Gravitational Imprints of Axion Clouds on Black-Hole Orbital Dynamics

Abstract

Black holes of primordial or astrophysical origin immersed in axion dark matter provide a natural laboratory for exploring the interplay between compact objects and ultralight scalar fields. While previous studies have primarily focused on superradiance and horizon-scale phenomena, the gravitational response of the surrounding axion distribution has received comparatively little attention. We investigate the dynamics of particles orbiting Schwarzschild and Kerr primordial black holes embedded in scalar-field dark matter halos. Using first-order perturbation theory, we show that the ambient halo redistributes the gravitationally bound axion cloud, shifting the characteristic radius of the gravitational atom. Numerical integrations of timelike geodesics demonstrate that the maximum orbital response consistently occurs at this perturbed radius, establishing a direct correspondence between the microscopic structure of the axion wavefunction and the macroscopic dynamics of orbiting particles. Our results identify a new purely gravitational signature of scalar-field dark matter around primordial black holes and provide a framework for probing mixed axion--primordial black hole dark matter scenarios.