2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/211110The relativistic accretion rate of dark matter by a black hole is revisited. Under the assumption that the phase space density indicator, $Q=ρ_{\infty}/σ^3_{\infty}$, remains constant during the inflow, the derived accretion rate can be higher up to five orders of magnitude than the classical accretion formula, valid for non-relativistic and non-interacting particles, when typical dark halo conditions are considered. For these typical conditions, the critical point of the flow is located at distances of about 30-150 times the horizon radius. Application of our results to black hole seeds hosted by halos issued from cosmological simulations indicate that dark matter contributes to no more than ~10% of the total accreted mass, confirming that the bolometric quasar luminosity is related to the baryonic accretion history of the black hole.7 pages, 6 figures. Accepted for publication in Phys.Rev.DAstrophysicstext