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.;