**Publication date:** Dec 2007

**Abstract:**

Change of sign of the LNRF-velocity gradient has been found for

accretion discs orbiting rapidly rotating Kerr black holes with spin a

> 0.9953 for Keplerian discs and a > 0.99979 for marginally

stable thick discs. Such a "humpy" LNRF-velocity profiles occur just

above the marginally stable circular geodesic and could be related to

oscillations of accretion discs. The frequency of such "hump"-induced

oscillations can be identified with the maximal rate of change of the

orbital velocity within the "humpy" profile. Therefore, we introduce an

extended orbital resonance model (EXORM) of quasiperiodic oscillations

(QPOs) assuming non-linear resonant phenomena between oscillations with

the orbital epicyclic frequencies and the humpy frequency defined in a

fully general relativistic way. The EXORM is developed for both

Keplerian discs and perfect-fluid tori where the approximation of

oscillations with epicyclic frequencies is acceptable. Clearly, the

EXORM could be applied to the near-extreme Kerr black hole systems

exhibiting relatively complex QPO frequency patterns. Assuming a

Keplerian disc, it can be shown that in the framework of the EXORM, all

the QPOs observed in the microquasar GRS 1915+105 could be explained,

while it is not possible in the case of QPOs observed in the Galactic

Centre source Sgr A*.

**Authors:**

Stuchlík, Zdeněk; Slaný, Petr; Török, Gabriel;