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Three dimensional space is said to be spherically symmetric if it admitsSO(3) as the group of isometries. Under this symmetry condition, the EinsteinsField equations for vacuum, yields the Schwarzschild Metric as the uniquesolution, which essentially is the statement of the well known BirkhoffsTheorem. Geometrically speaking this theorem claims that the pseudo-Riemanianspace-times provide more isometries than expected from the original metricholonomy/ansatz. In this paper we use the method of Lie Symmetry Analysis toanalyze the Einsteins Vacuum Field Equations so as to obtain the SymmetryGenerators of the corresponding Differential Equation. Additionally, applyingthe Noether Point Symmetry method we have obtained the conserved quantitiescorresponding to the generators of the Schwarzschild Lagrangian and paving wayto reformulate the Birkhoffs Theorem from a different approach.

Birkhoffs Theorem and Lie Symmetry Analysis