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Spherically symmetric static fluid sources are endowed with rotation andembedded in Kerr empty space-time up to an including quadratic terms in anangular velocity parameter using Darmois junction conditions. Einstein'sequation's for the system are developed in terms of linear ordinarydifferential equations. The boundary of the rotating source is expressedexplicitly in terms of sinusoidal functions of the polar angle which differsomewhat according to whether an equation of state exists between internaldensity and supporting pressure

Letter: Slowly Rotating, Compact Fluid Sources Embedded in Kerr Empty Space-Time