We extend the Ori-Thorne-Kesden procedure to consistently describe the non-quasi-circular transition around the ISCO from inspiral to plunge into a black hole of arbitrary spin, including near-extremal. We identify that for moderate or high spins the transition is governed by the Painlev\'e transcendent equation of the first kind while for extremely high spins it is governed by a self-similar solution to the Korteweg-de Vries equation. We match the transition solution at leading order in the high spin limit with the analytical quasi-circular inspiral in the near-horizon region. We also show that the central black hole of an extreme mass ratio binary has a near-extremality parameter that scales at least as the mass ratio due to superradiant gravitational wave emission, which excludes extremely high spins.

中文翻译：

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从螺旋转入高度旋转的黑洞

我们扩展了 Ori-Thorne-Kesden 程序，以一致地描述 ISCO 周围的非准圆形过渡，从螺旋到陷入任意旋转的黑洞，包括接近极值。我们发现，对于中等或高自旋，过渡由第一类 Painlev\'e 超越方程控制，而对于极高自旋，它由 Korteweg-de Vries 方程的自相似解控制。我们将高自旋极限的超前阶跃迁解与近地平线区域的解析准圆螺旋相匹配。我们还表明，由于超辐射引力波发射，极端质量比双星的中心黑洞具有近乎极端的参数，该参数至少与质量比成比例，不包括极高的自旋。