Non-static spherically symmetric solution of Einstein vacuum field equations with Λ

The Schwarschild-de Sitter metric is the known solution of Einstein field equations with cosmological constant term for vacuum spherically symmetric space around a point mass M. Recently it has been reported that in a Lambda-dominant world the Schwarzschild type coordinate systems are disqualified by redshift-magnitude test as a proper frame of reference (gr-qc/9812092). We derive the solution in a FRW type coordinate system which is qualified according to the mentioned test. Asymptotically it approachs to the non-static form of deSitter metric. The obtained metric is transformable to Schwarzschild-de Sitter metric. It is an analytic function of r for all values except r = 0 which is singular. This is carried out with no making use of Eddington-Finkelstein coordinates and without entering any cross term in the metric.