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

TL;DR

This paper investigates the asymptotic behavior of null geodesics near future null infinity, revealing conditions for photon surfaces and their dimensional differences, with implications for gravitational physics.

Contribution

It introduces a new analysis of geometrical quantities controlling photon surfaces near null infinity, highlighting differences between four and higher dimensions.

Findings

Non-expanding photon surface can exist near null infinity in 4D with high energy flux.

No such photon surface exists in higher dimensions.

Dynamically transversely trapping surfaces can have arbitrarily large radii in 4D.

Abstract

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. As a consequence, in four dimensions, such a non-expanding 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.