Note on the Kerr Spinning-Particle Equations of Motion

We implement a probe counterpart of Newman-Janis algorithm, which Wick rotates the all-orders geodesic deviation equation into a part of exact spinning-particle equations of motion. Consequently, the gravitational dynamics of the Kerr black hole in its point-particle effective theory is completely constrained in the self-dual sector for a hidden symmetry, implying the spin exponentiation of same-helicity gravitational Compton amplitudes to all multiplicities.