在魏爾重力中，一般的輻射黑洞所帶有的能量動量張量與愛因斯坦重力論中的不同，並不是只有帶有能量項。在魏爾重力中，我們仍然能構造只帶有能量項的輻射黑洞，發現其會有額外的線性項貢獻。我們將可達瑪向量推廣到魏爾重力中，並用量子穿隧的方法研究魏爾重力中輻射黑洞的輻射率。我們也考慮時空的超平移對稱性，並計算經過超平移之後的輻射黑洞所帶有的能量動量張量。最後，我們也透過量子穿隧的方法計算超平移之輻射黑洞的輻射率，我們會發現該輻射仍然是滿足波茲曼分布，並且其帶有的溫度會與角度相關，而此結果是和愛因斯坦重力論中所得到的結果相同。

Vaidya metric describe a radiating black hole in Einstein gravity. The usual Vaidya metric in Einstein gravity is not a null dust solution in Weyl gravity. However, we find a family of null dust Vaidya solutions for Weyl gravity, which receive an extra linear term. We also use the tunneling method to study the radiation profile of Vaidya metrics by extending the definition of the Kodama vector to Weyl gravity. Finally, we introduce supertranslation to asymptotically flat black hole in Weyl gravity and find out the corresponding energy momentum tensor needed to implant supertranslation hair onto it. We also apply tunneling method to supertranslated Vaidya black hole in Weyl gravity. We find out that the radiation is still thermal and the radiation temperature has the same angular dependence as in the Einstein case.

1. Introduction 3
2. Weyl gravity 4
2.1 Weyl gravity 4
2.2 Black hole solutions in Weyl gravity 6
2.3 Galactic rotational curve 7
2.4 Linearized equation of motion 9
2.5 Vaidya metric in Weyl gravity 11
3. Hawking radiation as tunneling 13
3.1 Radiation of Schwarzschild metric in Eintein gravity 13
3.2 Radiation of Vaidya metric in Eintein gravity 14
3.3 Radiation of Vaidya metric in Weyl gravity 16
4. Supertranslation 18
4.1 BMS symmetry 18
4.2 Supertranslated Schwarzschild metric in Einstein gravity 20
4.3 Supertranslated Vaidya metric in Einstein gravity 22
4.4 Supertranslated Vaidya metric in Weyl gravity 24
5. Conclusions 27
Appendices 28
A Equation of motion for Weyl gravity 28
B Linearized equation of motion 29
C Details for perturbation computation 31
D The WKB approximation 33

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