Values of Tvµ and the Christoffel symbols for a line element of considerable generality

In the general theory of relativity the mechanical properties of any region of the universe are expressed by the energy-momentum tensor, Tvµ, which is itself calculable from the form of the line element, ds2 = gµvdxµdx4, applicable to that region. The expressions for Tvµ in the most general case, in which all the gµv are arbitrary functions of the four coordinates, x1, x2, x3, x4, are exceedingly complicated, but considerable simplification is introduced if it is assumed that gµv(µ ≠ v) = 0.