Compatibility of General Relativity with SO(3)

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General Relativity (GR) is compatible with the SO(3) symmetry in the context of its local structure, as vielbeins transform under SO(3,1), which includes SO(3) as a subalgebra. However, solutions to Einstein's equations do not necessarily require global rotational symmetry, indicating that GR can accommodate a variety of geometries. The discussion highlights that while local symmetries are maintained, global solutions may not reflect these symmetries. The compatibility with SO(3) symmetry within the Lorentz group follows a similar reasoning. Overall, GR's flexibility allows for diverse solutions beyond strict rotational symmetry.
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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 :)
 
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What about compatibility to SO(3) symmetry Lorentz group?
 

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