**Publication date:** Mar 2014

**Abstract:**

Small oscillations of current-carrying string loops around stable

equilibrium positions corresponding to minima of the effective potential

in the equatorial plane of the Kerr black holes are studied using the

perturbation method. In the lowest approximation, two uncoupled harmonic

oscillators are obtained that govern the radial and vertical

oscillations; the higher-order terms determine nonlinear phenomena and

transition to chaotic motion through quasiperiodic stages of the

oscillatory motion. The radial profiles of frequencies of the radial and

vertical harmonic oscillations that are also relevant in the

quasiperiodic stages of the oscillatory motion are given, and their

properties, independent of the spin of the black holes and the angular

momentum and tension of the string loops, are determined. It is shown

that the radial profiles differ substantially from those corresponding

to the radial and vertical frequencies of the geodetical epicyclic

motion; however, they have the same mass scaling and their magnitude is

of the same order. Therefore, we are able to demonstrate that, assuming

the relevance of resonant phenomena of radial and vertical string-loop

oscillations at their frequency ratio 3∶2, the oscillatory frequencies

of string loops can be related to the frequencies of the twin high-

frequency quasiperiodic oscillations (HF QPOs) observed in the

microquasars GRS 1915+105, XTE 1550-564, GRO 1655-40. We can conclude

that oscillating current-carrying string loops have to be considered as

one of the possible explanations of the HF QPOs occurring in the field

of compact objects.

**Authors:**

Stuchlík, Z.; Kološ, M.;