本篇論文研究在帶電的萊斯納-諾德斯特洛姆黑洞幾何背景時空下自發性的粒子成對產生。在這種背景下的粒子成對生主要藉由與重力場作用``Hawking radiation'，或是與電磁場交互作用``Schwinger mechanism'產生。背景的電場和幾何間存在交互作用，因此這兩者對於粒子成對產生的效應也是密不可分的。在極限或接近極限兩種情況，RN黑洞背景中成對產生率的解析型式可藉由加入兩種邊界條件得出。所考慮的這個系統等價於在AdS2×S2背景幾何中加入一個測試用的帶電純量場。已知在極限黑洞下不會發生Hawking radiation，所以在這種背景下的粒子成對產生是藉由Schwinger mechanism來達成。這個黑洞因此損失了電荷，而從極限黑洞變成接近極限的黑洞，這個時候Hawking radiation和Schwinger mechanism將會共同主導粒子產生的機制。我們發現在偏離但接近極限的黑洞背景下的粒子產生率比在極限黑洞下還低。這是因為此時黑洞的表面重力增加在加強Hawking radiation之外，也會抵消電場的排斥力效應，造成Schwinger pair production被大幅的抑制。這兩種粒子成對產生機制無法單純由引用本文所介紹的邊界條件來作區別。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 becausethe increased surface gravity which enhance Hawking radiation will compete the compelling electric force, and lower the Schwinger pair production rate. Since the increasein 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.
