  Three dimensional space is said to be spherically symmetric if it admits
SO(3) as the group of isometries. Under this symmetry condition, the Einsteins
Field equations for vacuum, yields the Schwarzschild Metric as the unique
solution, which essentially is the statement of the well known Birkhoffs
Theorem. Geometrically speaking this theorem claims that the pseudo-Riemanian
space-times provide more isometries than expected from the original metric
holonomy/ansatz. In this paper we use the method of Lie Symmetry Analysis to
analyze the Einsteins Vacuum Field Equations so as to obtain the Symmetry
Generators of the corresponding Differential Equation. Additionally, applying
the Noether Point Symmetry method we have obtained the conserved quantities
corresponding to the generators of the Schwarzschild Lagrangian and paving way
to reformulate the Birkhoffs Theorem from a different approach.
