I was especially interested in Carlip's comment #2 about uncertainty.....
There have been some long discussions in these forums and I thought I had a reasonable
understanding, but what is meant by
The uncertainty principle prevents us from simply saying,"A black hole is present."

is really baffling....
Mentz:
Algebraic symmetries are at the heart of GR and are used to classify spacetimes into 'families' according to the structure of the Lie group formed by all possible solutions of Killings equation.

These were, then, discovered after the formulation of GR??.....they were likely not formal input restrictions which Einstein recognized and which guided him beforehand????
When Einstein was deciding what mathematics to use for his new theory, I seem to recall he was aware of 'stress, strain' and these are described by symmetric tensors.....we now know.....was such 'symmetry' understood/known in the 1920's???