量子力學告訴人們，任何物理演化過程應該滿足因果律：
信息是守恆的，即信息不會丟失。早期的研究指出黑洞向外蒸
發物質是熱輻射過程，人們無法從被輻射出來的物質中提取形
成黑洞物質的任何信息。那麼有關形成黑洞的物質的信息去哪
兒了呢？
Parikh 和Wilczek用量子穿隧的方法，並且考慮總系統能
量守恆討論了Schwarzschild 黑洞的幅射率，得出非純熱譜的
Hawking 幅射，此結果暗示黑洞幅射過程訊息守恆的可能性。
本文主要以球殼模型及Parikh-Wilczek 的量子穿隧法討論
Hawking 幅射率。第二章介紹Parikh-Wilczek 所做的計算，此
計算採用Painlevé-Gullstrand 座標系。第三章討論度規(gμν)在
視界處不發散的情況下，用量子穿隧法計算的結果不隨座標選
取而改變。第四章我們討論有靜止質量的Hawking 幅射,為此
目標我們採用自引力的球殼模型,因為此模型本身即有總系統
能量守恆的性質,最後我們也得出同樣非純熱譜的Hawking幅
射率。第五章我們利用相同的方法對Kerr-Newman黑洞做計
算，得出幅射的修正譜，其結果支持黑洞幅射過程訊息守恆。

Hawking and Bekenstein made a remarkable connection between thermodynamics, quantum mechanics and black holes which predicted that black holes will slowly radiate away. But this theory violated the laws of quantum mechanics and created a contradiction known as the ”information paradox”. We have studied the Hawking radiation as a semiclassical tunneling process. Using the method proposed by Parikh and Wilczek, the calculation indicates that the black hole radiation contains a correction to the thermal spectrum. This result suggests a possibility of informationcarrying correlations in the radiation. In chaper 3, we have verified that, for nonrotating cases, the tunneling calculation will give the same result if the black hole metric is smooth at horizon. In chapter 4, we verify the tunneling approach by an other possible picture that that the radiation contains many tiny self-gravitating shells whose dynamics is determined by the effective action. In chaper 5, we have calculated the coaxial rotating radiation in Kerr-Newman black hole.

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