Irrotational and conformally Ricci-flat perfect fluids |
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Authors: | N Van den Bergh |
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Institution: | (1) Theoretical Astronomy Unit, School of Mathematical Sciences, Queen Mary College, E1 4NS London, UK;(2) Physics Department, Universitaire Instelling Antwerpen, B2610 Antwerpen, Belgium |
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Abstract: | When a space-time, containing an irrotational perfect fluid withw + p 0, is conformally Ricci-flat, three possibilities arise: (a) When the gradient of the conformal scalar field is aligned with the fluid velocity, the solution is conformally flat; (b) when the gradient is orthogonal to the fluid velocity, solutions are either shearfree, nonexpanding and (pseudo-) spherically or plane-symmetric, or they are conformally related to a particular new vacuum solution admitting a three-dimensional group of motions of Bianchi type VIo on a timelike hypersurface; (c) in the general case solutions are (pseudo) spherically or plane-symmetric and have nonvanishing expansion. |
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