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)