Now that an equivalence of Navier Stokes and Einstein equations has been establi

Question

Now that an equivalence of Navier Stokes and Einstein equations has been established, and it is known solutions to Einstein-Maxwell-Boltzmann exist and are unique, and it is known that Einstein equations in a wave guage with electromagnetic source with a lorentz gauge also have unique solutions that exist, what are the next steps? What are the good references on research for existence and uniqueness for einsten solutions without electromagnetic sources? Also, what does it mean physically that there are unique solutions to Einstein Field equations when electromagnetic sources are included?

For those struggling with the concept of existance and uniqueness, I think this post provides some good insight.

Explanation / Answer

The formal classification of solutions to Einstein field equations is the Penrose-Petrov-Pirani scheme. This classifies solutions according to eigen-Killing vectors of the Weyl tensor. These solutions range from the type D solutions for black holes to the type N solutions for gravity waves. In between there are type I II and III solutions for Robinson-Trautman spacetimes. These turn out to have a relationship to each other, where type D solutions are near source terms and type N solutions are far field. The other solutions are in between. This is a gravitational analogue of the near and far field solutions for Mazwell

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