Gravitational Waves from Extreme-Mass-Ratio Systems in Astrophysical Environments

: We establish a generic, fully relativistic formalism to study gravitational-wave emission by extreme-mass-ratio systems in spherically symmetric, nonvacuum black hole spacetimes. The potential applications to astrophysical setups range from black holes accreting baryonic matter to those within axionic clouds and dark matter environments, allowing one to assess the impact of the galactic potential, of accretion, gravitational drag, and halo feedback on the generation and propagation of gravitational waves. We apply our methods to a black hole within a halo of matter. We find fluid modes imparted to the gravitational-wave signal (a clear evidence of the black hole fundamental mode instability) and the tantalizing possibility to infer galactic properties from gravitational-wave measurements by sensitive, low-frequency detectors.