Relativity and Cosmology


Geometrodynamic Mass Decrease During Gravitational Collapse

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.

Download: PDF

Submission history

[v1] 2012-01-12 10:37:43

Unique-IP document downloads: 145 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus