The circular loop equation of a cosmic string with time-varying tension

TL;DR

This paper derives the equation governing circular cosmic string loops with time-varying tension and finds conditions under which these loops avoid collapsing into black holes, depending on the tension's time dependence.

Contribution

It introduces a new equation for cosmic string loops with time-dependent tension and analyzes their collapse conditions in different spacetimes.

Findings

Loops with tension depending on a power of time do not form black holes below a critical power.

The derived equations apply to Minkowski and Robertson-Walker spacetimes.

Time-varying tension influences the stability and evolution of cosmic string loops.

Abstract

The equation of circular loops of cosmic string with time-dependent tension is studied in the Minkowski spacetime and Robertson-Walker universe. We find that, in the case where the tension depends on some power of the cosmic time, cosmic string loops with time-varying tension should not collapse to form a black hole if the power is lower than a critical value.