Probing Dark Matter with Gravitational Waves: Spin-Modulated Dephasing from Black Holes in Halos

Abstract

We develop a novel analytical framework for constructing axisymmetric black hole spacetimes sourced by dark matter (DM) halos. Applying this to extreme mass ratio inspirals (EMRIs), we find that the DM induces a detectable gravitational-wave dephasing, scaling monotonically with the halo's compactness. Notably, BH spin significantly suppresses this dephasing, indicating that analyses neglecting rotation would overestimate DM signatures. Faithfulness calculations confirm that future space-borne detectors can robustly distinguish such DM environments, establishing EMRIs as a novel probe for galactic DM distributions.