Extreme mass-ratio inspirals around a spinning horizonless compact object

Extreme mass-ratio inspirals (EMRIs) detectable by the Laser Interferometer Space Antenna are unique probes of the nature of supermassive compact objects. We compute the gravitational-wave signal emitted by a stellar-mass compact object in a circular equatorial orbit around a Kerr-like horizonless supermassive object defined by an effective radius and a reflectivity coefficient. The Teukolsky equations are solved consistently with suitable (frequency-dependent) boundary conditions, and the modified energy and angular-momentum fluxes are used to evolve the orbital parameters adiabatically. The gravitational fluxes have resonances corresponding to the low-frequency quasinormal modes of the central object, which can contribute significantly to the gravitational-wave phase. Overall, the absence of a classical event horizon in the central object can affect the gravitational-wave signal dramatically, with deviations even larger than those previously estimated by a model-independent analysis of the tidal heating. We estimate that EMRIs could potentially place the most stringent constraint on the reflectivity of supermassive compact objects at the remarkable level of $\mathcal{O}({10}^{\ensuremath{-}6})%$ and would allow one to constrain various models which are not ruled out by the ergoregion instability. In particular, an EMRI detection could allow one to rule out (or provide evidence for) signatures of quantum black-hole horizons with Boltzmann reflectivity. Our results provide motivation for performing rigorous parameter estimation to assess the detectability of these effects.