# Cartan formalism

1. Jul 6, 2010

### paweld

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?

2. Jul 6, 2010

### Passionflower

Because it "neutralizes" spacetime curvature and projects a continuously flat (Minkowski) spacetime along a wordline of an observer.

3. Jul 7, 2010

### Mentz114

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.