Chaotic signatures in extreme-mass-ratio systems surrounded by bosonic environments

Abstract

Extreme-mass-ratio inspirals are key gravitational-wave sources for testing strong gravity and the environments of massive black holes. While orbital motion in Kerr black hole spacetimes is integrable, realistic black holes may be surrounded by environments that break integrability. We investigate conservative orbital dynamics around rotating black holes surrounded by scalar clouds using fully nonlinear numerical solutions and an analytical post-Newtonian model. Poincaré sections and rotation curves reveal finite-width resonant islands, providing evidence for non-integrability even when the cloud carries only a small fraction of the black-hole mass. We show that the post-Newtonian description reproduces the dominant resonance and its island width for weak clouds, but underestimates the width in the configurations with stronger, more compact clouds examined here. Moreover, we find that for a scalar cloud as massive as the black hole, the phase space exhibits wider resonant islands as well as scattered layers indicative of chaotic motion. Together with earlier work, these results show that environmental effects can generically break the integrability of geodesic motion, motivating further study of resonance crossings and their gravitational-wave signatures once radiation reaction is included.