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

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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.
8 pages, 3 figures. accepted by Modern Physics Letters A

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