Hawking, S.W. and Ellis, G.F.R. (1975) Large Scale Structures of Space-Time (Cambridge Monographs of Mathematical Physics). Cambridge University Press, Cambridge.

has been cited by the following article:

• TITLE: Birkhoff’s Theorem and Lie Symmetry Analysis

  AUTHORS: Avijit Mukherjee, Subham B. Roy

  KEYWORDS: Birkhoff’s Theorem, Lie Symmetry Analysis, Noether Point Symmetry

  JOURNAL NAME: Journal of High Energy Physics, Gravitation and Cosmology, Vol.7 No.4, September 8, 2021

  ABSTRACT: Three dimensional space is said to be spherically symmetric if it admits SO(3) as the group of isometries. Under this symmetry condition, the Einstein’s Field equations for vacuum, yields the Schwarzschild Metric as the unique solution, which essentially is the statement of the well known Birkhoff’s 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 Einstein’s 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 Birkhoff’s Theorem from a different approach.