The Finsler Spacetime Condition for (α,β)-Metrics and Their Isometries

authored by: Nicoleta Voicu, Annamária Friedl-Szász, Elena Popovici-Popescu, Christian Pfeifer
Abstract: For the general class of pseudo-Finsler spaces with (Formula presented.) -metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means that the fundamental tensor has a Lorentzian signature on a conic subbundle of the tangent bundle and thus the existence of a cone of future-pointing time-like vectors is ensured. The identified (Formula presented.) -Finsler spacetimes are candidates for applications in gravitational physics. Moreover, we completely determine the relation between the isometries of an (Formula presented.) -metric and the isometries of the underlying pseudo-Riemannian metric a; in particular, we list all (Formula presented.) -metrics which admit isometries that are not isometries of a.
External Organisation(s): Transilvania University of Brasov
University of Bremen
Type: Article
Journal: Universe
Volume: 9
Publication date: 20.04.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Physics and Astronomy(all)
Electronic version(s): https://doi.org/10.3390/universe9040198 (Access: Open)

BibTeX

@article{8d802acb27d8423e82d32ec1792e4b3d,
title = "The Finsler Spacetime Condition for (α,β)-Metrics and Their Isometries",
abstract = "For the general class of pseudo-Finsler spaces with (Formula presented.) -metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means that the fundamental tensor has a Lorentzian signature on a conic subbundle of the tangent bundle and thus the existence of a cone of future-pointing time-like vectors is ensured. The identified (Formula presented.) -Finsler spacetimes are candidates for applications in gravitational physics. Moreover, we completely determine the relation between the isometries of an (Formula presented.) -metric and the isometries of the underlying pseudo-Riemannian metric a; in particular, we list all (Formula presented.) -metrics which admit isometries that are not isometries of a.",
keywords = "(α,β)-metric, Finsler geometry, isometry",
author = "Nicoleta Voicu and Annam{\'a}ria Friedl-Sz{\'a}sz and Elena Popovici-Popescu and Christian Pfeifer",
note = "Funding information: This article is based upon work from COST Action CA21136 (Addressing observational tensions in cosmology with systematics and fundamental physics CosmoVerse) and the authors would like to acknowledge networking support by the COST Action CA18108 (Quantum Gravity Phenomenology in the Multi-Messenger Approach), supported by COST (European Cooperation in Science and Technology). The authors are grateful to Andrea Fuster and Sjors Heefer for numerous useful discussions and their insight. C.P. is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) Project Number 420243324 and acknowledges the excellence cluster Quantum Frontiers funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany{\textquoteright}s Excellence Strategy EXC-2123 QuantumFrontiers 390837967. ",
year = "2023",
month = apr,
day = "20",
doi = "10.3390/universe9040198",
language = "English",
volume = "9",
journal = "Universe",
issn = "2218-1997",
publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",
number = "4",
}