Spacetimes with a preferred null direction and a two-dimensional group of isometries: the null dust case
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peer reviewed
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Classical and Quantum Gravity
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The authors consider spacetimes of general relativity admitting a preferred null direction l mu and a two-dimensional Abelian group of isometries G 2 . A null tetrad formulation of the Killing equations is given, as well as a classification of G 2 according to the orientation of l mu with respect to the group transitivity surfaces. Two theorems concerning the action of the isometry group on l mu are presented: the first one deals with spacetimes admitting at least one Killing vector, while the second one deals with spacetimes admitting a G 2 . The Einstein field equations with a shear-free and diverging null dust source are integrated under the assumptions: (i) the spacetime admits an Abelian G 2 whose transitivity surfaces are non-orthogonal to and do not contain the null dust propagation vector; (ii) there exists a Killing vector k mu whose magnitude is almost everywhere bounded at the endpoints of the null dust rays. These spacetimes are of Petrov type II, non-asymptotically flat, and the G 2 is non-orthogonally transitive. By switching off the null dust the authors have explicitly obtained the underlying vacuum metrics which generalise some of the diverging Petrov type D vacuum metrics found by Kinnersley (1969).
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http://stacks.iop.org/0264-9381/4/i=3/a=018
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Πανεπιστήμιο Ιωαννίνων. Σχολή Επιστημών και Τεχνολογιών. Τμήμα Βιολογικών Εφαρμογών και Τεχνολογιών