Gravitational floating orbits around hairy black holes

We show that gravitational floating orbits may exist for black holes with rotating hairs. These black hole hairs could originate from the superradiant growth of a light axion field around the rotating black holes. If a test particle rotates around the black hole, its tidal field may resonantly trigger the dynamical transition between a co-rotating state and a dissipative state of the axion cloud. A tidal bulge is generated by the beating of modes, which feeds angular momentum back to the test particle. Following this mechanism, an extreme-mass-ratio-inspiral (EMRI) system, as a source for LISA, may face delayed merger as the EMRI orbit stalls by the tidal response of the cloud, until the cloud being almost fully dissipated. If the cloud depletes slower than the average time separation between EMRI mergers, it may lead to interesting interaction between multiple EMRI objects at comparable radii. Inclined EMRIs are also expected to migrate towards the black hole equatorial plane due to the tidal coupling and gravitational-wave dissipation. Floating stellar-mass back holes or stars around the nearby intermediate-mass black holes may generate strong gravitational-wave emission detectable by LISA.