Key points are not available for this paper at this time.
Extreme-mass-ratio inspirals (EMRIs) are one of the key targets for future space-based gravitational wave detectors, such as LISA. The scientific potential of these sources can only be fully realized with fast and accurate waveform models. In this work, we extend the fastemriwaveform (few) framework by providing fully relativistic waveforms at adiabatic order for circular, equatorial orbits in Kerr spacetime, for mass ratios up to 10^-3. We investigate the significance of including relativistic corrections in the waveform for both vacuum and nonvacuum environments. Specifically, we develop relativistic nonvacuum EMRI waveforms including two different environmental effects in the EMRI waveforms: power-law migration torques and superradiance scalar clouds. For EMRIs in vacuum, we find that nonrelativistic waveforms incorrectly estimate the predicted source's horizon redshift by approximately 35% error. Our analysis shows that incorporating relativistic corrections enhances constraints on accretion disks, modeled through power-law torques, and improves the constraints on disk parameter estimates (error 8%), representing a significant improvement over previous estimates. Additionally, we assess the evidence for models in a scenario where ignoring the accretion disk biases the parameter estimation, reporting a log₁₀ Bayes factor of 1. 1 in favor of the accretion disk model. In a fully relativistic setup, we also estimate the parameters of superradiant scalar clouds with relative errors 0. 3% for the scalar cloud's mass. These results demonstrate that incorporating relativistic effects is essential for Laser Interferometer Space Antenna science objectives with EMRIs.
Khalvati et al. (Mon,) studied this question.