**Publication date:** Apr 2007

**Abstract:**

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

accretion discs orbiting a rapidly rotating Kerr black hole with spin a

> 0.9953 (Keplerian discs) and a > 0.99979 (marginally stable

thick discs). The maximal positive rate of change of the orbital

velocity in terms of the proper radial distance introduces a locally

defined critical frequency characterizing any processes in the disc

capable to excite possible oscillations connected with the velocity

hump. Comparing the "humpy frequency" related to distant observers with

the epicyclic frequencies, we shall show that in Keplerian discs

orbiting extremely rapid Kerr holes (1-a < 10-4) the

ratio of the epicyclic frequencies and the humpy frequency is constant,

i.e., independent of spin, being ˜3:2 for the radial epicyclic

frequency and ˜11:2 for the vertical epicyclic frequency. For

black holes with a ≈ 0.996, i.e., when the resonant phenomena with

ratio 3:1 between the vertical and radial epicyclic oscillations occur

near the radius of the critical humpy frequency, there is ratio of the

radial epicyclic and the humpy frequency ˜1:12, i.e., the

critical frequency is close to the low-frequency QPOs related to the

high-frequency QPOs in such spacetimes. For a > 0.996 the resonant

orbit with the ratio 4:1 between the vertical and radial epicyclic

oscillations occurs in the region of the hump. In the case of thick

discs, the situation is more complex due to the dependence on the

distribution of the specific angular momentum L characterizing the disc

rotation. For L = const tori and (1-a) < 10-6 the

frequency ratios of the humpy frequency and the epicyclic frequencies

are again constant and independent of both the spin and the specific

angular momentum.

**Authors:**

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