 Quote by TSny
They have dimension of 1/length if all the coordinates xj have the dimension of length. Without thinking, that's what I was assuming  .
However, generally the coordinates do not need to have dimension of length (for example, in spherical coordinates where some of the coordinates are angles.) For a given coordinate system it is possible for different Christoffel symbols to have different dimesions. |
With no loss of generality, it is possible to think of the spatial coordinates as merely numbers laid on a grid, without any units; in this scheme of things, the coordinate basis vectors then all have units of distance (length). From this it follows that the components of the metric tensor all have units of length squared. From this it follows in this scheme that the Christoffel symbols of the first kind also all have units of length squared. From this it follows that the Christoffel symbols of the second kind are all dimensionless.
Chet
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