Self-consistent adiabatic inspiral and transition motion

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 Painleve transcendent equation of the first kind. Using an asymptotically matched expansions scheme, we consistently match the quasi-circular adiabatic inspiral with the transition motion. The matching requires 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.