Asymptotic behavior of null geodesics near future null infinity: Significance of gravitational waves. (arXiv:2106.03150v3 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Amo_M/0/1/0/all/0/1">Masaya Amo</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Izumi_K/0/1/0/all/0/1">Keisuke Izumi</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Tomikawa_Y/0/1/0/all/0/1">Yoshimune Tomikawa</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Yoshino_H/0/1/0/all/0/1">Hirotaka Yoshino</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Shiromizu_T/0/1/0/all/0/1">Tetsuya Shiromizu</a>
We investigate the behavior of null geodesics near future null infinity in
asymptotically flat spacetimes. In particular, we focus on the asymptotic
behavior of null geodesics that correspond to worldlines of photons initially
emitted in the directions tangential to the constant radial surfaces in the
Bondi coordinates. The analysis is performed for general dimensions, and the
difference between the four-dimensional cases and the higher-dimensional cases
is stressed. In four dimensions, some assumptions are required to guarantee the
null geodesics to reach future null infinity, in addition to the conditions of
asymptotic flatness. Without these assumptions, gravitational waves may prevent
photons from reaching null infinity. In higher dimensions, by contrast, such
assumptions are not necessary, and gravitational waves do not affect the
asymptotic behavior of null geodesics.
We investigate the behavior of null geodesics near future null infinity in
asymptotically flat spacetimes. In particular, we focus on the asymptotic
behavior of null geodesics that correspond to worldlines of photons initially
emitted in the directions tangential to the constant radial surfaces in the
Bondi coordinates. The analysis is performed for general dimensions, and the
difference between the four-dimensional cases and the higher-dimensional cases
is stressed. In four dimensions, some assumptions are required to guarantee the
null geodesics to reach future null infinity, in addition to the conditions of
asymptotic flatness. Without these assumptions, gravitational waves may prevent
photons from reaching null infinity. In higher dimensions, by contrast, such
assumptions are not necessary, and gravitational waves do not affect the
asymptotic behavior of null geodesics.
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