Extreme-Mass-Ratio Inspirals in Ultralight Dark Matter

Previous works have argued that future gravitational-wave detectors will be able to probe the properties of astrophysical environments where binaries coalesce, including accretion disks, but also dark matter structures. Most analyses have resorted to a Newtonian modeling of the environmental effects, which are not suited to study extreme-mass-ratio inspirals immersed in structures of ultralight bosons. In this Letter, we use relativistic perturbation theory to consistently study these systems in spherical symmetry. We compute the flux of scalar particles and the rate at which orbital energy is dissipated via gravitational radiation and depletion of scalars, i.e., dynamical friction. Our results confirm that the Laser Interferometer Space Antenna will be able to probe ultralight dark matter structures by tracking the phase of extrememass-ratio inspirals.