在這篇論文裡我們利用微分形式引進principal conformal Killing–Yano tensor (PCKYT)並用於解決旋轉時空下的電磁場問題。我們依據Hertz和Debye potential的形式提出利用PCKYT 和Debyepotential得到在四維Kerr-NUT-Ads時空下Hertz potential的假設。最後我們可以得出此假設下的Debyepotential與Newman-Penrose形式中的φ1類似。

In this thesis we introducce the principal Killing-Yano tensor (PCKYT) using differential forms to solve for the electromagnetic fields in curved spacetime. We take the ansatz in which the PCKYT is related to the Hertz and the Debye potential in the 4-dimensional Kerr-NUT-AdS metric. According to the ansatz, we find that the Debye potential is the same as the potential φ1 in the Newman-Penrose formalism.

1 Introduction...1
2 Differential forms and Killing-Yano equations...3
 2.1 De finition and properties of differential forms...3
 2.2 Killing and Killing-Yano equations in terms of differential forms...4
 2.3 Principal conformal Killing-Yano tensors and Canonical basis of Kerr spacetime...6
3 Debye Potential from Killing-Yano forms...8
 3.1 Debye potential in Minkowski spacetime...8
 3.2 Debye potential of PCKYT in Kerr spacetime...9
4 Comparison to the Teukolsky equation...14
 4.1 Teukolsky equation and decoupled equation...14
 4.2 From the Debye potential equation to a separable equation...16
5 Discussion...19
A Appendix...21
 A.1 KT associated with KYT and parallel propagation of KYT...21
 A.2 Generalized PCKYT...21
 A.3 Harmonic operator on Hertz potential in terms of differential forms...23
 A.4 Ricci 2-form...24
 A.5 Identity in the NP formalism...26
Bibliography...28

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