 Defining again the space metric tensor γαβ = −"g"αβ one has, therefore
The special space coordinate is written as "x"3 = "z" and the time coordinate is written as "x"0 = ξ (as different from proper time "t"); it will be shown that ξ corresponds to the same variable defined in homogeneous models.Differentiation by ξ and "z" is designated, respectively, by dot and prime.Latin indices "a", "b", "c" take values 1, 2, corresponding to space coordinates "x"1, "x"2 which will be also written as "x", "y".