**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;