Cosmic String in the BTZ Black Hole Background with Time-Dependant Tension

In this paper, we study the equation of circular loops with time-dependant tension in the BTZ black hole background. We obtain various cases where cosmic string loops finally collapse to form black holes. Also, we study effect of the BTZ black hole mass and angular momentum on the evolution of cosmic string loops. We find the critical values of initial radii as a limit for the cosmic string loops collapsing to form black holes.