Speaker
Description
Tidal Love numbers (TLNs) encode the deformability of compact objects under external tidal fields and leave observable imprints in gravitational wave signals. While black hole TLNs vanish in vacuum general relativity, the presence of surrounding matter can alter this picture. This talk presents a study of the axial (magnetic) TLNs of a Schwarzschild black hole embedded in a spherically symmetric dark matter distribution, modeled as an anisotropic fluid with three astrophysically motivated density profiles: Einasto, Hernquist, and NFW. Analytic closed-form expressions are derived via a small-compactness expansion and benchmarked against direct numerical integration of the perturbation equations. A key finding is that profiles without compact support generically produce logarithmic terms in the asymptotic expansion of the perturbation variable, obstructing the standard tidal matching procedure and pointing to the subtleties of defining tidal observables for black holes dressed by matter. The broader implications for gravitational wave detectability with next-generation detectors are discussed, highlighting dark matter environments around compact objects as a promising multi-messenger target.