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Using the simple but robust model of a shell of dark matter (DM) around aSchwarzschild black hole (BH), represented by the mass ratio of the shell andBH ${\Delta}M/M$, the shell extension ${\Delta}r_s$ and its inner radius $r_s$,we study the influence of DM on the spacetime structure and geodesic motion,and provide a classification of the BH+DM shell spacetimes according to theproperties of the stable circular geodesics governing Keplerian disks. We focusour attention on the epicyclic motion around circular geodesics that can berelated to observational phenomena in X-ray radiation from Keplerian accretiondisks, assumed to be influenced by the DM shell only gravitationally. We givethe frequencies of the orbital and epicyclic motions and discuss theirproperties in terms of the parameters governing the DM shell. Using thefrequencies in relevant variants of the standard geodesic model ofhigh-frequency quasiperiodic oscillations (HF QPOs), we test the role of DM byfitting the HF QPO data from some microquasars and active galactic nuclei withsupermassive BHs where no variant of the geodesic model applied in the standardvacuum BH background is able to explain the data. We thus provide a robustreview of the applicability of the geodesic model of HF QPOs, and also providelimits on the amount of DM around a BH. We demonstrate that the geodesic modelcould be well applied to most observations of active galactic nuclei, withstrong restrictions on the amount of invisible matter around BHs.

Geodesic Model of HF QPOs Tested for Black Holes in Spacetimes Reflecting the Effect of Surrounding Dark Matter