**Publication date:** Feb 2008

**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:**

Stuchlik, Zdenek; Slany, Petr; Torok, Gabriel;