Existence and uniqueness of solutions for Einstein equations 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 gauge 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 Einstein 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 existence and uniqueness, I think this post provides some good insight.
 A: 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’s equations.  A source on these solutions is in:
H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, E. Herlt, Exact Solutions of Einstein’s Field
Equations, Cambridge: Cambridge University Press. (2003)
A: Classically, there are initial configurations in general relativity without closed timelike curves which can be shown to evolve into future states with closed timelike curves. The boundary between both regions is the Cauchy horizon, and evolution across the Cauchy horizon is nondeterministic.
For anti de Sitter space without any conformal boundary conditions, we also have nondeterministic evolution, even far away from conformal infinity.
Also, classically, anything can come out of a white hole singularity.

Probably the best bet for dealing with questions about existence and uniqueness is to work with the ADM time-slicing Hamiltonian approach.
