  In this article, we provide a discussion on a composite class of exact static
spherically symmetric vacuum solutions of Einstein's equations. We construct
the composite solution of Einstein field equation by match the interior vacuum
metric in Schwarzschild original gauge, to the exterior vacuum metric in
isotropic gauge, at a junction surface. This approach allows us to associate
rigorously with both gauges as a same "space", which is a unique differentiable
manifold M^4
