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A generalized Lie derivative and homothetic or Killing vectors in the Geroch-Held-Penrose formalism
Univ Alberta, Dept Math Sci, Edmonton, AB T6G 1S6, Canada Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden.
Univ Alberta, Dept Math Sci, Edmonton, AB T6G 1S6, Canada Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden.
2000 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 17, no 7, 1683-1705 p.Article in journal (Refereed) Published
Abstract [en]

A generalized Lie derivative operator suitable for use within the GHP formalism and the notion of preferred GHP tetrads relative to a vector are introduced. The usual homothetic or Killing equations are then replaced by an equivalent but much more manageable set of equations involving the commutators of this new operator with the four GHP derivative operators. This allows for an efficient treatment of the homothetic or Killing condition when constructing new solutions of Einstein's field equations or when obtaining the homothetic and/or Killing vectors for a given metric. Two applications are given. The first sheds new light on the vacuum twisting type N problem with one or two homothetic/Killing vectors. In the second we find the subclass of ail type N, and of all conformally flat, pure radiation metrics (with tau not equal 0) which possess one or more homothetic or Killing vectors.

Place, publisher, year, edition, pages
2000. Vol. 17, no 7, 1683-1705 p.
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:liu:diva-49790OAI: oai:DiVA.org:liu-49790DiVA: diva2:270686
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-12

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