Cartan Formalism: Mapping Tetrad Field to Minkowski Spacetime

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Why it is said that tetrad field e^I = e^I_\mu \textrm{d} x^\mu is a mapping
from tangent space of the spacetime into Minkowski spacetime?
 
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paweld said:
Why it is said that tetrad field e^I = e^I_\mu \textrm{d} x^\mu is a mapping
from tangent space of the spacetime into Minkowski spacetime?
Because it "neutralizes" spacetime curvature and projects a continuously flat (Minkowski) spacetime along a wordline of an observer.
 
Passionflower said:
Because it "neutralizes" spacetime curvature and projects a continuously flat (Minkowski) spacetime along a wordline of an observer.

Yes, and the same thing can be achieved in GR by changing to a frame-field basis. It seems that Cartan formalism starts with the frame (tetrad) field and not the metric.
 

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