Publication date: Oct 2012
Abstract:
We study motion of current-carrying string loops in the field of
braneworld spherically symmetric black holes and naked singularities.
The spacetime is described by the Reissner-Nordström geometry with
tidal charge b reflecting the non-local tidal effects coming from the
external dimension; both positive and negative values of the spacetime
parameter b are considered. We restrict attention to the axisymmetric
motion of string loops when the motion can be fully governed by an
appropriately defined effective potential related to the energy and
angular momentum of the string loops. In dependence on these two
constants of the motion, the string loops can be captured, trapped, or
can escape to infinity. In close vicinity of stable equilibrium points
at the centre of trapped states the motion is regular. We describe how
it is transformed to chaotic motion with growing energy of the string
loop. In the field of naked singularities the trapped states located off
the equatorial plane of the system exist and trajectories unable to
cross the equatorial plane occur, contrary to the trajectories in the
field of black holes where crossing the equatorial plane is always
admitted. We concentrate our attention to the so called transmutation
effect when the string loops are accelerated in the deep gravitational
field near the black hole or naked singularity by transforming the
oscillatory energy to the energy of the transitional motion. We
demonstrate that the influence of the tidal charge can be substantial
especially in the naked singularity spacetimes with b > 1 where the
acceleration to ultrarelativistic velocities with Lorentz factor γ
~ 100 can be reached, being more than one order higher in comparison
with those obtained in the black hole spacetimes.
Authors:
Stuchlík, Z.; Kološ, M.;