PeterDonis said:
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.
Brilliant, but way over my head.
