Solutions of the Einstein equations involving functions of only one variable
Edward Kasner · Transactions of the American Mathematical Society · 1925
are satisfied. The results are given in (14), (20), and (17) below. They involve only elementary functions, and the corresponding four-dimensional manifolds can be represented as imbedded in flat space of seven dimensions. Making use of the formulas for Rik calculated in a previous papert we find that, of the ten equations (2), the six with unlike subscript vanish identically, while the four with like subscripts become