Towards some generalization of Birkhoff's theorem

Details Towards some generalization of Birkhoff's theorem Towards some generalization of Birkhoff's theorem

May 2009

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009aipc.1122..300h&link_type=abstract

PHYSICS AND MATHEMATICS OF GRAVITATION: Proceedings of the Spanish Relativity Meeting 2008. AIP Conference Proceedings, Volume

Mathematics

Numerical Approximation And Analysis, Ordinary And Partial Differential Equations, Boundary Value Problems, Approximation Methods, Equations Of Motion

Scientific paper

As is known, Birkhoff's theorem states the uniqueness of the solution of Einstein vacuum field equations for an spherical and isolated compact body. Moreover, that solution, the Schwarzschild metric, only possesses one multipole moment which is the mass, and so, Birkhoff's theorem allows to establish a relationship between the spherical symmetry and the multipole structure of the so-called Monopole solution.
Hence, the question is whether we can extrapolate this feature of Birkhoff's theorem to any other solution of the Weyl family of axisymmetric vacuum solutions of Einstein field equations. Is there any kind of symmetry which let us characterize the solutions possessing any finite set of multipole moments?.

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