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The classical no‐hair theorems tell us that, under standard assumptions, black holes (BH) cannot support nontrivial scalar “hair”. However, Jacobson earlier noted (arXiv: 9905303) that even with a minimally coupled scalar, i.e. staying within GR, a BH can acquire scalar hair if the scalar field is time-dependent far from the BH. I will review the paper arXiv: 1904.12803 , where the authors systematically explore the scalar profile around the black hole for different scalar (dark matter) masses. While producing the 1/r profile in the small mass limit, consistent with Jacobson's result, the scalar field has a 1/r^{3/4} profile yielding a pile-up close to the horizon, while distinctive nodes occur for intermediate masses.
Related reference: arXiv:1904.12783