Some Remarks on Symmetries and Transformation Groups in General Relativity |
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Authors: | G. S. Hall |
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Abstract: | The motivation for this paper is the recent interest in the study of symme tries in general relativity and its purpose is to discuss the mathematical foundations required for such a study. The general (formal and informal) ideas of what constitutes a symmetry of space-time are discussed and developed and the idea of a Lie algebra of symmetry vector fields is studied in detail. The relationship between such Lie algebras and the ideas of Lie transformation group theory (Palais' theorems) is stated and a general theorem regarding the orbits of such symmetries is given. Finally some specific symmetries in general relativity are explored and some of their similarities and differences noted. |
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Keywords: | SYMMETRIES TRANSFORMATIONS PROJECTIVE CONFORMAL AFFINE |
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