The Circular Loop Equation of a Cosmic String with Time-Varying Tension in de Sitter Spacetimes

Abstract

In this work the equation of circular loops of cosmic string possessing time-dependent tension is studied in the de Sitter spacetime. We find that the cosmic string loops with initial radius r(t0)>0.707L, L de Sitter radius, should not collapse to form a black hole. It is also found that in the case of r(t0)<0.707L a loop of cosmic string whose tension depends on some power of cosmic time can not become a black hole if the power is lower than a critical value which is associated with the initial size of the loop. Our research gives rise to some important corrections to the conclusion in the case of loops of cosmic string with constant tension in the same background.