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.