There is an interesting development concerning propuslion by general relativity. The method is using the Alcubierre metric in connection with woliton waves. The Alcubierre metric has already been analysed in our book on Einstein criticism.

https://iopscience.iop.org/article/10.1088/1361-6382/abe692

The oroginal article is not freely accessible, but there is a German web site which gives more info about the article. Put
https://www.derstandard.de/story/2000125099281/neue-theoretische-loesungen-fuerreisen-mit-ueberlichtgeschwindigkeit-entdeckt
into a translator.

Excerpt from the content:

This includes, for example, the famous warp drive, on which, among other things, the spaceship Enterprise from the Star Trek universe relies. Such a drive could actually work on paper, wrote the Mexican physicist Miguel Alcubierre in 1994. His theoretical solution for locomotion at faster than light speed does not contradict at least the general and special theory of relativity. The thought experiment, also known as the Alcubierre drive, is based on a local deformation of space-time, like a wave on which a hypothetical spaceship could even reach ten times the speed of light.

Abstract of the original paper:

Solitons in space-time capable of transporting time-like observers at superluminal speeds have long been tied to violations of the weak, strong, and dominant energy conditions of general relativity. The negative-energy sources required for these solitons must be created through energy-intensive uncertainty principle processes as no such classical source is known in particle physics. This paper overcomes this barrier by constructing a class of soliton solutions that are capable of superluminal motion and sourced by purely positive energy densities. The solitons are also shown to be capable of being sourced from the stress–energy of a conducting plasma and classical electromagnetic fields. This is the first example of hyper-fast solitons resulting from known and familiar sources, reopening the discussion of superluminal mechanisms rooted in conventional physics.

In a recent article, the author G. O. Ludwig presents an explanation of galactic rotation curves, based on gravitomagnetism, not dark matter:

https://link.springer.com/article/10.1140/epjc/s10052-021-08967-3

Although he does not refer to ECE theory, he uses concepts of fluid electrodynamics and the gravitomagnetic field, both well developed by the AIAS group.
Science daily writes about Ludwig’s article in a contribution:

(https://www.sciencedaily.com/releases/2021/03/210304145458.htm)

The Very Concept of Dark Matter Itself, Questioned in New Research

TOPICS:AstrophysicsDark MatterSpringer

By Springer March 9, 2021

Factoring in Gravitomagnetism Could Do Away With Dark Matter

Models of galactic rotation curves built of a general relativistic framework could use gravitomagnetism to explain the effects of dark matter.

Observations of galactic rotation curves give one of the strongest lines of evidence pointing towards the existence of dark matter, a non-baryonic form of matter that makes up an estimated 85% of the matter in the observable Universe. Current assessments of galactic rotation curves are based upon a framework of Newtonian accounts of gravity, a new paper published in EPJ C, by Gerson Otto Ludwig, National Institute for Space Research, Brazil, suggests that if this is substituted with a general relativity-based model, the need to recourse to dark matter is relieved, replaced by the effects of gravitomagnetism.

The main role of dark matter, Ludwig points out in the paper, has historically been to resolve the disparity between astrophysical observations and current theories of gravity. Put simply, if baryonic matter — the form of matter we see around us every day which is made up of protons, neutrons, and electrons — is the only form of matter, then there shouldn’t be enough gravitational force to prevent galaxies from flying apart.

By disregarding general relativistic corrections to Newtonian gravity arising from mass currents, and by neglecting these mass currents, Ludwig asserts these models also miss significant modifications to rotational curves — the orbital speeds of visible stars and gas plotted against their radial distance from their galaxy’s center. This is because of an effect in general relativity not present in Newton’s theory of gravity — frame-dragging or the Lense Thirring effect. This effect arises when a massive rotating object like a star or black hole ‘drags’ the very fabric of spacetime along with it, in turn giving rise to a gravitomagnetic field.

In this paper, Ludwig presents a new model for the rotational curves of galaxies which is in agreement with previous efforts involving general relativity. The researcher demonstrates that even though the effects of gravitomagnetic fields are weak, factoring them into models alleviates the difference between theories of gravity and observed rotational curves — eliminating the need for dark matter. The theory still needs some development before it is widely accepted, with the author particularly pointing out that the time evolution of galaxies modeled with this framework is a complex problem that will require much deeper analysis.

Ludwig concludes by suggesting that all calculations performed with thin galactic disk models performed up until this point may have to be recalculated, and the very concept of dark matter itself, questioned.

Reference: “Galactic rotation curve and dark matter according to gravitomagnetism” by G. O. Ludwig, 23 February 2021, The European Physical Journal C.
DOI: 10.1140/epjc/s10052-021-08967-3