Thermal interpretation of Schwinger effect in near-extremal RN black hole

Abstract

We propose a thermal interpretation of the Schwinger effect for charged spinless scalars and spin-1/2 fermions in an extremal and near-extremal Reissner-Nordström (RN) black hole. The emission of charges has the distribution with an effective temperature determined by the Davies-Unruh temperature for accelerating charges by the electric field and the scalar curvature of AdS2 from the near-horizon geometry AdS2 × S2. We find a charge bound for the extremal micro-black hole to remain stable against the Schwinger emission in analogy with the Breitenlohner-Freedman bound for the AdS space. In the in-out formalism, we find the one-loop QED effective action consistent with the vacuum persistence and interpret the vacuum persistence as the leading Schwinger effect and the effect of a charged vacuum of the Coulomb field.