Context : At least four high-frequency quasiperiodic oscillations ( QPOs ) at frequencies 41 Hz , 67 Hz , 113 Hz , and 167 Hz were reported in a binary system GRS 1915+105 hosting near-extreme Kerr black hole with a dimensionless spin a > 0.98 .

Aims : We attempt to explain all four observed frequencies by an extension of the standard resonant model of epicyclic oscillations .

Methods : We use the idea of oscillations induced by the hump of the orbital velocity profile ( related to locally non-rotating frames–LNRF ) in discs orbiting near-extreme Kerr black holes , which are characterized by a “ humpy frequency ” \nu _ { h } , that could excite the radial and vertical epicyclic oscillations with frequencies \nu _ { r } , \nu _ { v } .
Due to non-linear resonant phenomena , the combinational frequencies are allowed as well .

Results : Assuming mass M = 14.8 M _ { \odot } and spin a = 0.9998 for the GRS 1915+105 Kerr black hole , the model predicts frequencies \nu _ { h } = 41 Hz , \nu _ { r } = 67 Hz , \nu _ { h } + \nu _ { r } = 108 Hz , and \nu _ { v } - \nu _ { r } = 170 Hz corresponding quite well to the observed ones .

Conclusions : For black-hole parameters being in good agreement with those given observationally , the forced resonant phenomena in non-linear oscillations , excited by the ” hump-induced ” oscillations in a Keplerian disc , can explain high-frequency QPOs in near-extreme Kerr black-hole binary system GRS 1915+105 within the range of observational errors .