  A general class of solutions of Einstein's equation for a slowly rotating
fluid source, with supporting internal pressure, is matched using Lichnerowicz
junction conditions, to the Kerr metric up to and including first order terms
in angular speed parameter. It is shown that the match applies to any
previously known non-rotating fluid source made to rotate slowly for which a
zero pressure boundary surface exists. The method is applied to the dust source
of Robertson-Walker and in outline to an interior solution due to McVittie
describing gravitational collapse. The applicability of the method to
additional examples is transparent. The differential angular velocity of the
rotating systems is determined and the induced rotation of local inertial frame
is exhibited.
