  A new sufficient condition for photons emitted near future null infinity to
reach future null infinity is derived by studying null geodesics in the Bondi
coordinates in asymptotically flat spacetimes. In our previous works
[arXiv:2106.03150, arXiv:2110.10917], such a condition was established for
photons emitted in outward or tangential directions to constant radial
surfaces. This paper improves our previous result by including photons emitted
in inward directions. In four dimensions, imposing the same assumptions on the
metric functions as previously, we prove that photons reach future null
infinity if their initial values of $|dr/du|$ are smaller than a certain
quantity, where $r$ and $u$ are the radial and retarded time coordinates,
respectively. This quantity is determined by the asymptotic properties of the
metric and is connected to the conjectured maximal luminosity. In higher
dimensions, photons emitted with $dr/du>-(1-1/\sqrt{3})\approx -0.423$ are
shown to reach future null infinity without the assumptions on the metric
functions.
