Dark matter distributions around Schwarzschild-like black holes in bumblebee and Kalb-Ramond models

Abstract: A central black hole can attract a dark matter cluster and generate a spike in the density profile, as demonstrated by detailed analysis of Schwarzschild and Kerr black holes in the past. Do different black holes attract dark matter differently? To get a fair answer to this question, we customize a relativistic framework to grow general static spherical black holes in dark matter halos and investigate how deviations from the Schwarzschild geometry modify the dark matter spike for the first time. The framework is applied to a class of Schwarzschild-like black hole solutions in Lorentz-violated gravity models -- one in the bumblebee model and two in the Kalb-Ramond model. For these black holes, the answer is no if initially the dark matter has a constant distribution, but the answer is yes if it has a Hernquist profile initially.