Asymptotic behavior of null geodesics near future null infinity. II. Curvatures, photon surface, and dynamically transversely trapping surface

Bearing in mind our previous study on asymptotic behavior of null geodesics near future infinity, we analyze the geometrical quantities such as a certain extrinsic curvature and Riemann tensor Bondi coordinates. In sense asymptotics, condition for an $r$-constant hypersurface to be photon surface is shown controlled by key quantity that determines fate photons initially emitted angular directions. As consequence, four dimensions, non-expanding can realized even infinity presence enormous energy flux short period time. By contrast, higher-dimensional cases, no exist. This result also implies dynamically transversely trapping surface, which proposed extension have arbitrarily large radius dimensions.