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 non-linear phenomena and transition to chaotic motion through quasi-periodic stages of the oscillatory motion. The radial profiles of frequencies of the radial and vertical harmonic oscillations that are relevant also in the quasi-periodic stages of the oscillatory motion are given, and their properties in dependence on 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 relevance of resonant phenomena of the radial and vertical string-loop oscillations at their frequency ratio 3:2, the oscillatory frequencies of string loops can be well related to the frequencies of the twin high-frequency quasi-periodic 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.
Z. Stuchlik and M. Kolos
Thu, 13 Mar 14