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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Conformally Reducible Perfect Fluids with 2-Spaces of Constant Curvature
verfasst von : Norbert Van den Bergh
Erschienen in: Progress in Mathematical Relativity, Gravitation and Cosmology
Verlag: Springer Berlin Heidelberg
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Abstract
I discuss conformally reducible but non-conformally flat space-times, which are solutions of the Einstein field equations with a perfect fluid source and for which the factor spaces are 2-spaces of constant curvature. These space-times are necessarily of Petrov type D. When the fluid velocity is aligned with the plane of principal null directions, they are locally rotationally symmetric of Stewart–Ellis class II and are determined up to two first order partial differential equations. When the fluid is non-aligned, the general solution can be given in terms of elementary functions.