论文标题
克尔黑洞周围的球形光子轨道的确切公式
Exact Formulas for Spherical Photon Orbits Around Kerr Black Holes
论文作者
论文摘要
将球形光子轨道的半径与黑洞的旋转参数以及轨道的有效倾斜角有关的精确公式仅针对赤道和极性轨道而闻名。在这里，我们为位于这些极限之间的非试样轨道提供了精确的公式。对于黑洞的给定旋转参数，有一个临界倾斜角，其中有四个无效的光子轨道，其中两个在外部区域。在临界角度，这些轨道的半径明确发现。我们还为任何轨道提供了近似但非常准确的公式。为了达到这些分析溶液，我们仔细研究了用于无效球形大地测量的半径中的六个多项式。
Exact formulas relating the radii of the spherical photon orbits to the black hole's rotation parameter and the effective inclination angle of the orbit have been known only for equatorial and polar orbits up to now. Here we provide exact formulas for nonequatorial orbits that lie between these extreme limits. For a given rotation parameter of the black hole, there is a critical inclination angle below which there are four null photon orbits two of which are in the exterior region. At the critical angle, the radii of these orbits are explicitly found. We also provide approximate but very accurate formulas for any orbit. To arrive at these analytical solutions, we carefully study the sextic polynomial in the radius that arises for null spherical geodesics.
