ar X iv : g r - qc / 0 00 50 66 v 1 1 6 M ay 2 00 0 SELF - SIMILAR PERFECT FLUIDS
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چکیده
Space-times admitting an r-parameter Lie group of homotheties are studied for r > 2 devoting a special attention to those representing perfect fluid solutions to Einstein's field equations. 1 Basic facts about homotheties Throughout this paper (M, g) will denote a space-time: M then being a Haus-dorff, simply connected, four-dimensional manifold, and g a Lorentz metric of signature (-,+,+,+). All the structures will be assumed smooth. A global vector field X on M is called homothetic if either one of the following conditions holds on a local chart L X g ab = 2λg ab , X a;b = λg ab + F ab , (1) where λ is a constant on M , L stands for the Lie derivative operator, a semicolon denotes a covariant derivative with respect to the metric connection, and F ab = −F ba is the so-called homothetic bivector. If λ = 0, X is called proper homothetic and if λ = 0, X is a Killing vector field (KV) on M. For a geometrical interpretation of (1) we refer the reader to 5,6 .
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تاریخ انتشار 2000