论文标题
Kerr黑洞及其阴影周围的轨道
Orbits around a Kerr black hole and its shadow
论文作者
论文摘要
由于相对论的完整一般理论已于1915年向科学界推出，因此已经找到并研究了真空爱因斯坦田间方程的许多解决方案。本文旨在详尽地记录了天空斑块的形状，该贴片是由Kerr Solutions在Boyer-Lindquist坐标中描述的旋转黑洞完全黑色的。观察者天空中的黑暗区域称为黑洞阴影。首先引入了允许进行粒子轨道分析的保守量，并在其帮助下由两个冲击参数（Azimuthal方向L和无量纲Carter的常数Q）唯一描述了光子的轨迹。然后，我们在黑洞捕获光子所需的那些参数上得出条件。然后将这些条件转换为黑洞阴影的方程式。我们通过在两个单独的情况下为赤道观察者提取黑洞阴影来结束纸张。
Since the full General Theory of Relativity has been unveiled to the scientific community in 1915, many solutions to the vacuum Einstein field equations have been found and studied. This paper aims at documenting exhaustively the derivation of the shape of the patch of the sky that is left completely black by a spinning black hole described by the Kerr solutions in Boyer-Lindquist coordinates. This dark zone in the observer's sky is called the black hole shadow. Conserved quantities which allow for the analysis of particle orbits are first introduced, with the help of which the trajectories of photons are uniquely described by two impact parameters (Specific angular momentum in the azimuthal direction L and dimensionless Carter's constant Q). We then derive the conditions on those parameters required for a photon to be captured by the black hole. These conditions are then translated into an equation for the black hole shadow. We conclude the paper by drawing out the black hole shadows for an equatorial observer for two separate cases.
