Section 1 of the article shows that the Schwarzschild metric and cosmological models with similar metrics are invalid because the spatial part of the metric is not a valid Riemannian metric in local Cartesian coordinates, as it should. Theorem 1 proves that a metric for the spatial part given in the spherical coordinates of R3 with only dr2, dθ2 and dϕ2 defines a valid metric in local Cartesian coordinates only if the spatial part of the metric is a scalar metric, i.e., a metric induced by a scalar field. Section 2 has some solutions for a scalar metric in the situation of a point mass in an otherwise empty space. Section 3 and 4 look at the Friedmann’s cosmological model from Chapter 5 of Einstein’s book combined from his lectures in Princeton. The findings are that each of Einstein’s equation can be solved for a model that only depends on t and r, but the Einstein equations do not have a solution that solves them all and gives a valid metric. Additionally the Friedmann model does not give the cosmological solution that Einstein’s book says.