The transition motion of a point particle around the last stable orbit of Kerr is described at leading order in the transition-timescale expansion. Taking systematically into account all self-force effects, we prove that the transition motion is still described by the Painlevé transcendent equation of the first kind. Using an asymptotically matched expansions scheme, we consistently match the quasicircular adiabatic inspiral with the transition motion. The matching requires us to take into account the secular change of angular velocity due to radiation reaction during the adiabatic inspiral, which consistently leads to a leading-order radial self-force in the slow timescale expansion.

中文翻译：

---

自洽绝热吸气和过渡运动

点粒子围绕克尔的最后一个稳定轨道的跃迁运动在跃迁时间尺度扩展中以领先顺序描述。系统地考虑所有自力效应，我们证明过渡运动仍然由第一类 Painlevé 超越方程描述。使用渐近匹配的扩展方案，我们始终将准圆形绝热螺旋与过渡运动相匹配。匹配要求我们考虑在绝热螺旋过程中由于辐射反应引起的角速度的长期变化，这始终导致在缓慢的时间尺度膨胀中具有领先的径向自力。