Ultra-strong Elelctric Fields and Vacuum Breakdown: Search for an Astrophysical Scenario

In some models of $\gamma$-ray bursts super-strong electric fields ($E\sim 10^{14} {\rm statvolt cm}^{-1}$) have been surmized. Such large fields may provide copious pair production through vacuum polarization. Here we examine various astrophysical scenarios where huge electric field can be present. It is shown that when the conditions for quantistic vacuum breakdown are met, pair creation through conventional processes is likely to be always more important. Although of great physical interest, quantum pair production seems therefore of little astrophysical relevance.