https://doi.org/10.1140/epjc/s10052-023-11960-7
Regular Article - Theoretical Physics
The validity of Birkhoff’s theorem in modified teleparallel equivalent theories of gravity
1
Deep Space Exploration Laboratory/School of Physical Sciences, University of Science and Technology of China, 230026, Hefei, Anhui, China
2
CAS Key Laboratory for Researches in Galaxies and Cosmology/Department of Astronomy, School of Astronomy and Space Science, University of Science and Technology of China, 230026, Hefei, Anhui, China
Received:
6
July
2023
Accepted:
25
August
2023
Published online:
9
September
2023
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 
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.
© The Author(s) 2023
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