Probing the quantum nature of black holes with ultra-light boson environments

Quantum black holes (BHs), thought of as an excited multilevel system, can be effectively modelled by replacing an event horizon with a partially reflective membrane. This emergent feature affects their interaction with hosting environments, with the most pronounced effects happening for particles with mass~$m_{\rm p}\lesssim (10 M_{\odot}/M)\,10^{-11}\mathrm{\,eV}$, where~$M$ is the BH mass. We show that ultra-light bosons -- a viable dark matter candidate -- can be used to probe the quantum nature of BHs. We derive analytical expressions for the accretion rate and dynamical friction acting on exotic compact objects moving through an ultra-light scalar field, finding that while the accretion rate is sensitive to the quantum BH's reflectivity, the dynamical friction is the same as for classical BHs. We then use these expressions to estimate the orbital dephasing in the inspiralling of different binaries in the Laser Interferometer Space Antenna (LISA) band. Our results indicate that LISA may be able to discriminate quantum from classical BHs through their different accretion rates.