Current-carrying string loops in black-hole spacetimes with a repulsive cosmological constant

Abstract

Current-carrying string loop dynamics in Schwarzschild-de Sitter spacetimes characterized by the cosmological parameter $\ensuremath{\lambda}=\frac{1}{3}\ensuremath{\Lambda}{M}^{2}$ is investigated. With attention concentrated to the axisymmetric motion of string loops it is shown that the resulting motion is governed by the presence of an outer tension barrier and an inner angular momentum barrier that are influenced by the black hole gravitational field given by the mass $M$ and the cosmic repulsion given by the cosmological constant $\ensuremath{\Lambda}$. The gravitational attraction could cause capturing of the string having low energy by the black hole or trapping in its vicinity; with high enough energy, the string can escape (scatter) to infinity. The role of the cosmic repulsion becomes important in vicinity of the so-called static radius where the gravitational attraction is balanced by the cosmic repulsion---it is demonstrated both in terms of the effective potential of the string motion and the basin boundary method reflecting its chaotic character, that a potential barrier exists along the static radius behind which no trapped oscillations may exist. The trapped states of the string loops, governed by the interplay of the gravitating mass $M$ and the cosmic repulsion, are allowed only in Schwarzschild-de Sitter spacetimes with the cosmological parameter $\ensuremath{\lambda}<{\ensuremath{\lambda}}_{\mathrm{trap}}\ensuremath{\sim}0.00497$. The trapped oscillations can extend close to the radius of photon circular orbit, down to ${r}_{\mathrm{mt}}\ensuremath{\sim}3.3M$.