| (a) | gij(m) | = |  |
|
= | ± ij |
||||
| (b) | gij,k(m) | = | 0 | for every k. |
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 xi at m such that:
| (a) | gij(m) | = | |
|
= | ±ij |
||||
| (b) | gij,k(m) | = | 0 | for every k. |
We call such a coordinate system a local inertial frame.
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