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Primordial black holes may have been produced in the early stages of thethermal history of the Universe after cosmic inflation. If so, dark matter inthe form of elementary particles can be subsequently accreted around theseobjects, in particular when it gets non-relativistic and further streams freelyin the primordial plasma. A dark matter mini-spike builds up gradually aroundeach black hole, with density orders of magnitude larger than the cosmologicalone. We improve upon previous work by carefully inspecting the computation ofthe mini-spike radial profile as a function of black hole mass, dark matterparticle mass and temperature of kinetic decoupling. We identify a phase-spacecontribution that has been overlooked and that leads to changes in the finalresults. We also derive complementary analytical formulae using convenientasymptotic regimes, which allows us to bring out peculiar power-law behaviorsfor which we provide tentative physical explanations.

In-depth analysis of the clustering of dark matter particles around primordial black holes I: density profiles