Irrotational and conformally Ricci-flat perfect fluids
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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.
KeywordsScalar Field Differential Geometry Fluid Velocity Perfect Fluid Bianchi Type
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