Asymptotic simplicity

Asymptotic simplicity requires a suitable smooth conformal completion with $\tilde{g}={\Omega }^{2}g$, $\Omega >0$ in the physical spacetime, and $\Omega =0$, $d\Omega \ne 0$ on null infinity, such that every inextendible null geodesic has both past and future endpoints there. It is stronger than merely possessing an asymptotically flat exterior. Null geodesics ending on singularities or on omitted finite-affine-distance horizons prevent this global condition.