Thermal interpretation of Schwinger effect in near-extremal RN black hole
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 [Formula: see text] from the near-horizon geometry [Formula: see text]. 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 [Formula: see text] 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.