||The spontaneous pair production in a charged geometrical background is studied. In this background, pair productions are driven by either gravity (Hawking radiation) or electromagnetic force (Schwinger mechanism). The electric ﬁeld and geometry are coupled together to implement particle productions. The analytically obtained pair production rate in a (near) extremal Reissner-Nordstr¨om (RN) black hole is done by applying two equivalent boundary conditions. The present system is equivalent to a charged scalar ﬁeld probed into a AdS 2 × S 2 geometry. It is known that in the extremal RN geometry no Hawking radiation will happen, so the pair production is totally caused by Schwinger mechanism. After the black hole losses its charge via Schwinger mechanism, the extremal black hole becomes near-extremal, and Hawking radiation together with Schwinger pair production are responsible for particle pro-|
duction rate now. It is shown that the particle production rate in the near-extremal RN black holes are lower than that in the extremal RN black holes. This is because
the increased surface gravity which enhance Hawking radiation will compete the compelling electric force, and lower the Schwinger pair production rate. Since the increase
in Hawking pair production can not compensate the decrease in Schwinger pair production, the particle production rate in the near-extremal RN geometry is lower than the extremal case. Therefore, Hawking radiation and Schwinger pair production are indistinguishable by simply applying these boundary conditions.
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