Quantum Electrodynamics in the Gravitational Field of a Cosmic String

We evaluate the cross section for electron-positron pair production by a single high energy photon in the space-time of a static, straight cosmic string. Energy and momentum conservation precludes this process in empty Minkowski space. It happens around a cosmic string, in spite of the local flatness of the metric, as a consequence of the conical structure of space. Previous results based on a simplified model with scalar fields are here extended to the realistic QED case. Analytic expressions are found in three different regimes: near the threshold, at energies much larger than the electron rest mass M, and at ultrahigh energies, much larger than $M\mathrm{/}\delta$, with $\delta$ the string mass per unit length in Planck units.