The time-space metric is a fundamental concept of general relativity, and it is the logical foundation of cosmology and astrophysics. A time-related space scale factor is introduced into a 4-dimensional time-space interval model. The transformations among the flat metric, the Schwarzschild metric and the Robertson-Walker (R-W) metric are obtained in spherical coordinate system. Based on the time-space interval of the time-related scale factor coordinate, the solutions of R-W metric with parameter k=1 and the non-vacuum metric outside stars are deduced. A new point of view is advanced to comprehend the modern physical non-flat time-space.