Can general relativity be reinterpreted via continuum mechanics or in particular Non-Newtonian fluid mechanics of some hypothetical continuous medium filling space-time ? That is, gravitation and gravitational waves relate to the stress, strain, compression and oscillations of this medium ? The Ricci tensor is like the Cauchy stress tensor, Ricci curvature like pressure ? Galaxies as vortices ? Maybe what we call mass, is nothing more than a manifestation of structured (self-similar) turbulence ? Ordinary gravitation is some kind of current or flow towards the direction of the mass.
Since Birkhoff, people have been trying to subordinate the geometry of curved space to the properties of the medium in flat space. However, there is no direct match yet. And yet, if you are interested in this question, then the author of this post has his own approach to this topic, outlined in the book
Research Proposal MATHEMATICAL NOTES ON THE NATURE OF THINGS
The short answer is, Yes. Cf. for instance, https://www.jstor.org/stable/1970699
and https://www.physics.rutgers.edu/het/video/keeler11a.pdf
There are subtleties related to dimensionality, however.
What's relevant is the symmetry group; general relativity has as isometry group that of spacetime diffeomorphisms.
Relativity always seemed to me as an attempt to reduce physics entirely to geometry, at least macroscopic physics and I have thought in the past a little about this. But I later found that this was already in fact a project of Wheeler:
https://en.wikipedia.org/wiki/Geometrodynamics
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