We consider the high spin expansion for the null geodesics in the Kerr spacetime. We expand the null geodesic equation successively to higher orders in deviation from extremity. Via the method of matched asymptotic expansion, the radial integrals are obtained analytically. It turns out that the analytic expressions are very sensitive to the value of the shifted Carter constant $q$. We show that for a large $q$, the analytic expressions can be used to study observational electromagnetic signatures for astrophysical black holes like M87*. However, for a small $q$, the high spin expansion method can only be applied to (near-) extreme black holes.

中文翻译：

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零测地线的高自旋扩展

我们考虑克尔时空空测地线的高自旋膨胀。我们将零测地线方程依次扩展到偏离极值的更高阶。通过匹配渐近展开法，解析得到径向积分。事实证明，解析表达式对移位的卡特常数 $q$ 的值非常敏感。我们表明，对于大 $q$，解析表达式可用于研究像 M87* 这样的天体物理黑洞的观测电磁特征。然而，对于较小的 $q$，高自旋膨胀方法只能应用于（近）极端黑洞。