Abstract
The Senovilla family for a subclass of Petrov type-D stationary axisymmetric differentially rotating perfect fluids is considered. A scheme is presented to construct from a solution an interior of a rotating compact body satisfying dominant energy conditions and with a boundary of vanishing pressure. The equatorial disk of the body is a surface layer due to a jump in the second fundamental form. However, unlike previous results, the body is free from curvature singularities.
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