The form of Killing vectors in expanding ℋℋ spaces
- 1 January 1982
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 23 (1) , 116-122
- https://doi.org/10.1063/1.525196
Abstract
The Killing vector structure of those spaces of complexified general relativity known as expanding hyperheavens is investigated using the methods of spinor calculus. The Killing equations for all left-algebraically degenerate Einstein vacuum spaces are completely integrated. Using the available gauge freedom, the resulting homothetic and isometric Killing vectors are classified in an invariant way according to Petrov–Penrose type. A total of four distinct kinds of isometric Killing vectors and three distinct kinds of homothetic Killing vectors are found. A master Killing vector equation is found which gives the form that the Lie derivative of the metric potential function W must take in order that it admit a given Killing vector.Keywords
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