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Dark matter density can be significantly enhanced by the supermassive blackhole at the galactic center, leading to a structure called dark matter spike.Dark matter spike may change the spacetime properties of black holes thatconstitute deviations from GR black holes. Based on these interestingbackground, we construct a set of solutions of black holes in a dark matterspike under the Newtonian approximation and full relativity. Combining the massmodel of M87, we study the quasinormal modes of black holes in the scalar fieldperturbation and compared the with Schwarzschild black hole. Besides, theimpacts of dark matter on the quasinormal mode of black holes have been studiedin depth. In particular, our results show that the impacts of dark matter spikeon the quasinormal mode of black holes can reach up to $10^{-4}$. These newfeatures from quasinormal mode of black holes under the Newtonian approximationand full relativity may provide some help for the establishment of the finaldark matter model, and provide a new thought for the indirect detection of darkmatter.

Probing black holes in a dark matter spike of M87 using quasinormal mode