The Ghp Conformal Killing Equations and Their Integrability Conditions, with Application to Twisting Type-N Vacuum Spacetimes
Abstract
Type
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peer reviewed
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General Relativity and Gravitation
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Description
The conformal Killing equations in resolved form and their first and second integrability conditions are obtained in the compact spin coefficient formalism for arbitrary spacetimes. To facilitate calculations an operator L(xi) is introduced which agrees with the Lie derivative L(xi) only when operating on quantities with GHP weights (0, 0). The resulting equations are used to find the conditions for the existence of a two dimensional non-Abelian group of homothetic motions in a twisting type N vacuum spacetime. The equivalence of two such sets of metrics is established, metrics that were recently the subject of independent investigations by Herlt on the one hand and by Ludwig and Yu on the other.
Description
Keywords
two-dimensional group, homothetic-motions, metrics, isometries, vectors, fields
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Citation
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<Go to ISI>://A1993LD26700009
http://www.springerlink.com/content/x6734381j0474766/fulltext.pdf
http://www.springerlink.com/content/x6734381j0474766/fulltext.pdf
Language
en
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Πανεπιστήμιο Ιωαννίνων. Σχολή Επιστημών και Τεχνολογιών. Τμήμα Βιολογικών Εφαρμογών και Τεχνολογιών