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

Author:

Lin Wenbin12ORCID

Affiliation:

1. School of Mathematics and Physics, University of South China, Hengyang 421001, China

2. School of Physical Science and Technology, Southwest Jiaotong University, Chengdu 610031, China

Abstract

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.

Funder

National Natural Science Foundation of China

Program for New Century Excellent Talents in University

Publisher

MDPI AG

Reference17 articles.

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4. Singular hypersurfaces and thin shells in general relativity;Israel;Nuovo C. B,1966

5. Lightman, A., Press, W., Price, R., and Teukolsky, S. (1975). Problem Book in Relativity and Gravitation, Princeton Univiversity Press.

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