Asymptotic behavior of null geodesics near future null infinity. III. Photons towards inward directions
Asymptotic behavior of null geodesics near future null infinity. III. Photons towards inward directions
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DOI：
10.1103/physrevd.106.084007
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发表时间：
2022-08
影响因子：
5
通讯作者：
Masaya Amo;K. Izumi;Yoshimune Tomikawa;H. Yoshino;T. Shiromizu
中科院分区：
文献类型：
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作者：
Masaya Amo;K. Izumi;Yoshimune Tomikawa;H. Yoshino;T. Shiromizu
通过研究渐近平坦时空中邦迪坐标中的零测地线，得出了在近未来零无穷远发射的光子到达未来零无穷大的新充分条件。在我们之前的工作 [1, 2] 中，为向外或切向方向发射到恒定径向表面的光子建立了这样的条件。这篇论文通过包括向内方向发射的光子来改进我们之前的结果。在四个维度中，对度量函数施加与 [1, 2] 相同的假设，我们证明，如果光子的初始值 | ，则光子达到未来的零无穷大。博士/杜 |小于一定量，其中 r 和 u 分别是径向时间坐标和延迟时间坐标。该量由度量的渐近性质确定，并与推测的最大光度相关。在更高维度中，发射的光子 dr/du > − (1 − 1 / √ 3) ≈ − 0 。 423 被证明在没有度量函数假设的情况下达到未来的零无穷大。
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 [1, 2], 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 [1, 2], 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 / √ 3) ≈ − 0 . 423 are shown to reach future null infinity without the assumptions on the metric functions.