Non-Linear Effects In Many Body Self-Gravitating Systems

Gravity Amplification And Shielding In Complex Many Bodies Systems Analyzed With Newtonian Gravity

In order to to develop good intuition about the emergent non-linear behavior of gravity and its dependence upon the shape of the matter distribution involved in complex many bodied systems (even analyzed with Newtonian gravity alone), there is really no alternative to the difficult work of actually running the numbers in various test cases. This is especially true in cases where the computational crutch of spherically symmetric natter distributions is not available. A new paper does that and its conclusions are intriguing and suggestive.

The language is a bit opaque, but the article is basically explaining in a very sterile and mathematical context, how homogeneous matter arranged in sheet and cylinder shapes can enhance gravitational pulls in a manner akin to dark matter phenomena, and how spherical arrangements of matter can give rise to repulsive effects at large distances phenomenologically similar to dark energy phenomena due to gravitational shielding.

The present work analyzes perturbed potentials due to test mass that is added instantaneously at the center of symmetry of the equilibrium isothermal self-gravitating gases. We examine gravitational amplification in the isothermal sheet, cylinder, and sphere, assuming that the systems are highly collisional and reach a new state of thermal equilibrium after perturbation.

Under the assumptions, the isothermal sheet and cylinder amplify gravitational fields due to test sheet and line masses by 68 % and 53 % maximally. On the one hand, in the isothermal sphere, gravitational fields due to test point mass are amplified oscillatorily with radius and show a repulsive effect at large radii.

Yuta Ito, "Gravitational Amplification of Test-Mass Potential in the Self-gravitating Isothermal Gaseous Systems" arXiv:2303.02631 (March 5, 2023) (Subjects:Astrophysics of Galaxies; Solar and Stellar Astrophysics; Statistical Mechanics).

Can The Shape And Matter Density Of Galaxies Explain Their Flat Rotation Curves With Only Newtonian Gravity?

In the same vein, see also, this new preprint which argues that the right mass density variation with radius and proper consideration of the shape of the matter distribution can give rise to the correct non-Keplerian flat rotation curves in four galaxies considered (a result that I am inclined to be more skeptical of, but do not dismiss out of hand):

Dark matter has been a long-standing and important issue in physics, but direct evidence of its existence is lacking. This work aims to elucidate the mystery and show that the dark matter hypothesis is unnecessary. 

We can nicely reproduce the observed rotation curves using only conventional Newtonian dynamics based on experimental surface brightness profiles of several galaxies. Our success is based on realizing that the mass radial distribution follows a stretched exponential decay with a small exponent over a few hundred kiloparsecs. Our quantitative analysis indicates that for these four example galaxies, there is no need to invoke the hypothetical dark matter presently unknown to humans or the modified Newtonian dynamics (MOND) paradigm.

Jau Tang, Qiang Tang, "Reproducing some observed galactic rotation curves without dark matter or modified Newtonian dynamics" arXiv:2303.02811 (March 6, 2023).

A Conjecture About Early Dark Energy

As an aside, I'll also mention a personal observation not supported by papers of which I am aware.

Modified gravity theories, generically predict the formation of galaxies earlier than in LambdaCDM models.

In Deur's model of gravity, and probably some other gravitational models as well (such as the one discussed above), the same mechanisms that give rise to dark matter phenomena can also lead to what amounts to gravitational shielding that reduces the gravitational pull of the galaxy on objects outside it. This looks observationally, similar to dark energy.

One common approach to trying to resolve the Hubble tension between the apparent Hubble constant in the early universe and the apparent Hubble constant much closer to today, is to hypothesize "early dark energy."

If dark energy phenomena really arise hand in hand with galaxy formation, however, then the early galaxy formation that occurs in modified gravity theories should also give rise to earlier dark energy phenomena. And, since galaxy formation appears to be particular concentrated in the very early universe when there is a sudden burst of galaxy formation that exhausts much of the supply of star forming material almost as soon as it is possible to form galaxies, a burst of early dark energy which would distort the Hubble constant is exactly what one would expect.

Explaining High Energy Neutrino Bursts

Finally, while not strictly on topic, an analysis in a new preprint provides a possible explanation of high energy neutrino bursts seen at at the IceCube neutrino observatory, using only careful consideration of boring well established physics, which had previously puzzled astronomers.