also asked Stacy McGaugh this on his blog and his reply is a positive cosmological constant acts as negative pressure acting against gravity.

 

[mitchell porter]

I suspect Deur wasn't cited since this paper is based on Ludwig GEM proposal rather than GR self-interaction.

Not just that, but Deur is actually making a claim about quantum gravity, whereas these are all classical papers.

 

[kodama]

Not just that, but Deur is actually making a claim about quantum gravity, whereas these are all classical papers.

what do GR experts say of GR self-interaction in classical non-quantum GR? there is gravitational energy that also contribute to gravity

 

[malawi_glenn]

Btw: shouldn't this thread be tagged with "A"? This is not an undergraduate topic afaik.

 

[ohwilleke]

Not just that, but Deur is actually making a claim about quantum gravity, whereas these are all classical papers.

Not the case. His initial papers were quantum gravity, but he has reproduced the result in two or three recent papers classically. The insights are certainly quantum gravity inspired, but the results flow from purely classical GR. See, e.g., 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).

 

[dextercioby]

Btw: shouldn't this thread be tagged with "A"? This is not an undergraduate topic afaik.

Yes, you can report the original message and a moderator will change it. This subforum has no dedicated moderator coming daily to review the messages.

 

[kodama]

Not the case. His initial papers were quantum gravity, but he has reproduced the result in two or three recent papers classically. The insights are certainly quantum gravity inspired, but the results flow from purely classical GR. See, e.g., 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).

any GR experts like authors Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler agree

 

[kodama]

MOND requires force of gravity to switch from 1/r square to 1/r by ao
does DEUR reproduce the results

 

[ohwilleke]

any GR experts like authors Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler agree

MTW is really part of the problem, which some shallow analysis that has discouraged others from taking possibilities seriously based upon their authority rather than their logic and reasoning.

 

[ohwilleke]

MOND requires force of gravity to switch from 1/r square to 1/r by ao
does DEUR reproduce the results

Yes.

 

[kodama]

I have proposed a combination, at the classical level, though also quantum, of both self-interaction AND contribution of the cosmological constant, which is positive. the energy of empty space also contributes but is so feeble that it is only apparent in the MOND regime

 

[kodama]

Yes.

how does he get 1/r in the MOND regime? 1/r scaling suggests to me something like a 2D surface, perhaps some sort of 2 dimensional membrane

 

[PeterDonis]

Moderator's note: Thread level changed to "A".

 

[PeterDonis]

gravitomagnetic is very weak effect

More precisely, it's weak compared to other gravitational effects of a system if the system is approximately spherical, like the Earth.

One of the key claims being made in the research being discussed in this thread is that the fact that a galaxy is not approximately spherical, but is much closer to a flat disk, with some bulge in the center but still much smaller in "vertical" extent than the "horizontal" extent of the disk, makes a large difference in the comparative strengths of the various possible gravitational effects. In other words, you can't just assume (as up to now researchers looking at galaxies have assumed, and which assumption is key in arriving at the dark matter hypothesis for galaxies) that because gravitomagnetic effects are comparatively weak for planets and stars, they will also be comparatively weak for galaxies.

 

[PeterDonis]

Deur is actually making a claim about quantum gravity,

Some of Deur's papers in this area do, but not all. Some are investigating models that are purely classical. We have had some prior threads on this, though I think it's been some time since the last one.

 

[PeterDonis]

MTW is really part of the problem

What parts of MTW have caused a problem for this research?

 

[PeterDonis]

I have proposed

Can you give a reference?

 

[kodama]

Can you give a reference?

Emergent Gravity and the Dark Universe​

Erik P. Verlinde

Recent theoretical progress indicates that spacetime and gravity emerge together from the entanglement structure of an underlying microscopic theory. These ideas are best understood in Anti-de Sitter space, where they rely on the area law for entanglement entropy. The extension to de Sitter space requires taking into account the entropy and temperature associated with the cosmological horizon. Using insights from string theory, black hole physics and quantum information theory we argue that the positive dark energy leads to a thermal volume law contribution to the entropy that overtakes the area law precisely at the cosmological horizon. Due to the competition between area and volume law entanglement the microscopic de Sitter states do not thermalise at sub-Hubble scales: they exhibit memory effects in the form of an entropy displacement caused by matter. The emergent laws of gravity contain an additional `dark' gravitational force describing the `elastic' response due to the entropy displacement. We derive an estimate of the strength of this extra force in terms of the baryonic mass, Newton's constant and the Hubble acceleration scale a_0 =cH_0, and provide evidence for the fact that this additional `dark gravity~force' explains the observed phenomena in galaxies and clusters currently attributed to dark matter.

Comments:	5 figures
Subjects:	High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmolo

 

[PeterDonis]

Emergent Gravity and the Dark Universe

Erik P. Verlinde

As you are aware since you've posted in at least one of them, this paper has been discussed in previous PF threads. It is off topic in this thread since the discussion here is about the paper referenced in the OP.

 

[ohwilleke]

What parts of MTW have caused a problem for this research?

The citations that follow are from MTW, "Gravitation" (1973).

Section 18.3 "the energy momentum conservation formulated here contains no contributions or effects of gravity! From this one sees that linearized theory assumes that gravitational forces do no significant work." But the text is shallow in really quantifying the limits of linearized theory in weak fields rigorously.

Section 19.2 "If the particle is sufficiently far from the source, its motion is affected hardly at all by the source's angular momentum or by the gravitational waves; only the spherical, Newtonian part of the gravitational field has a significant influence. Hence, the particle moves in an elliptical Keplerian orbit."

Section 20.4 stating "Anybody who looks for a magic formula for 'local gravitational energy-momentum' is looking for the right answer to the wrong question. Unhappily, enormous time and effort were devoted in the past to trying to 'answer this question' before investigators realized the futility of the enterprise. Toward the end, above all mathematical arguments, one came to appreciate the quiet but rock-like strength of Einstein's equivalence principle. One can always find in any given locality a frame of reference in which all local 'gravitational fields' (all Christoffel symbols . . . . disappear. No [Christoffel symbols] means no 'gravitational fields' and no local gravitational field means no 'local gravitational energy-momentum.' Nobody can deny or wants to deny that gravitational forces make a contribution to the mass-energy of a gravitationally interacting system. The mass-energy of the Earth-moon system is less than the mass-energy that the system would have if the two objects were at infinite separation. The mass-energy of a neutron star is less than the mass-energy of the same number of baryons at infinite separation. Surrounding a region of empty space where there is a concentration of gravitational waves, there is a net attraction, betokening a positive net mass-energu ion that region of space. . . .At issue is not the existence of gravitational energy, but the localizability of gravitational energy. It is not localizable. The equivalence principle forbids. . . . The over-all effect one is looking at is a global effect, not a local effect. That is what the mathematics cries out."

Section 20.5 stating the interbody non-Newtonian gravitational potential can be ignored in "The solar system . . . the Galaxy . . . [and] clusters of galaxies, but [not] the universe as a whole."

See also Section 16.5 disavowing the notion that a gravitational field can be defined precisely. Section 18.1 and Box 18.1 (comparing the Einstein derivation and Spin-2 derivation of Einstein's field equations, but largely discounting the Spin-2 derivation from which the analysis of self-interaction effects is more intuitively obvious, in the rest of the material).

It isn't that MTW deny the effects that people using GR effects to explain dark matter rely upon are using in later treatments (and maybe editions of textbooks in the subject post-1973 have improved), but the discomfort express about "going there" at all, supported by the ad hominem argument that everybody looked and didn't find anything as if every other scientist examining the issue was an idiot, and the specific ruling out of an effect, without much analysis based upon a back of napkin heuristic in Section 20.5 that there could be an effect in galaxies and galaxy clusters.

There is also sloppiness in the Section 20.4 discussion, on one hand acknowledging that a system as localized as the Earth-Moon system, or a neutron star can have gravitational contributions to the mass of the system from the perspective of a distant observer, in particular to systems much smaller than a light year relative to a vast universe, and then denying that any kind of localization whatsoever is possible when verbally, the authors have just localized the gravitational energy effect on mass to a fairly localized system.

Basically, the attitude seems to be that since we didn't find a way to address the question of gravitational field self-interaction that many researchers grappled with, that it is futile and impossible to do so, even through they don't really have a rigorous no go theory that means what they imply or a rigorous quantification of the magnitude of the effects in galaxy and galaxy cluster scale systems.

Another big name whose work may have been generalized beyond its technical holdings is S. Deser who often co-authored with Misner. He makes an analysis of the gravitational self-interaction (1970); clarified and expanded upon in 2009. And, he makes some related non-obvious observations about the properties of stress energy tensors.

Criticism

Criticism of S. Deser's conclusions about gravitational self-interactions and a similar one by Feynman in 1995 that shows an out of the box thinking alternative analysis can be found here.

A.I. Nikishov of the P.N. Lebedev Physical Institute in Moscow states in an updated July 23, 2013 version of an October 13, 2003 preprint (arXiv:gr-qc/0310072), these arguments "do not seem convincing enough." For example, Feynman's lectures on gravitation assumed that gravity was mediated by a graviton that could be localized with a self-interaction coupling strength equal to the graviton's energy, just as the graviton would with any other particle. String theory and supergravity theories, generically make the same assumptions.

Nikishov also made the same analysis of Deur in his paper "Problems in field theoretical approach to gravitation" dated February 4, 2008 in its latest preprint version arXiv:gr-qc/04100999 originally submitted October 20, 2004, when he states in the first sentence of his abstract that:

We consider gravitational self interaction in the lowest approximation and assume that graviton interacts with gravitational energy-momentum tensor in the same way as it interacts with particles.

Deur and Nikishov are not the only investigators to note the potential problems with the anomalous ways that conventional General Relativity treats gravitational self-interactions, and they are not alone in this respect. Carl Brannen has also pursued some similar ideas.

As another example, consider this statement by A.L. Koshkarov from the University of Petrozavodsk, Russia in his November 4, 2004 preprint (arXiv:gr-qc/0411073) in the introduction to his paper entitled "On General Relativity extension."

But in what way, the fact that gravitation is nonabelian does get on with widely spread and prevailing view the gravity source is energy-momentum and only energy-moment? And how about nonabelian self-interaction? Of course, here we touch very tender spots about exclusiveness of gravity as physical field, the energy problem, etc. . . .All the facts point out the General Relaivity is not quite conventional nonabelian theory.

Koshkarov then goes on to look at what one would need to do in order to formulate gravity as a conventional nonabelian theory like conventional Yang-Mills theory.

Alexander Balakin, Diego Pavon, Dominik J. Schwarz, and Winfried Zimdahl, in their paper "Curvature force and dark energy" published at New.J.Phys.5:85 (2003), preprint at arXiv:astro-ph0302150 similarly noted that "curvature self-interaction of the cosmic gas is shown to mimic a cosmological constant or other forms of dark energy." Balakin, et al., reach their conclusions using the classical geometric expression of general relativity, rather than a quantum gravity analysis, suggesting that the overlooked self-interaction effects do not depend upon whether one's formulation of gravity is a classical or a quantum one, but the implication once again, is that a failure to adequately account for the self-interaction of gravitational energy with itself may account for all or most dark sector phenomena.

A suggestion that the order of magnitude of the non-Newtonian implications of General Relativity (possibly generalized slightly) may be sufficient to explain the entire dark sector comes from Hong Sheng Zho in a preprint last modified on June 9, 2008 and originally submitted on May 27, 2008 arXiv:0805.4046 [gr-qc] that "the negative pressure of the cosmological dark energy coincides with the positive pressure of random motion of dark matter in bright galaxies."

Another indication that these effects may be of the right order of magnitude to explain dark energy as well as dark matter comes from Greek scientists K. Kleidis and N.K. Spyrou in their paper "A conventional approach to the dark-energy concept" (arXiv: 1104.0442 [gr-qc] (April 4, 2011). They too note that energy from the internal motions of the matter in the universe (both baryonic and dark) in a collisional dark matter model are of the right scale to account for existing observational data without dark energy or the cosmological constant.

It is also worth noting that the cosmological constant is small enough that other kinds of careful analysis of sources for dark energy effects in the Standard Model and non-Newtonian effects in general relativity other than the cosmological constant may explain some or all of it.

For example, Ralf Schutzhold in an April 4, 2002 preprint at arXiv:gr-qc/0204018 in a paper entitled "A cosmological constant from the QCD trace anomaly" noted that "non-perturbative effects of self-interacting quantum fields in curved space times may yield a significant contribution" to the observed cosmological constant. The calculations in his four page page conclude that: "Focusing on the trace anomaly of quantum chromo-dynamics (QCD), a preliminary estimate of the expected order of magnitude yields a remarkable coincidence with the empirical data, indicating the potential relevance of this effect."

See also Sourav Kesharee Sahoo, Ashutosh Dash, Radhika Vathsan, Tabish Qureshi, "Testing Gravitational Self-interaction via Matter-Wave Interferometry" arXiv:2203.01787 (March 3, 2022) (applying gravitational self-interaction to decoherence issues).

Also related

The gravitational stability of a two-dimensional self-gravitating and differentially rotating gaseous disk in the context of post-Newtonian (hereafter PN) theory is studied. Using the perturbative method and applying the second iterated equations of PN approximation, the relativistic version of the dispersion relation for the propagation of small perturbations is found. We obtain the PN version of Toomre's local stability criterion by utilizing this PN dispersion relation. In other words, we find relativistic corrections to Toomre's criterion in the first PN approximation.

Two stability parameters η and μ related to gravity and pressure are introduced. We illustrate how these parameters determine the stability of the Newtonian and PN systems. Moreover, we show that, in general, the differentially rotating fluid disk is more stable in the context of PN theory relative to the Newtonian one. Also, we explicitly show that although the relativistic PN corrections destabilize non-rotating systems, they have the stabilizing role in the rotating thin disks. Finally, we apply the results to the relativistic disks around hypermassive neutron stars (HMNSs), and find that although Newtonian description predicts the occurrence of local fragmentations, PN theory remains in agreement with the relevant simulations, and rules out the existence of local fragmentations.

Ali Kazemi, Mahmood Roshan, Elham Nazari "Post-Newtonian corrections to Toomre's criterion" (August 17, 2018) (accepted in ApJ).

And another paper noting the usefulness of a scalar theory of gravitation as a way to approximate self-interaction of gravitational field effects in full GR or the Post-Newtonian approximation.

We construct a general stratified scalar theory of gravitation from a field equation that accounts for the self-interaction of the field and a particle Lagrangian, and calculate its post-Newtonian parameters. Using this general framework, we analyze several specific scalar theories of gravitation and check their predictions for the solar system post-Newtonian effects.

Diogo P. L. Bragança, José P. S. Lemos "Stratified scalar field theories of gravitation with self-energy term and effective particle Lagrangian" (June 29, 2018).

The conclusion to this paper notes that:

In this paper, we presented a general stratified scalar field theory of gravitation in a Minkowski background. Then, we calculated two post-Newtonian parameters from three general parameters of the theory B, C and k, concluding that it is perfectly possible for such a scalar theory to explain the four solar system tests. Finally, we used this general theory to rapidly compute the PPN parameters β and γ for a set of scalar theories of gravitation to verify if they agree with the experimental tests of gravitation in the solar system. Therefore, with this formalism, one can directly find those two PPN parameters only from the field equation and the particle Lagrangian of a given scalar theory of gravitation. Although this is a very efficient method to calculate β and γ for a given theory, it does not allow one to compute the other PPN parameters. It would be interesting to generalize this approach to efficiently calculate the remaining PPN parameters for scalar theories and verify if it is possible for such a theory to explain every phenomenon predicted by general relativity.

The stratified theories that were analyzed (Page and Tupper’s, and Ni’s) yielded the correct PPN parameters relevant for solar system tests. One could wonder whether this indicates that they are valid theories, and the answer to that relies in analyzing the remaining PPN parameters. This analysis was done by Nordtvedt and Will [60] and Ni [50] and the conclusion was that stratified theories cannot account for Earth-tide measurements due to the motion of the solar system relative to the preferred frame (defined by the distant stars).

The conformal theories that were analyzed did not yield the correct γ parameter even in very general cases. This motivates future work on the analysis of a relativistic scalar theory including a derivative coupling in the Lagrangian, of the type T ab(∂aΦ)(∂bΦ). Such a theory would not have preferred frame effects (it would respect Lorentz symmetries), so if it predicted the correct parameters β and γ it would not have the problem of Earth-tide measurements.

If such a scalar theory correctly predicts the outcome of every weak field gravity experiment, then we can only rule it out using strong gravity experiment results (e.g. LIGO, neutron star binaries, cosmology). Note also that a scalar theory of gravity is much simpler than general relativity, since it describes gravity with one function instead of ten. In such theories, unlike general relativity, it is generally possible to define a local gravitational energy-momentum tensor, which is always an attractive feature, and is still a problem in general relativity.

Note that some of the preprints cited (maybe most) have been subsequently published, but I haven't clicked through to update the status of these papers since a last took note of them.

 

[PeterDonis]

@ohwilleke thanks for all the references! You've added a bunch of items to my reading list.

Regarding MTW, their basic position on the "energy stored in the gravitational field" not being "localizable" is simple: there is no tensor that describes any such thing, indeed there can't be if the equivalence principle is correct, and anything that is "localizable" in the sense they are using the term must be described by a tensor. I realize there is a significant portion of the literature that does not agree with that position, but I don't think MTW itself is sloppy or ambiguous in describing the position they are taking.

Of course their position assumes that standard GR is correct within its domain of validity and that theories containing extra fields associated with "gravity", such as scalar-tensor theories, are not necessary to explain the data. Whether the voluminous amount of data collected since 1973 when MTW was published includes effects that standard GR cannot easily explain is, of course, the point of very open area of research we are discussing, at least with regard to the data on galaxy rotation curves. If it turns out that standard GR can, when calculated properly, explain the galaxy rotation curve properties that are currently believed by many to require dark matter, that might invalidate some of the more specific statements MTW makes, but not their general position on "energy stored in the gravitational field" not being "localizable" in their particular precise sense of that term.

 

[ohwilleke]

@ohwilleke thanks for all the references! You've added a bunch of items to my reading list.

Regarding MTW, their basic position on the "energy stored in the gravitational field" not being "localizable" is simple: there is no tensor that describes any such thing, indeed there can't be if the equivalence principle is correct, and anything that is "localizable" in the sense they are using the term must be described by a tensor. I realize there is a significant portion of the literature that does not agree with that position, but I don't think MTW itself is sloppy or ambiguous in describing the position they are taking.

Of course their position assumes that standard GR is correct within its domain of validity and that theories containing extra fields associated with "gravity", such as scalar-tensor theories, are not necessary to explain the data. Whether the voluminous amount of data collected since 1973 when MTW was published includes effects that standard GR cannot easily explain is, of course, the point of very open area of research we are discussing, at least with regard to the data on galaxy rotation curves. If it turns out that standard GR can, when calculated properly, explain the galaxy rotation curve properties that are currently believed by many to require dark matter, that might invalidate some of the more specific statements MTW makes, but not their general position on "energy stored in the gravitational field" not being "localizable" in their particular precise sense of that term.

What I am calling "sloppiness" in their discussion is using the term "localizable" only to refer to an exact point value, basically a well defined point gradient function (without clearly calling out that they are using such a restrictive definition) when they are recognizing that the effects can be isolated to essentially any closed system of any size as a whole (even one of just a few km in longest dimension), which is far from what one is usually talking about when one says that an effect can only be "global" (particularly after following on with a discussion about effects being negligible below the scale of the entire universe in a following section).

Another area of sloppiness is their logic that because there is some frame of reference in which you can take localized gravitational energy to zero for any given free falling system, that this means that you can't use mutually consistent well chosen frames of reference to provide useful information about the gravitational energy of a system. By analogy, you can always set "potential energy" to zero in classical Newtonian gravity, but that doesn't limit the usefulness of giving it positive value from other frames of reference.

 

[PeterDonis]

Ali Kazemi, Mahmood Roshan, Elham Nazari "Post-Newtonian corrections to Toomre's criterion" (August 17, 2018) (accepted in ApJ).

Btw, is the "Toomre" of "Toomre's criterion" Alar Toomre? It looks like it could be from the references in the paper. Alar Toomre was a professor of math at MIT when I was there; his class in complex analysis was the one that convinced me that I should be taking the math classes I needed for my degree (which was not in math) from the physics department instead of the math department. Brilliant, but way over my head.

 

[ohwilleke]

Btw, is the "Toomre" of "Toomre's criterion" Alar Toomre? It looks like it could be from the references in the paper. Alar Toomre was a professor of math at MIT when I was there; his class in complex analysis was the one that convinced me that I should be taking the math classes I needed for my degree (which was not in math) from the physics department instead of the math department. Brilliant, but way over my head.

I hear you. Complex analysis was probably among the classes I took that convinced me that I should not pursue a math PhD (although I considered other heavily math dependent fields like actuarial science, operations research, and quantitative economics seriously before going to the dark side to become a lawyer).