Abstract
Petrov type III, shear-free, perfect fluid solutions of the Einstein field equations, with a barotropic equation of state p=p(w) satisfying w+p≢0, are investigated. It is shown that if the acceleration of the fluid is orthogonal to the two-spaces spanned by the repeated principal null direction of the Weyl tensor and the fluid four-velocity, or if the fluid four-velocity lies in the two-spaces spanned by the principal null directions of the Weyl tensor, then the fluid’s volume expansion is zero.
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