Relativity and Cosmology

    

An Inconsistency in Birkhoff's Theorem re Spherical Shells

Authors: Jeff Sorensen

According to Birkhoff's theorem the interior and exterior vacuum intervals for a spherically symmetric shell are the flat Minkowski metric and the static Schwarzschild solution respectively. Although these results are generally accepted individually, they should be considered in conjunction with each other. Here we examine the junction of the interior and exterior vacuum intervals across a thin spherical shell. The results show Birkhoff's theorem is not self consistent. The interior interval cannot be the Minkowski metric and, for a non-static shell, the overall solution cannot be static. As such, Birkhoff's theorem should not be relied upon as a basis for determining the properties of a given space-time.

Comments: 7 Pages.

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[v1] 2026-05-13 05:01:42

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