Sneppen Albert
Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Ø 2200, Copenhagen, Denmark.
Cosmic Dawn Center (DAWN), Copenhagen, Denmark.
Sci Rep. 2021 Jul 9;11(1):14247. doi: 10.1038/s41598-021-93595-w.
From any location outside the event horizon of a black hole there are an infinite number of trajectories for light to an observer. Each of these paths differ in the number of orbits revolved around the black hole and in their proximity to the last photon orbit. With simple numerical and a perturbed analytical solution to the null-geodesic equation of the Schwarzschild black hole we will reaffirm how each additional orbit is a factor [Formula: see text] closer to the black hole's optical edge. Consequently, the surface of the black hole and any background light will be mirrored infinitely in exponentially thinner slices around the last photon orbit. Furthermore, the introduced formalism proves how the entire trajectories of light in the strong field limit is prescribed by a diverging and a converging exponential. Lastly, the existence of the exponential family is generalized to the equatorial plane of the Kerr black hole with the exponentials dependence on spin derived. Thereby, proving that the distance between subsequent images increases and decreases for respectively retrograde and prograde images. In the limit of an extremely rotating Kerr black hole no logarithmic divergence exists for prograde trajectories.
从黑洞事件视界之外的任何位置出发，光到达观察者的轨迹有无数条。这些路径中的每一条在围绕黑洞公转的轨道数量以及它们与最后一个光子轨道的接近程度上都有所不同。通过对史瓦西黑洞的零测地线方程进行简单的数值求解和微扰解析求解，我们将再次确认每增加一个轨道，就会向黑洞的光学边缘靠近一个因子[公式：见原文]。因此，黑洞表面和任何背景光将在最后一个光子轨道周围以指数级变薄的切片中被无限次反射。此外，引入的形式体系证明了在强场极限下光的整个轨迹由一个发散指数和一个收敛指数规定。最后，指数族的存在被推广到克尔黑洞的赤道平面，并得出指数对自旋的依赖性。从而证明，对于逆行图像和顺行图像，后续图像之间的距离分别增大和减小。在极端旋转的克尔黑洞的极限情况下，顺行轨迹不存在对数发散。
