We have known that all the information of the Lorentian
Manifold is in it's metric g_{ij}. But physicists really don't
like those quantities which are dependent on the choice of
coordinates. So we need to extract information from g_{ij}
and discard those unwanted. But how can we achieve that?
First, we don't want to relate g_{ij} at one point with
g_{ij} at another point because physicists believe in locality.
Then what left is just derivatives. That's something physicists
really like. Maybe it
