Compatibility of General Relativity with SO(3)

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I have question, is GR compatible with SO(3)?
 
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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 possesses rotational symmetry. You should be a bit more specific :)
 
Thanks.
What about compatibility to SO(3) symmetry Lorentz group?
 

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