# Physics Quantity Corresponding to Christoffel

1. Feb 28, 2012

### dpa

Hi Everyone!

Somewhere I read <:uhhr possibly I think so and am wrong> that christoffel symbols correspond to gravitational field.

Is there any physical Quantity corresponding to Christoffel symbols? Could you be more explicit as to how the physical quantity corresponds to Christoffel Symbol?

Thank You

Sincerely
DPA

2. Feb 29, 2012

### Matterwave

The Christoffel symbols are the coordinate representation (in a coordinate basis) of the covariant derivative given by the Levi-Civita connection.

The Christoffel symbols are adjustments for how basis vectors "twist around" in a general curved geometry (or even in a flat space but with curved coordinates). As such, they are not, strictly speaking, "the gravitational field", since they can exist in the absence of the gravitational field if we just choose curvilinear coordinates rather than cartesian coordinates. Additionally, even in the presence of a gravitational field, they can be locally (at a point) set to zero by choosing local Lorentz coordinates around that point.