Compatibility of General Relativity with SO(3)

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Discussion Overview

The discussion revolves around the compatibility of General Relativity (GR) with the SO(3) symmetry, specifically in the context of the Lorentz group. Participants explore the implications of this compatibility in terms of rotational symmetry and the structure of the theory.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions whether GR is compatible with SO(3).
  • Another participant clarifies that vielbeins transform under so(3,1) and that SO(3) is a subalgebra, but notes that solutions to the Einstein equations do not necessarily require rotational symmetry.
  • A later post seeks clarification on the compatibility of GR with SO(3) symmetry specifically within the Lorentz group.
  • The same participant suggests that the previous answer regarding compatibility likely applies here as well.

Areas of Agreement / Disagreement

The discussion does not reach a consensus on the compatibility of GR with SO(3), as participants express differing views on the implications of rotational symmetry in the context of GR.

Contextual Notes

Participants do not specify the conditions under which compatibility might hold or the implications of lacking rotational symmetry in solutions to the Einstein equations.

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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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