Birkhoff theorem for Berwald-Finsler spacetimes

authored by: Nicoleta Voicu, Samira Cheraghchi, Christian Pfeifer
Abstract: Finsler spacetime geometry is a canonical extension of Riemannian spacetime geometry. It is based on a general length measure for curves (which does not necessarily arise from a spacetime metric) and it is used as an effective description of spacetime in quantum gravity phenomenology as well as in extensions of general relativity aiming to provide a geometric explanation of dark energy. A particular interesting subclass of Finsler spacetimes are those of Berwald type, for which the geometry is defined in terms of a canonical affine connection that uniquely generalizes the Levi-Civita connection of a spacetime metric. In this sense, Berwald Finsler spacetimes are Finsler spacetimes closest to pseudo-Riemannian ones. We prove that all Ricci-flat, spatially spherically symmetric Berwald spacetime structures are either pseudo-Riemannian (Lorentzian), or flat. This insight enables us to generalize the Jebsen-Birkhoff theorem to Berwald spacetimes.
External Organisation(s): Center of Applied Space Technology and Microgravity (ZARM)
Type: Article
Journal: Physical Review D
Volume: 108
ISSN: 2470-0010
Publication date: 27.11.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Nuclear and High Energy Physics
Electronic version(s): https://doi.org/10.48550/arXiv.2306.07866 (Access: Open)
https://doi.org/10.1103/PhysRevD.108.104060 (Access: Closed)

BibTeX

@article{f8edebb6a693443480c5b5fb77bea98c,
title = "Birkhoff theorem for Berwald-Finsler spacetimes",
abstract = "Finsler spacetime geometry is a canonical extension of Riemannian spacetime geometry. It is based on a general length measure for curves (which does not necessarily arise from a spacetime metric) and it is used as an effective description of spacetime in quantum gravity phenomenology as well as in extensions of general relativity aiming to provide a geometric explanation of dark energy. A particular interesting subclass of Finsler spacetimes are those of Berwald type, for which the geometry is defined in terms of a canonical affine connection that uniquely generalizes the Levi-Civita connection of a spacetime metric. In this sense, Berwald Finsler spacetimes are Finsler spacetimes closest to pseudo-Riemannian ones. We prove that all Ricci-flat, spatially spherically symmetric Berwald spacetime structures are either pseudo-Riemannian (Lorentzian), or flat. This insight enables us to generalize the Jebsen-Birkhoff theorem to Berwald spacetimes.",
author = "Nicoleta Voicu and Samira Cheraghchi and Christian Pfeifer",
note = "Publisher Copyright: {\textcopyright} 2023 American Physical Society.",
year = "2023",
month = nov,
day = "27",
doi = "10.48550/arXiv.2306.07866",
language = "English",
volume = "108",
journal = "Physical Review D",
issn = "2470-0010",
publisher = "American Institute of Physics",
number = "10",
}