- 學位論文
球對稱黑洞時空中的重力微子場
Gravitino fields in the spherically symmetric black hole spacetime
摘要
在本論文內，我們考慮了高維度史瓦西黑洞時空中的重力微子微擾場。在研究重力微子微擾的課題中，通常會引進 Newman-Penrose 方法，不過這個方法只適用在四維的時空中，而不能直接推廣到高維度時空，所以我們採用了另外一種較為直接的觀點來研究這個課題。我們首先研究旋量-向量場在N維球膜中的本徵值問題，並得到一個完整態。利用這些本徵值與本徵態分離了維度史瓦西黑洞時空中的重力微子微擾運動方程式的球對稱部分，並定義了運動方程式中的不變量，進而得到徑向方程式。我們討論了徑向方程式中的有效位勢，並研究了重力微子在高維史瓦西黑洞時空中的吸收機率以及準正則模的相關課題。
並列摘要
In this thesis we consider the gravitino perturbation on a general dimensional Schwarzschild black hole spacetime. The analysis of gravitino fields in curved spacetimes is usually carried out by using the Newman-Penrose formalism, which is useful in four dimensional cases but cannot be generalized to higher dimensions in a straightforward manner. We consider a more direct approach to derive the radial equations. We start this study by finding a complete set of spinor-vector eigenmodes on an N-sphere which includes the "non TT eigenmodes" and the "TT eigenmodes". We separate the angular part of the gravitino equations of motion by these eigenmodes. With the consideration of the gauge symmetry, we write down the Schrödinger like radial equations for the gauge invariant variables. We then discuss the effective potentials. Lastly, we obtain the quasinormal modes and the absorption probabilities of the gravitino field in D dimensional Schwarzschild black hole spacetimes.