Proposition 9.2 (Existence of a Local Inertial Frame)
If m is any point in the Riemannian manifold M, then there exists a local coordinate system x^{i} at m such that:
(a)  g_{ij}(m)  = 

=  ±_{ij}  
(b)  g_{ij,k}(m)  =  0  for every k. 
We call such a coordinate system a local inertial frame.
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