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

Automated summary

By analyzing the behavior of geometrical quantities in the Bondi coordinates, the condition for a nonexpanding photon surface to exist is determined by a key quantity that determines the fate of photons initially emitted in angular directions. In four dimensions, such a surface can exist even near future null infinity with enormous energy flux, while in higher-dimensional cases, it is not possible. This result also suggests that the dynamically transversely trapping surface can have arbitrarily large radius in four dimensions.