We derive closed formulas for the mass M and spin a parameters of a Kerr black hole in terms of a minimal quantity of observational data: the red‐/blue‐shifts of photons emitted by massive particles (stars) moving on geodesics around the black hole and their respective orbital radius. It turns out that for a single star orbiting the black hole, we need a minimal set of four observational measurements to analytically determine both parameters. Indeed, given a set of two (three) stars revolving around the black hole, these formulas involve just eight (twelve) observational data.

中文翻译：

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关于克尔黑洞质量和自旋的红移和轨道参数的一般相对论公式

我们推导了质量M的封闭公式，并根据最少的观测数据旋转了Kerr黑洞的参数：大质量粒子（恒星）在围绕黑洞的测地线上移动的光子的红/蓝位移和它们各自的轨道半径。事实证明，对于绕黑洞运行的单个恒星，我们需要最少的四个观测值集来解析地确定两个参数。的确，给定两（三）颗围绕黑洞旋转的恒星，这些公式仅涉及八（十二）个观测数据。