Authors: K. Sandale
The proof of Birkhoff's Theorem relies on a coordinate transformation to diagonalize the metric. This coordinate transformation is made to affect the vacuum region, but will nevertheless cause the matter in the non-vacuum region to have a different velocity in the new coordinate system than in the old coordinate system, because a coordinate transformation cannot be abruptly turned off where the two regions meet without violating the holonomy requirement. The effects of this coordinate transformation on the matter have never before been studied. In fact, the coordinate transformation turns out to cause part of a gravitationally collapsing mass distribution to at some point start to move backwards in time. This causes problems which invalidate the proof. Furthermore, we provide an actual counterexample to Birkhoff’s Theorem: In the particular circumstance of a spherically symmetric thin shell of matter collapsing it is shown that the Bianchi Identities give results contrary to Birkhoff’s Theorem.
Comments: 13 Pages.
[v1] 2012-01-12 10:37:43
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