  This paper examines the inhomogeneous Einstein equation for a static
spherically symmetric metric with a source term corresponding to a perfect
fluid with p=-rho. By a careful treatment of the equation near the origin we
find an analytic solution for the metric, dependent on a small parameter
epsilon, which can be made arbitrarily close to the Schwarzschild solution as
\epsilon} tends to zero and which in that same limit can be viewed as arising
from a point-like source structure.
