The construction given here is specific to the flat metric of Minkowski space. However, such a construction generalizes to other asymptotically flat spaces as well. In such scenarios, null infinity still exists as a three dimensional null surface at the boundary of the spacetime manifold, but the manifold's overall structure might be different. For instance, in Minkowski space, all null geodesics begin at past null infinity and end at future null infinity. However, in the Schwarzschild black hole spacetime, the black hole event horizon leads to two possibilities: geodesics may end at null infinity, but may also end at the black hole's future singularity. The presence of null infinity (along with the other regions of conformal infinity) guarantees geodesic completion on the spacetime manifold, where all geodesics terminate either at a true singularity or intersect the boundary of infinity.