Killing spinors and affine symmetry tensors in Godel's Universe Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/0c483p793

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  • The existence of generalized symmetries of Maxwell's equations in G¨odel's Universe is investigated. It is shown that their existence is in turn tied to the existence of certain spinorial objects called Killing spinors. The conformal algebra, corresponding to valence (1; 1) Killing spinors, for G¨odel's Universe is discussed in detail. Following this, higher valence Killing spinors are investigated, enabling a classification of generalized symmetries of orders one and two, and a partial classification for order three. A new class of symmetry tensor is defined, which generalizes the notion of an affine vector of a spacetime, and its properties investigated. It is shown that there are nontrivial examples in several spacetimes of scholarly interest, including the G¨odel's Universe. Finally, some information about higher valence Killing spinors, the enumeration of which is necessary in order to find further generalized symmetries, is given, followed by a conjecture about the nature of same.
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