Formation of primordial black holes by cosmic strings

We calculate the density of primordial black holes formed by cosmic strings. When these black holes evaporate due to Hawking radiation, they produce $\gamma$ bursts. We find that comparison with observations of the $\gamma$ burst and $\gamma$ background yields a new nontrivial upper limit for the string linear mass density. Our result is in good agreement with that found by Hawking. However, we use a quite different method to estimate the probability of black-hole formation. It should be mentioned that the adoption of a measure in the space of the parameter describing the form of loops is the key point. We present two reasonable choices, but the physical measure may be very different, so quantitative results may be changed, while qualitative conclusions remain valid.