We present the geodesical completion of the Schwarzschild black hole in four dimensions which covers the entire space in (u,v) Kruskal-Szekeres coordinates, including the spacetime behind the black and white hole singularities. The gravitational constant switches sign abruptly at the singularity, thus we interpret the other side of the singularity as a region of antigravity. The presence of such sign flips is a prediction of local (Weyl) scale invariant geodesically complete spacetimes which improve classical general relativity and string theory. We compute the geodesics for our new black hole and show that all geodesics of a test particle are complete. Hence, an ideal observer, that starts its journey in the usual space of gravity, can reach the other side of the singularity in a finite amount of proper time. As usual, an observer outside of the horizon cannot verify that such phenomena exist. However, the fact that there exist proper observers that can see this, is of fundamental significance for the construction of the correct theory and the interpretation of phenomena pertaining to black holes and cosmology close to and beyond the singularities.
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