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## Main Question or Discussion Point

I understand that writing the E-H action in terms of tetrads makes evident GR is a gauge theory. IOW general covariance/diffeomorphism invariance in GR is a form of gauge invariance.

However unlike other gauge theories(for instance EM dependence on Minkowski spacetime), this gauge invariance in GR is accompanied by background independence(no prior global geometry/topology), wich makes us see GR's manifold abstractly as a simple differentiable manifold, that only has a casual geometric appearance when for practical requirements of the problem at hand like exploiting its symmetries we make a gauge choice and use some preferred coordinates(i.e. FRW coordinates in cosmology or Schwarzschild coordinates for isolated sources) but if GR is a gauge theory those gauge choices are not physical.

Assuming this is not a wrong depiction of GR's general covariance, background independence and gauge invariance, a questions occurs to me:

If GR is background independent, solutions of the EFE are valid locally like are all the observables derived from this local curvature geometry, but we shouldn't be able to infer any global geometry/topology from them, so I don't see any justification for "maximally extended solutions" like say, Kruskal-Szekeres solution. Being rigorous it seems there is no physical grounds to use it if we take seriously gauge invariance. How is this usually dealt with?

However unlike other gauge theories(for instance EM dependence on Minkowski spacetime), this gauge invariance in GR is accompanied by background independence(no prior global geometry/topology), wich makes us see GR's manifold abstractly as a simple differentiable manifold, that only has a casual geometric appearance when for practical requirements of the problem at hand like exploiting its symmetries we make a gauge choice and use some preferred coordinates(i.e. FRW coordinates in cosmology or Schwarzschild coordinates for isolated sources) but if GR is a gauge theory those gauge choices are not physical.

Assuming this is not a wrong depiction of GR's general covariance, background independence and gauge invariance, a questions occurs to me:

If GR is background independent, solutions of the EFE are valid locally like are all the observables derived from this local curvature geometry, but we shouldn't be able to infer any global geometry/topology from them, so I don't see any justification for "maximally extended solutions" like say, Kruskal-Szekeres solution. Being rigorous it seems there is no physical grounds to use it if we take seriously gauge invariance. How is this usually dealt with?