Is the Schwarzschild Metric a Vacuum Solution of the Einstein Equation?

Abstract

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.