在1974年，霍金計算彎曲時空中一顆塌縮的恆星正在形成黑洞的量子效應發現黑洞像個黑體具有溫度 $T_H$ 的熱輻射。2005年，Robinson 和 Wilczek 提出在球對稱黑洞視界附近可藉由抵銷引力反常的方法來推導霍金輻射。在這篇論文中，我們把這樣的概念應用在五維的 uplifted Reissner-Nordstr/"om /(RN/) 黑洞。使用維度約化，我們發現在視界附近五維的 uplifted RN 黑洞作用量可以被/(1+1/)維帶有U/(1/) 電荷 $k$ 的有效作用量來描述。藉由Iso, Umetsu 和 Wilczek 所提出的分析方法，加上適當的邊界條件，我們可以證明五維的 uplifted RN 黑洞的霍金輻射可被量子反常所決定。

In 1974, Hawking calculated the quantum effect in curved spacetime from a collapsed
star which forms a black hole. He found that a black hole, similar to blackbody with
temperature, can emit thermal radiation. In 2005, Robinson and Wilczek proposed a
different viewpoint that the Hawking radiation, for the spherically symmetric black
holes, can be derived by the gravitational anomaly cancelation. The holographic
description of such mechanism is an interesting subject. In this thesis, we apply this
anomaly cancelation idea to the uplifted 5D Reissner-Nordstr¨om (RN) black holes.
The action of a probe scalar field in the near horizon region of the uplifted 5D RN
black holes can be equivalently described by infinite collection of (1+1)-dimensional
charged scalar field. Following the analytic methods proposed by Iso, Umetsu and
Wilczek, we can show that the Hawking flux from the uplifted 5D RN black holes can
be determined by the values of the quantum anomalies.

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