Asymptotic behavior of null geodesics near future null infinity. III. Photons towards inward directions

Abstract

A new sufficient condition for photons emitted near future null infinity to reach future null infinity is derived by studying null geodesics in the Bondi coordinates in asymptotically flat spacetimes. In our previous works [arXiv:2106.03150, arXiv:2110.10917], such a condition was established for photons emitted in outward or tangential directions to constant radial surfaces. This paper improves our previous result by including photons emitted in inward directions. In four dimensions, imposing the same assumptions on the metric functions as previously, we prove that photons reach future null infinity if their initial values of $|dr/du|$ are smaller than a certain quantity, where $r$ and $u$ are the radial and retarded time coordinates, respectively. This quantity is determined by the asymptotic properties of the metric and is connected to the conjectured maximal luminosity. In higher dimensions, photons emitted with $dr/du>-(1-1/\sqrt{3})\approx -0.423$ are shown to reach future null infinity without the assumptions on the metric functions.

arXiv comment19 pages, no figures

References in corpus (15)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• The geometry of photon surfaces
• Shadows and strong gravitational lensing: a brief review
• Fundamental photon orbits: black hole shadows and spacetime instabilities
• Asymptotic Flatness and Bondi Energy in Higher Dimensional Gravity
• Asymptotic flatness at null infinity in arbitrary dimensions
• Extension of photon surfaces and their area: Static and stationary spacetimes
• Area bound for a surface in a strong gravity region
• Transversely trapping surfaces: Dynamical version
• Asymptotic flatness at null infinity in higher dimensional gravity
• Higher Dimensional Bondi Energy with a Globally Specified Background Structure
• Gravitational Machines
• Asymptotic behavior of null geodesics near future null infinity: Significance of gravitational waves
• Asymptotic behavior of null geodesics near future null infinity II: curvatures, photon surface and dynamically transversely trapping surface

Cited by in corpus (2)

• A generalization of photon sphere based on escape/capture cone
• Asymptotic behavior of null geodesics near future null infinity IV: Null-access theorem for generic asymptotically flat spacetime