Revisit Birkhoff’s Theorem: The Post-Newtonian Metric of a Self-Gravitating and Collapsing Thin Spherical Shell

We calculate the metric of a self-gravitating and collapsing infinitely thin spherical shell in the weak-field and slow-motion limits, and we demonstrate that Birkhoff’s theorem is not consistent with the theory of the post-Newtonian approximation. More importantly, it is illustrated that performing...

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Veröffentlicht in:Symmetry (Basel) 2024-08, Vol.16 (8), p.998
1. Verfasser: Lin, Wenbin
Format: Artikel
Sprache:eng
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Zusammenfassung:We calculate the metric of a self-gravitating and collapsing infinitely thin spherical shell in the weak-field and slow-motion limits, and we demonstrate that Birkhoff’s theorem is not consistent with the theory of the post-Newtonian approximation. More importantly, it is illustrated that performing a coordinate transformation in solving Einstein field equations may change the matter energy-momentum tensor, making the resultant solution not correspond to the original problem.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym16080998