Stone Skipping Black Holes in Ultralight Dark Matter Solitons

The orbit of a black hole moving within an ultralight dark matter (ULDM) soliton is naively expected to decay due to dynamical friction. However, in isolated near-circular soliton--black-hole systems, single black holes can undergo ``stone skipping'', with their orbital radius varying quasi-periodically. We show that, within this controlled setting, stone skipping is driven by a dipole excitation of the soliton. We model the effect as a resonance in a forced, damped harmonic oscillator, demonstrating that the coherent response of the soliton can significantly modify the dynamics of objects orbiting within it. In this regime, a dipole perturbation of a soliton can modify inspiral timescales when the black hole masses are significantly smaller than the soliton mass, with implications for supermassive black hole dynamics, the final parsec problem and gravitational wave observations in a ULDM cosmology.