The remaining three Einstein equations contain only first order time derivatives of the metric tensor. They give three time-independent relations that must be imposed as necessary conditions on the coordinate functions in . This, together with the condition λ = 0, makes four conditions. These conditions bind ten different coordinate functions: three components of each of the vectors l, m, n, and one function in the powers of t (any one of the functions pl, pm, pn, which are bound by the conditions ). When calculating the number of physically arbitrary functions, it must be taken into account that the synchronous system used here allows time-independent arbitrary transformations of the three space coordinates. Therefore, the final solution contains overall 10 − 4 − 3 = 3 physically arbitrary functions which is one less than what is needed for the general solution in vacuum.
