The Christoffel symbols are tensor-like objects derived from a Riemannian metric. They are used to study the geometry of the metric and appear,
for example, in the geodesic equation. There
are two closely related kinds of Christoffel symbols, the first
kind,
and the second kind. Christoffel symbols of the second kind are also
known as affine connections (Weinberg 1972, p. 71) or connection coefficients
(Misner et al. 1973, p. 210).
It is always possible to pick a coordinate system on a Riemannian manifold such that the Christoffel symbol vanishes at a chosen point. In general
relativity, Christoffel symbols are "gravitational forces," and the preferred
coordinate system referred to above would be one attached to a body in free fall.
. They are used to study the geometry of the metric and appear,
for example, in the geodesic equation. There
are two closely related kinds of Christoffel symbols, the first
kind 
,
and the second kind 
. Christoffel symbols of the second kind are also
known as affine connections (Weinberg 1972, p. 71) or connection coefficients
(Misner et al. 1973, p. 210).
