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Type-N, shear-free, perfect-fluid spacetimes with a barotropic equation of state. (English) Zbl 0657.53046
We present the class of Petrov-type N, shear-free, perfect-fluid solutions of Einstein’s field equations in which the fluid satisfies a barotropic equation of state $$p=p(w)$$ and $$w+p/0$$. All solutions are stationary and possess a three-parameter, abelian group of local isometries which act simply transitively on timelike hypersurfaces. Furthermore, there exists one Killing vector parallel to the vorticity vector and another parallel to the four-velocity. This class of solutions is identified as part of a larger class present in the literature.

##### MSC:
 53B50 Applications of local differential geometry to the sciences 83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
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##### References:
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