Symmetries of the Stephani
نویسنده
چکیده
Two classes of solutions for conformally at perfect uids exist depending on whether the uid expansion vanishes or not. The expanding solutions have become known as the Stephani universes and are generalisations of the well-known Friedmann-Robertson-Walker solutions; the solutions with zero expansion generalise the interior Schwarzschild solution. The isometry structure of the expansion-free solutions was completely analysed some time ago. For the Stephani universes it is shown that any Killing vector is orthogonal to the uid ow and so the situation for expanding case is somewhat simpler than the expansion-free case wherètilted' Killing vectors may exist. The existence of isometries in Stephani universes depends on the dimension r of the linear space spanned by certain functions of time a(t), b(t), c 1 (t), c 2 (t) and c 3 (t) which appear in the metric. If r is 4 or 5, no Killing vectors exist. If r = 3, the isometry group is 1-dimensional. If r = 2, the spacetime admits a complete 3-dimensional isometry group with 2-dimensional orbits. If r = 1, there are 6 Killing vectors and the spacetime is Friedmann-Robertson-Walker. Not all choices of the metric functions a(t), b(t) c 1 (t), c 2 (t) and c 3 (t) lead to distinct spacetimes: the ten-dimensional conformal group, which acts on each of the hypersurfaces orthogonal to the uid ow, preserves the overall form of the metric, but induces a group of transformations on these ve metric functions which is locally isomorphic to SO(4; 1). A result of the same ilk is derived for the non-expanding solutions. y
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تاریخ انتشار 1998