On the flatness of spacetime

We have proven with mathematical rigor that spacetime in Schwarzschild metric is flat as measured by the Riemann curvature scalar. We have also shown that Einstein's field equation describes the equipotential surface, and the equation of a geodesic describes the trajectory of an object moving in a gravitational field. The curving of the equipotential and the trajectory should not be misunderstood as the curving of space and time. It has been pointed out that spacetime as defined in the Robertson‐Walker metric is mathematically curved, but such curving is not due to the existence of gravity, but due to two hypothetical postulations: (1) The existence of certain nonphysical extra dimension in addition to the three-dimensional physical space, and the assertion that the real physical space is a three-dimensional hypersphere embedded in the Euclidean hyperspace of higher dimension; (2) The existence of certain universal repulsion force that is supposed to be responsible for controlling the curvature of the universe. We have shown that even if we accept Einstein's hypothesis at its face value, the fine tuning of the density parameter with a relative tolerance of less than 10⁻⁵⁸ attests to the flatness of the spacetime.