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

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.10917
 Bibcode:
 2021arXiv211010917A
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Theory
 EPrint:
 17 pages, no figures