The validity of Birkhoff’s theorem in modified teleparallel equivalent theories of gravity
Abstract Birkhoff’s theorem is a vitally important theorem in studying local systems in theories of gravity. In this paper we provide a straightforward proof of the validity of Birkhoff’s theorem in modified teleparallel equivalent theories of gravity, which states that if the matter distribution is...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-09-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-023-11960-7 |
| _version_ | 1797647194121043968 |
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| author | Ji-Yu Cheng |
| author_facet | Ji-Yu Cheng |
| author_sort | Ji-Yu Cheng |
| collection | DOAJ |
| description | Abstract Birkhoff’s theorem is a vitally important theorem in studying local systems in theories of gravity. In this paper we provide a straightforward proof of the validity of Birkhoff’s theorem in modified teleparallel equivalent theories of gravity, which states that if the matter distribution is spherically symmetric, then the spacetime is static in a region in which t remains timelike and $$(r,\theta ,\phi )$$ ( r , θ , ϕ ) stay spacelike. This version of Birkhoff’s theorem is rather trivial. The theorem also reveals the fact that the gravitational field of a spherically symmetric distribution of matter and of the spherically symmetric vacuum spacetime are both static in modified teleparallel equivalent theories of gravity. |
| first_indexed | 2024-03-11T15:13:46Z |
| format | Article |
| id | doaj.art-659f7f65dd914e42aaa67fffd9f8317c |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-03-11T15:13:46Z |
| publishDate | 2023-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-659f7f65dd914e42aaa67fffd9f8317c2023-10-29T12:33:42ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522023-09-018391810.1140/epjc/s10052-023-11960-7The validity of Birkhoff’s theorem in modified teleparallel equivalent theories of gravityJi-Yu Cheng0Deep Space Exploration Laboratory/School of Physical Sciences, University of Science and Technology of ChinaAbstract Birkhoff’s theorem is a vitally important theorem in studying local systems in theories of gravity. In this paper we provide a straightforward proof of the validity of Birkhoff’s theorem in modified teleparallel equivalent theories of gravity, which states that if the matter distribution is spherically symmetric, then the spacetime is static in a region in which t remains timelike and $$(r,\theta ,\phi )$$ ( r , θ , ϕ ) stay spacelike. This version of Birkhoff’s theorem is rather trivial. The theorem also reveals the fact that the gravitational field of a spherically symmetric distribution of matter and of the spherically symmetric vacuum spacetime are both static in modified teleparallel equivalent theories of gravity.https://doi.org/10.1140/epjc/s10052-023-11960-7 |
| spellingShingle | Ji-Yu Cheng The validity of Birkhoff’s theorem in modified teleparallel equivalent theories of gravity European Physical Journal C: Particles and Fields |
| title | The validity of Birkhoff’s theorem in modified teleparallel equivalent theories of gravity |
| title_full | The validity of Birkhoff’s theorem in modified teleparallel equivalent theories of gravity |
| title_fullStr | The validity of Birkhoff’s theorem in modified teleparallel equivalent theories of gravity |
| title_full_unstemmed | The validity of Birkhoff’s theorem in modified teleparallel equivalent theories of gravity |
| title_short | The validity of Birkhoff’s theorem in modified teleparallel equivalent theories of gravity |
| title_sort | validity of birkhoff s theorem in modified teleparallel equivalent theories of gravity |
| url | https://doi.org/10.1140/epjc/s10052-023-11960-7 |
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