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

— In some models of γ-ray bursts super-strong electric fields (E ∼ 10 14 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. Pair production by quantum vacuum polarization (or vacuum breakdown, VB in the following) has been invoked by some authors (e.g. [1, 2, 3, 4]) in connection with the modeling of γ-ray bursts (GRBs). However little attention was paid to the astrophysical picture where the VB condition might occur. Here we examine various astrophysical scenarios where large electric field may be expected and explore the possibility of inducing the VB. In section 2 large B-field pulsars (" magnetars ") are considered, following a proposal by Usov [5]. In section 3 the case of a magnetic field frozen in the matter accreting onto black hole is examined, and in section 4 we consider the E-field due to charge separation, induced by a flash of radiation propagating through a plasma, in the context of the GRB scenario proposed by Lieu et al [2]. Since we are interested in a preliminary assessment of the relevance of quantum pair production under astrophysical conditions, we assume that the condition for vacuum breakdown (Klein instability) is given by the semi-classical expression (see e.g. [6]) eEλ c = 2m e c 2 (1)