在本論文中，我們研究了近極端克爾-紐曼-德西特黑洞中的旋量粒子對產生。我們考慮兩種極端限制：內視界與外視界重合，以及外視界與宇宙視界重合，分別對應於冷黑洞與納里艾黑洞。透過座標轉換，我們推導了近極端冷黑洞與納里艾黑洞的近視界幾何，分別由AdS3 × S1/Z2與dS3 × S1/Z2所描述。 基於上述近視界幾何，我們選擇合適的四重標架並建立狄拉克方程。接著，我們對旋量場進行轉換並應用分離變數法來化簡狄拉克方程。然後，我們著重求解耦合的徑向或時間系統，此系統可進一步解耦為超幾何方程。利用玻戈留波夫變換，我們將近視界區域與漸近區域的入射、反射及透射模式相互關聯，由此得到粒子對產生的平均數。 我們的結果表明粒子對產生的平均數是由霍金輻射與施溫格效應共同決定的。對於冷黑洞來說，旋轉參數抑制了粒子對產生的平均數。而對於納里艾黑洞來說，旋轉參數則增強了粒子對產生的平均數。我們比較了這兩種情況並證明粒子對產生的平均數滿足互逆關係。這種關係源自於穿隧和散射等量子過程。;In this thesis， we investigate spinor pair production in near-extremal Kerr-Newman-de Sitter (KNdS) black holes. We consider two extremal limits: the coincidence of the inner and outer horizons， and the coincidence of the outer and cosmological horizons， corresponding to the cold and Nariai black holes， respectively. Applying coordinate transformations， we derive the near-horizon geometries of near-extremal cold and Nariai black holes， which are described by AdS3 × S1/Z2 and dS3 × S1/Z2， respectively. Based on these near-horizon geometries， we choose the appropriate tetrads and formulate the Dirac equation. Next， we perform a transformation of the spinor field and apply the method of separation of variables to reduce the Dirac equation. We then focus on solving the coupled radial or time system， which can be further decoupled into hypergeometric equations. Using the Bogoliubov transformation， we relate the incident， reflected， and transmitted modes in the near-horizon region to those in the asymptotic region， from which the mean number of pair production is obtained. Our results show that the mean number of pair production is determined by both Hawking radiation and the Schwinger effect. For cold black holes， the rotation parameter suppresses pair production， while for Nariai black holes， it enhances pair production. We compare both cases and show that the mean number of pair production satisfies a reciprocal relation. This relation arises from the quantum processes of tunneling and scattering.
