We study the Schwinger effect in near-extremal Reissner-Nordström (RN) black holes with electric and/or magnetic charges in the (Anti-) de Sitter (AdS) space. The formula for the Schwinger effect takes a universal form for near-extremal black holes with the near-horizon geometry of AdS2×S 2 and with the proper radii for the AdS2 space and the two-sphere S 2 , regardless of the asymptotically flat or (A)dS space. The asymptotic AdS boundary enhances and the dS boundary suppresses the Schwinger effect and the small radius of the AdS (dS) space reinforces the enhancement and suppression.PACS numbers: 04.62.+v, 04.70.Dy,
I. INTRODUCTIONQuantum fluctuations spontaneously create particle pairs from the vacuum unless there exists an external mechanism preventing annihilation of pairs. The event horizon of a black hole casually separates pairs into the interior and the exterior and the black hole emits all species of particles [1]. A sufficiently strong electric field separates charged pairs and accelerates them in opposite directions, the so-called Schwinger pair production [2, 3]. The Hawking radiation and Schwinger effect are consequence of the nonperturbative effects of quantum field theory.The Hawking radiation and Schwinger effect both act as the emission channels of charged pairs from charged black holes. Hawking radiation obeying the Bose-Einstein or Fermi-Dirac distribution with the Hawking temperature emits charges with a chemical potential of Coulomb potential on the horizon. Though the Hawking radiation from (near-) extremal black holes is exponentially suppressed due to vanishing Hawking temperature, the Schwinger mechanism triggers the emission of charges. The Schwinger effect has been extensively studied for (near-) extremal Reissner-Nordström (RN) black holes [4,5], Kerr-Newman (KN) black holes [6], dyonic KN black holes [7] (for review and references, see Ref.[8]). The Schwinger fermion production has also been studied for charged black holes in the (A)dS space [9][10][11].Primordial black holes have been studied from cosmology and astrophysics [12][13][14]. It was argued that dynonic extremal black holes are stable against Hawking radiation [15]. Black holes of planck scale are stable quantum mechanically and can be a candidate for dark matter [16]. The Schwinger effect from (near-) extremal RN and dyonic RN black holes in (Anti-) de Sitter space is interesting theoretically and cosmologically since the asymptotic (A)dS boundary affects the near-horizon geometry of (near-) extremal black holes [17]. In particular, the expanding early universe described by a dS space drastically changes the property and evolution of charged black holes.We study the effect of the asymptotic (A)dS boundary on Schwinger pair production in (near-) extremal RN black holes. The extremal RN-(A)dS black holes are obtained by degenerating the event horizon and the causal horizon while keeping the cosmological horizon separately from the black hole horizon. The near-horizon region of (near-) extremal RN-(A)dS black holes has the ...