I have question, is GR compatible with SO(3)?
In what sense? Vielbeins transform under so(3,1), having so(3) as subalgebra. But globally, a solution of the einsteineqn's doesn't need to possess rotational symmetry. You should be a bit more specific :)
What about compatibility to SO(3) symmetry Lorentz group?
Same answer, I guess.
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