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Bearing in mind our previous study on asymptotic behavior of null geodesicsnear future null infinity, we analyze the behavior of geometrical quantitiessuch as a certain extrinsic curvature and Riemann tensor in the Bondicoordinates. In the sense of asymptotics, the condition for an $r$-constanthypersurface to be a photon surface is shown to be controlled by a key quantitythat determines the fate of photons initially emitted in angular directions. Asa consequence, in four dimensions, such a non-expanding photon surface can berealized even near future null infinity in the presence of enormous energy fluxfor a short period of time. By contrast, in higher-dimensional cases, no such aphoton surface can exist. This result also implies that the dynamicallytransversely trapping surface, which is proposed as an extension of a photonsurface, can have an arbitrarily large radius in four dimensions.

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